diff --git a/benchmarks/runners/sandbox.py b/benchmarks/runners/sandbox.py
index 7663b9602..3956f0d36 100644
--- a/benchmarks/runners/sandbox.py
+++ b/benchmarks/runners/sandbox.py
@@ -96,7 +96,7 @@ def doit(self):
                 #{"PTO": 2, "FNS": "FFNS", "mc": 1.95, "mb": 1e6, "mt": 1e8, "NfFF": 4},
                 #{"PTO": 2, "FNS": "FONLL-C","NfFF":4,"IC":1,"mc":1.51,"Qmc":1.51,"mb":1e6,"mt":1e7,"ModEv":"TRN","MaxNfPdf":5,"MaxNfAs": 5, "Qmb":4.92,"Qmt":172.5,"alphas":0.118,"alphaqed":0.007496252,"Q0":1.65},
                 #{"PTO": 1, "FNS": "FONLL-A","IC":0},
-                {"PTO": 2, "FNS": "FONLL-C","IC":0},
+                {"PTO": 2, "FNS": "FONLL-C", "IC":0, "XIR": 2., "XIF": .7},
                 #{"PTO": 2, "FNS": "FONLL-B", "mc": 1.51, "NfFF": 4, "kbThr": 100, "ktThr": 100, "alphas": .3, "Qref": 3},
                 #{"PTO": 2, "FNS": "FONLL-B", "mc": 1.95, "mb": 1e6, "mt": 1e8, "NfFF": 4},
                 #{"PTO": 2, "FNS": "FONLL-C", "mc": 1.95, "mb": 1e6, "mt": 1e8, "NfFF": 4},
diff --git a/poetry.lock b/poetry.lock
index a8f057b7b..a467ee213 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -32,7 +32,7 @@ python-versions = "*"
 
 [[package]]
 name = "astroid"
-version = "2.12.9"
+version = "2.12.10"
 description = "An abstract syntax tree for Python with inference support."
 category = "dev"
 optional = false
@@ -88,10 +88,10 @@ optional = false
 python-versions = ">=3.5"
 
 [package.extras]
-dev = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "mypy (>=0.900,!=0.940)", "pytest-mypy-plugins", "zope.interface", "furo", "sphinx", "sphinx-notfound-page", "pre-commit", "cloudpickle"]
-docs = ["furo", "sphinx", "zope.interface", "sphinx-notfound-page"]
-tests = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "mypy (>=0.900,!=0.940)", "pytest-mypy-plugins", "zope.interface", "cloudpickle"]
-tests_no_zope = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "mypy (>=0.900,!=0.940)", "pytest-mypy-plugins", "cloudpickle"]
+dev = ["cloudpickle", "coverage[toml] (>=5.0.2)", "furo", "hypothesis", "mypy (>=0.900,!=0.940)", "pre-commit", "pympler", "pytest (>=4.3.0)", "pytest-mypy-plugins", "sphinx", "sphinx-notfound-page", "zope.interface"]
+docs = ["furo", "sphinx", "sphinx-notfound-page", "zope.interface"]
+tests = ["cloudpickle", "coverage[toml] (>=5.0.2)", "hypothesis", "mypy (>=0.900,!=0.940)", "pympler", "pytest (>=4.3.0)", "pytest-mypy-plugins", "zope.interface"]
+tests_no_zope = ["cloudpickle", "coverage[toml] (>=5.0.2)", "hypothesis", "mypy (>=0.900,!=0.940)", "pympler", "pytest (>=4.3.0)", "pytest-mypy-plugins"]
 
 [[package]]
 name = "babel"
@@ -164,11 +164,11 @@ webencodings = "*"
 
 [package.extras]
 css = ["tinycss2 (>=1.1.0,<1.2)"]
-dev = ["build (==0.8.0)", "flake8 (==4.0.1)", "hashin (==0.17.0)", "pip-tools (==6.6.2)", "pytest (==7.1.2)", "Sphinx (==4.3.2)", "tox (==3.25.0)", "twine (==4.0.1)", "wheel (==0.37.1)", "black (==22.3.0)", "mypy (==0.961)"]
+dev = ["Sphinx (==4.3.2)", "black (==22.3.0)", "build (==0.8.0)", "flake8 (==4.0.1)", "hashin (==0.17.0)", "mypy (==0.961)", "pip-tools (==6.6.2)", "pytest (==7.1.2)", "tox (==3.25.0)", "twine (==4.0.1)", "wheel (==0.37.1)"]
 
 [[package]]
 name = "certifi"
-version = "2022.9.14"
+version = "2022.9.24"
 description = "Python package for providing Mozilla's CA Bundle."
 category = "main"
 optional = false
@@ -224,7 +224,7 @@ optional = false
 python-versions = "*"
 
 [package.extras]
-test = ["hypothesis (==3.55.3)", "flake8 (==3.7.8)"]
+test = ["flake8 (==3.7.8)", "hypothesis (==3.55.3)"]
 
 [[package]]
 name = "contourpy"
@@ -238,11 +238,11 @@ python-versions = ">=3.7"
 numpy = ">=1.16"
 
 [package.extras]
-test-no-codebase = ["pillow", "matplotlib", "pytest"]
+bokeh = ["bokeh", "selenium"]
+docs = ["docutils (<0.18)", "sphinx", "sphinx-rtd-theme"]
+test = ["flake8", "isort", "matplotlib", "pillow", "pytest"]
 test-minimal = ["pytest"]
-test = ["isort", "flake8", "pillow", "matplotlib", "pytest"]
-docs = ["sphinx-rtd-theme", "sphinx", "docutils (<0.18)"]
-bokeh = ["selenium", "bokeh"]
+test-no-codebase = ["matplotlib", "pillow", "pytest"]
 
 [[package]]
 name = "coverage"
@@ -322,9 +322,9 @@ PyYAML = ">=6.0,<7.0"
 scipy = ">=1.7.3,<2.0.0"
 
 [package.extras]
+box = ["banana-hep (>=0.6.6,<0.7.0)", "matplotlib (>=3.5.1,<4.0.0)", "pandas (>=1.3.0,<2.0.0)", "sqlalchemy (>=1.4.21,<2.0.0)"]
 docs = ["Sphinx (>=4.3.2,<5.0.0)", "nbsphinx (>=0.8.8,<0.9.0)", "sphinx-rtd-theme (>=1.0.0,<2.0.0)", "sphinxcontrib-bibtex (>=2.4.1,<3.0.0)"]
 mark = ["banana-hep (>=0.6.6,<0.7.0)", "matplotlib (>=3.5.1,<4.0.0)", "pandas (>=1.3.0,<2.0.0)", "sqlalchemy (>=1.4.21,<2.0.0)"]
-box = ["banana-hep (>=0.6.6,<0.7.0)", "matplotlib (>=3.5.1,<4.0.0)", "pandas (>=1.3.0,<2.0.0)", "sqlalchemy (>=1.4.21,<2.0.0)"]
 
 [[package]]
 name = "entrypoints"
@@ -347,12 +347,15 @@ test = ["pytest (>=6)"]
 
 [[package]]
 name = "executing"
-version = "1.0.0"
+version = "1.1.0"
 description = "Get the currently executing AST node of a frame, and other information"
 category = "main"
 optional = false
 python-versions = "*"
 
+[package.extras]
+tests = ["asttokens", "littleutils", "pytest", "rich"]
+
 [[package]]
 name = "fancycompleter"
 version = "0.9.1"
@@ -367,14 +370,14 @@ pyrepl = ">=0.8.2"
 
 [[package]]
 name = "fastjsonschema"
-version = "2.16.1"
+version = "2.16.2"
 description = "Fastest Python implementation of JSON schema"
 category = "main"
 optional = false
 python-versions = "*"
 
 [package.extras]
-devel = ["colorama", "jsonschema", "json-spec", "pylint", "pytest", "pytest-benchmark", "pytest-cache", "validictory"]
+devel = ["colorama", "json-spec", "jsonschema", "pylint", "pytest", "pytest-benchmark", "pytest-cache", "validictory"]
 
 [[package]]
 name = "filelock"
@@ -390,16 +393,16 @@ testing = ["covdefaults (>=2.2)", "coverage (>=6.4.2)", "pytest (>=7.1.2)", "pyt
 
 [[package]]
 name = "fonttools"
-version = "4.37.2"
+version = "4.37.3"
 description = "Tools to manipulate font files"
 category = "main"
 optional = true
 python-versions = ">=3.7"
 
 [package.extras]
-all = ["fs (>=2.2.0,<3)", "lxml (>=4.0,<5)", "zopfli (>=0.1.4)", "lz4 (>=1.7.4.2)", "matplotlib", "sympy", "skia-pathops (>=0.5.0)", "uharfbuzz (>=0.23.0)", "brotlicffi (>=0.8.0)", "scipy", "brotli (>=1.0.1)", "munkres", "unicodedata2 (>=14.0.0)", "xattr"]
+all = ["brotli (>=1.0.1)", "brotlicffi (>=0.8.0)", "fs (>=2.2.0,<3)", "lxml (>=4.0,<5)", "lz4 (>=1.7.4.2)", "matplotlib", "munkres", "scipy", "skia-pathops (>=0.5.0)", "sympy", "uharfbuzz (>=0.23.0)", "unicodedata2 (>=14.0.0)", "xattr", "zopfli (>=0.1.4)"]
 graphite = ["lz4 (>=1.7.4.2)"]
-interpolatable = ["scipy", "munkres"]
+interpolatable = ["munkres", "scipy"]
 lxml = ["lxml (>=4.0,<5)"]
 pathops = ["skia-pathops (>=0.5.0)"]
 plot = ["matplotlib"]
@@ -408,7 +411,7 @@ symfont = ["sympy"]
 type1 = ["xattr"]
 ufo = ["fs (>=2.2.0,<3)"]
 unicode = ["unicodedata2 (>=14.0.0)"]
-woff = ["zopfli (>=0.1.4)", "brotlicffi (>=0.8.0)", "brotli (>=1.0.1)"]
+woff = ["brotli (>=1.0.1)", "brotlicffi (>=0.8.0)", "zopfli (>=0.1.4)"]
 
 [[package]]
 name = "greenlet"
@@ -423,7 +426,7 @@ docs = ["sphinx"]
 
 [[package]]
 name = "hypothesis"
-version = "6.54.5"
+version = "6.54.6"
 description = "A library for property-based testing"
 category = "dev"
 optional = false
@@ -435,8 +438,8 @@ exceptiongroup = {version = ">=1.0.0rc8", markers = "python_version < \"3.11\""}
 sortedcontainers = ">=2.1.0,<3.0.0"
 
 [package.extras]
-all = ["black (>=19.10b0)", "click (>=7.0)", "django (>=3.2)", "dpcontracts (>=0.4)", "lark-parser (>=0.6.5)", "libcst (>=0.3.16)", "numpy (>=1.9.0)", "pandas (>=1.0)", "pytest (>=4.6)", "python-dateutil (>=1.4)", "pytz (>=2014.1)", "redis (>=3.0.0)", "rich (>=9.0.0)", "importlib-metadata (>=3.6)", "backports.zoneinfo (>=0.2.1)", "tzdata (>=2022.2)"]
-cli = ["click (>=7.0)", "black (>=19.10b0)", "rich (>=9.0.0)"]
+all = ["backports.zoneinfo (>=0.2.1)", "black (>=19.10b0)", "click (>=7.0)", "django (>=3.2)", "dpcontracts (>=0.4)", "importlib-metadata (>=3.6)", "lark-parser (>=0.6.5)", "libcst (>=0.3.16)", "numpy (>=1.9.0)", "pandas (>=1.0)", "pytest (>=4.6)", "python-dateutil (>=1.4)", "pytz (>=2014.1)", "redis (>=3.0.0)", "rich (>=9.0.0)", "tzdata (>=2022.2)"]
+cli = ["black (>=19.10b0)", "click (>=7.0)", "rich (>=9.0.0)"]
 codemods = ["libcst (>=0.3.16)"]
 dateutil = ["python-dateutil (>=1.4)"]
 django = ["django (>=3.2)"]
@@ -478,9 +481,9 @@ python-versions = ">=3.7"
 zipp = ">=0.5"
 
 [package.extras]
-docs = ["sphinx", "jaraco.packaging (>=9)", "rst.linker (>=1.9)"]
+docs = ["jaraco.packaging (>=9)", "rst.linker (>=1.9)", "sphinx"]
 perf = ["ipython"]
-testing = ["pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.3)", "packaging", "pyfakefs", "flufl.flake8", "pytest-perf (>=0.9.2)", "pytest-black (>=0.3.7)", "pytest-mypy (>=0.9.1)", "importlib-resources (>=1.3)"]
+testing = ["flufl.flake8", "importlib-resources (>=1.3)", "packaging", "pyfakefs", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=1.3)", "pytest-flake8", "pytest-mypy (>=0.9.1)", "pytest-perf (>=0.9.2)"]
 
 [[package]]
 name = "importlib-resources"
@@ -494,8 +497,8 @@ python-versions = ">=3.7"
 zipp = {version = ">=3.1.0", markers = "python_version < \"3.10\""}
 
 [package.extras]
-docs = ["sphinx", "jaraco.packaging (>=9)", "rst.linker (>=1.9)", "jaraco.tidelift (>=1.4)"]
-testing = ["pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.3)", "pytest-black (>=0.3.7)", "pytest-mypy (>=0.9.1)"]
+docs = ["jaraco.packaging (>=9)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx"]
+testing = ["pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=1.3)", "pytest-flake8", "pytest-mypy (>=0.9.1)"]
 
 [[package]]
 name = "iniconfig"
@@ -528,7 +531,7 @@ stack-data = "*"
 traitlets = ">=5"
 
 [package.extras]
-all = ["black", "Sphinx (>=1.3)", "ipykernel", "nbconvert", "nbformat", "ipywidgets", "notebook", "ipyparallel", "qtconsole", "pytest (<7.1)", "pytest-asyncio", "testpath", "curio", "matplotlib (!=3.2.0)", "numpy (>=1.19)", "pandas", "trio"]
+all = ["Sphinx (>=1.3)", "black", "curio", "ipykernel", "ipyparallel", "ipywidgets", "matplotlib (!=3.2.0)", "nbconvert", "nbformat", "notebook", "numpy (>=1.19)", "pandas", "pytest (<7.1)", "pytest-asyncio", "qtconsole", "testpath", "trio"]
 black = ["black"]
 doc = ["Sphinx (>=1.3)"]
 kernel = ["ipykernel"]
@@ -538,7 +541,7 @@ notebook = ["ipywidgets", "notebook"]
 parallel = ["ipyparallel"]
 qtconsole = ["qtconsole"]
 test = ["pytest (<7.1)", "pytest-asyncio", "testpath"]
-test_extra = ["pytest (<7.1)", "pytest-asyncio", "testpath", "curio", "matplotlib (!=3.2.0)", "nbformat", "numpy (>=1.19)", "pandas", "trio"]
+test_extra = ["curio", "matplotlib (!=3.2.0)", "nbformat", "numpy (>=1.19)", "pandas", "pytest (<7.1)", "pytest-asyncio", "testpath", "trio"]
 
 [[package]]
 name = "isort"
@@ -549,10 +552,10 @@ optional = false
 python-versions = ">=3.6.1,<4.0"
 
 [package.extras]
-pipfile_deprecated_finder = ["pipreqs", "requirementslib"]
-requirements_deprecated_finder = ["pipreqs", "pip-api"]
 colors = ["colorama (>=0.4.3,<0.5.0)"]
+pipfile_deprecated_finder = ["pipreqs", "requirementslib"]
 plugins = ["setuptools"]
+requirements_deprecated_finder = ["pip-api", "pipreqs"]
 
 [[package]]
 name = "jedi"
@@ -619,7 +622,7 @@ tornado = ">=6.2"
 traitlets = "*"
 
 [package.extras]
-doc = ["ipykernel", "myst-parser", "sphinx-rtd-theme", "sphinx (>=1.3.6)", "sphinxcontrib-github-alt"]
+doc = ["ipykernel", "myst-parser", "sphinx (>=1.3.6)", "sphinx-rtd-theme", "sphinxcontrib-github-alt"]
 test = ["codecov", "coverage", "ipykernel (>=6.5)", "ipython", "mypy", "pre-commit", "pytest", "pytest-asyncio (>=0.18)", "pytest-cov", "pytest-timeout"]
 
 [[package]]
@@ -718,7 +721,7 @@ python-versions = ">=3.5"
 [package.extras]
 docs = ["sphinx (>=1.6.0)", "sphinx-bootstrap-theme"]
 flake8 = ["flake8"]
-tests = ["pytest (!=3.3.0)", "psutil", "pytest-cov"]
+tests = ["psutil", "pytest (!=3.3.0)", "pytest-cov"]
 
 [[package]]
 name = "markupsafe"
@@ -790,7 +793,7 @@ nest-asyncio = "*"
 traitlets = ">=5.2.2"
 
 [package.extras]
-sphinx = ["autodoc-traits", "mock", "moto", "myst-parser", "Sphinx (>=1.7)", "sphinx-book-theme"]
+sphinx = ["Sphinx (>=1.7)", "autodoc-traits", "mock", "moto", "myst-parser", "sphinx-book-theme"]
 test = ["black", "check-manifest", "flake8", "ipykernel", "ipython", "ipywidgets", "mypy", "nbconvert", "pip (>=18.1)", "pre-commit", "pytest (>=4.1)", "pytest-asyncio", "pytest-cov (>=2.6.1)", "setuptools (>=60.0)", "testpath", "twine (>=1.11.0)", "xmltodict"]
 
 [[package]]
@@ -821,8 +824,8 @@ tinycss2 = "*"
 traitlets = ">=5.0"
 
 [package.extras]
-all = ["ipykernel", "ipython", "ipywidgets (>=7)", "nbsphinx (>=0.2.12)", "pre-commit", "pyppeteer (>=1,<1.1)", "pyqtwebengine (>=5.15)", "pytest", "pytest-cov", "pytest-dependency", "sphinx-rtd-theme", "sphinx (==5.0.2)", "tornado (>=6.1)"]
-docs = ["ipython", "nbsphinx (>=0.2.12)", "sphinx-rtd-theme", "sphinx (==5.0.2)"]
+all = ["ipykernel", "ipython", "ipywidgets (>=7)", "nbsphinx (>=0.2.12)", "pre-commit", "pyppeteer (>=1,<1.1)", "pyqtwebengine (>=5.15)", "pytest", "pytest-cov", "pytest-dependency", "sphinx (==5.0.2)", "sphinx-rtd-theme", "tornado (>=6.1)"]
+docs = ["ipython", "nbsphinx (>=0.2.12)", "sphinx (==5.0.2)", "sphinx-rtd-theme"]
 qtpdf = ["pyqtwebengine (>=5.15)"]
 qtpng = ["pyqtwebengine (>=5.15)"]
 serve = ["tornado (>=6.1)"]
@@ -831,7 +834,7 @@ webpdf = ["pyppeteer (>=1,<1.1)"]
 
 [[package]]
 name = "nbformat"
-version = "5.5.0"
+version = "5.6.1"
 description = "The Jupyter Notebook format"
 category = "main"
 optional = false
@@ -840,11 +843,11 @@ python-versions = ">=3.7"
 [package.dependencies]
 fastjsonschema = "*"
 jsonschema = ">=2.6"
-jupyter_core = "*"
+jupyter-core = "*"
 traitlets = ">=5.1"
 
 [package.extras]
-test = ["check-manifest", "testpath", "pytest", "pre-commit", "pep440"]
+test = ["check-manifest", "pep440", "pre-commit", "pytest", "testpath"]
 
 [[package]]
 name = "nbsphinx"
@@ -903,7 +906,7 @@ pyparsing = ">=2.0.2,<3.0.5 || >3.0.5"
 
 [[package]]
 name = "pandas"
-version = "1.4.4"
+version = "1.5.0"
 description = "Powerful data structures for data analysis, time series, and statistics"
 category = "main"
 optional = false
@@ -911,10 +914,8 @@ python-versions = ">=3.8"
 
 [package.dependencies]
 numpy = [
-    {version = ">=1.18.5", markers = "platform_machine != \"aarch64\" and platform_machine != \"arm64\" and python_version < \"3.10\""},
-    {version = ">=1.19.2", markers = "platform_machine == \"aarch64\" and python_version < \"3.10\""},
-    {version = ">=1.20.0", markers = "platform_machine == \"arm64\" and python_version < \"3.10\""},
     {version = ">=1.21.0", markers = "python_version >= \"3.10\""},
+    {version = ">=1.20.3", markers = "python_version < \"3.10\""},
 ]
 python-dateutil = ">=2.8.1"
 pytz = ">=2020.1"
@@ -1038,8 +1039,8 @@ optional = false
 python-versions = ">=3.7"
 
 [package.extras]
-docs = ["furo (>=2021.7.5b38)", "proselint (>=0.10.2)", "sphinx-autodoc-typehints (>=1.12)", "sphinx (>=4)"]
-test = ["appdirs (==1.4.4)", "pytest-cov (>=2.7)", "pytest-mock (>=3.6)", "pytest (>=6)"]
+docs = ["furo (>=2021.7.5b38)", "proselint (>=0.10.2)", "sphinx (>=4)", "sphinx-autodoc-typehints (>=1.12)"]
+test = ["appdirs (==1.4.4)", "pytest (>=6)", "pytest-cov (>=2.7)", "pytest-mock (>=3.6)"]
 
 [[package]]
 name = "pluggy"
@@ -1050,8 +1051,8 @@ optional = false
 python-versions = ">=3.6"
 
 [package.extras]
-testing = ["pytest-benchmark", "pytest"]
-dev = ["tox", "pre-commit"]
+dev = ["pre-commit", "tox"]
+testing = ["pytest", "pytest-benchmark"]
 
 [[package]]
 name = "poethepoet"
@@ -1152,14 +1153,14 @@ plugins = ["importlib-metadata"]
 
 [[package]]
 name = "pylint"
-version = "2.15.2"
+version = "2.15.3"
 description = "python code static checker"
 category = "dev"
 optional = false
 python-versions = ">=3.7.2"
 
 [package.dependencies]
-astroid = ">=2.12.9,<=2.14.0-dev0"
+astroid = ">=2.12.10,<=2.14.0-dev0"
 colorama = {version = ">=0.4.5", markers = "sys_platform == \"win32\""}
 dill = ">=0.2"
 isort = ">=4.2.5,<6"
@@ -1182,7 +1183,7 @@ optional = false
 python-versions = ">=3.6.8"
 
 [package.extras]
-diagrams = ["railroad-diagrams", "jinja2"]
+diagrams = ["jinja2", "railroad-diagrams"]
 
 [[package]]
 name = "pyreadline"
@@ -1243,7 +1244,7 @@ pytest = ">=4.6"
 toml = "*"
 
 [package.extras]
-testing = ["fields", "hunter", "process-tests", "six", "pytest-xdist", "virtualenv"]
+testing = ["fields", "hunter", "process-tests", "pytest-xdist", "six", "virtualenv"]
 
 [[package]]
 name = "pytest-env"
@@ -1301,7 +1302,7 @@ python-versions = ">=3.6"
 
 [[package]]
 name = "pyzmq"
-version = "24.0.0"
+version = "24.0.1"
 description = "Python bindings for 0MQ"
 category = "main"
 optional = false
@@ -1447,8 +1448,8 @@ sphinxcontrib-serializinghtml = ">=1.1.5"
 
 [package.extras]
 docs = ["sphinxcontrib-websupport"]
-lint = ["flake8 (>=3.5.0)", "isort", "mypy (>=0.931)", "docutils-stubs", "types-typed-ast", "types-requests"]
-test = ["pytest", "pytest-cov", "html5lib", "cython", "typed-ast"]
+lint = ["docutils-stubs", "flake8 (>=3.5.0)", "isort", "mypy (>=0.931)", "types-requests", "types-typed-ast"]
+test = ["cython", "html5lib", "pytest", "pytest-cov", "typed-ast"]
 
 [[package]]
 name = "sphinx-rtd-theme"
@@ -1474,8 +1475,8 @@ optional = false
 python-versions = ">=3.5"
 
 [package.extras]
+lint = ["docutils-stubs", "flake8", "mypy"]
 test = ["pytest"]
-lint = ["docutils-stubs", "mypy", "flake8"]
 
 [[package]]
 name = "sphinxcontrib-bibtex"
@@ -1504,7 +1505,7 @@ python-versions = "*"
 Sphinx = ">=2.0"
 
 [package.extras]
-test = ["mypy", "pytest", "flake8-import-order", "flake8", "tox"]
+test = ["flake8", "flake8-import-order", "mypy", "pytest", "tox"]
 
 [[package]]
 name = "sphinxcontrib-devhelp"
@@ -1515,8 +1516,8 @@ optional = false
 python-versions = ">=3.5"
 
 [package.extras]
+lint = ["docutils-stubs", "flake8", "mypy"]
 test = ["pytest"]
-lint = ["docutils-stubs", "mypy", "flake8"]
 
 [[package]]
 name = "sphinxcontrib-htmlhelp"
@@ -1527,8 +1528,8 @@ optional = false
 python-versions = ">=3.6"
 
 [package.extras]
+lint = ["docutils-stubs", "flake8", "mypy"]
 test = ["html5lib", "pytest"]
-lint = ["docutils-stubs", "mypy", "flake8"]
 
 [[package]]
 name = "sphinxcontrib-jsmath"
@@ -1539,7 +1540,7 @@ optional = false
 python-versions = ">=3.5"
 
 [package.extras]
-test = ["mypy", "flake8", "pytest"]
+test = ["flake8", "mypy", "pytest"]
 
 [[package]]
 name = "sphinxcontrib-qthelp"
@@ -1550,8 +1551,8 @@ optional = false
 python-versions = ">=3.5"
 
 [package.extras]
+lint = ["docutils-stubs", "flake8", "mypy"]
 test = ["pytest"]
-lint = ["docutils-stubs", "mypy", "flake8"]
 
 [[package]]
 name = "sphinxcontrib-serializinghtml"
@@ -1562,7 +1563,7 @@ optional = false
 python-versions = ">=3.5"
 
 [package.extras]
-lint = ["flake8", "mypy", "docutils-stubs"]
+lint = ["docutils-stubs", "flake8", "mypy"]
 test = ["pytest"]
 
 [[package]]
@@ -1577,29 +1578,29 @@ python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,!=3.5.*,>=2.7"
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 [package.extras]
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-aiosqlite = ["typing_extensions (!=3.10.0.1)", "greenlet (!=0.4.17)", "aiosqlite"]
+aiomysql = ["aiomysql", "greenlet (!=0.4.17)"]
+aiosqlite = ["aiosqlite", "greenlet (!=0.4.17)", "typing_extensions (!=3.10.0.1)"]
 asyncio = ["greenlet (!=0.4.17)"]
-asyncmy = ["greenlet (!=0.4.17)", "asyncmy (>=0.2.3,!=0.2.4)"]
+asyncmy = ["asyncmy (>=0.2.3,!=0.2.4)", "greenlet (!=0.4.17)"]
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-mypy = ["sqlalchemy2-stubs", "mypy (>=0.910)"]
-mysql = ["mysqlclient (>=1.4.0,<2)", "mysqlclient (>=1.4.0)"]
+mypy = ["mypy (>=0.910)", "sqlalchemy2-stubs"]
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 mysql_connector = ["mysql-connector-python"]
-oracle = ["cx_oracle (>=7,<8)", "cx_oracle (>=7)"]
+oracle = ["cx_oracle (>=7)", "cx_oracle (>=7,<8)"]
 postgresql = ["psycopg2 (>=2.7)"]
-postgresql_asyncpg = ["greenlet (!=0.4.17)", "asyncpg"]
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 postgresql_pg8000 = ["pg8000 (>=1.16.6,!=1.29.0)"]
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 postgresql_psycopg2cffi = ["psycopg2cffi"]
-pymysql = ["pymysql (<1)", "pymysql"]
+pymysql = ["pymysql", "pymysql (<1)"]
 sqlcipher = ["sqlcipher3-binary"]
 
 [[package]]
 name = "stack-data"
-version = "0.5.0"
+version = "0.5.1"
 description = "Extract data from python stack frames and tracebacks for informative displays"
 category = "main"
 optional = false
@@ -1611,7 +1612,7 @@ executing = "*"
 pure-eval = "*"
 
 [package.extras]
-tests = ["cython", "littleutils", "pygments", "typeguard", "pytest"]
+tests = ["cython", "littleutils", "pygments", "pytest", "typeguard"]
 
 [[package]]
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@@ -1625,8 +1626,8 @@ python-versions = ">=3.6"
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-test = ["coverage", "pytest-isort", "pytest-flake8", "pytest-cov", "pytest"]
-doc = ["sphinx-rtd-theme", "sphinx"]
+doc = ["sphinx", "sphinx-rtd-theme"]
+test = ["coverage", "pytest", "pytest-cov", "pytest-flake8", "pytest-isort"]
 
 [[package]]
 name = "toml"
@@ -1646,7 +1647,7 @@ python-versions = ">=3.7"
 
 [[package]]
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-version = "0.11.4"
+version = "0.11.5"
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@@ -1688,8 +1689,8 @@ optional = false
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-secure = ["pyOpenSSL (>=0.14)", "cryptography (>=1.3.4)", "idna (>=2.0.0)", "certifi", "urllib3-secure-extra", "ipaddress"]
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 [[package]]
@@ -1750,8 +1751,8 @@ optional = false
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 [package.extras]
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 [extras]
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@@ -2982,10 +2600,7 @@ requests = [
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 scipy = [
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@@ -3011,10 +2626,7 @@ scipy = [
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@@ -3043,10 +2655,7 @@ sphinxcontrib-applehelp = [
     {file = "sphinxcontrib-applehelp-1.0.2.tar.gz", hash = "sha256:a072735ec80e7675e3f432fcae8610ecf509c5f1869d17e2eecff44389cdbc58"},
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-]
+sphinxcontrib-bibtex = []
 sphinxcontrib-details-directive = [
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@@ -3115,8 +2724,8 @@ sqlalchemy = [
     {file = "SQLAlchemy-1.4.41.tar.gz", hash = "sha256:0292f70d1797e3c54e862e6f30ae474014648bc9c723e14a2fda730adb0a9791"},
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+    {file = "stack_data-0.5.1-py3-none-any.whl", hash = "sha256:5120731a18ba4c82cefcf84a945f6f3e62319ef413bfc210e32aca3a69310ba2"},
+    {file = "stack_data-0.5.1.tar.gz", hash = "sha256:95eb784942e861a3d80efd549ff9af6cf847d88343a12eb681d7157cfcb6e32b"},
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@@ -3131,34 +2740,16 @@ tomli = [
     {file = "tomli-2.0.1.tar.gz", hash = "sha256:de526c12914f0c550d15924c62d72abc48d6fe7364aa87328337a31007fe8a4f"},
 ]
 tomlkit = [
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-    {file = "tomlkit-0.11.4.tar.gz", hash = "sha256:3235a9010fae54323e727c3ac06fb720752fe6635b3426e379daec60fbd44a83"},
-]
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+    {file = "tomlkit-0.11.5.tar.gz", hash = "sha256:571854ebbb5eac89abcb4a2e47d7ea27b89bf29e09c35395da6f03dd4ae23d1c"},
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 traitlets = [
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     {file = "traitlets-5.4.0.tar.gz", hash = "sha256:3f2c4e435e271592fe4390f1746ea56836e3a080f84e7833f0f801d9613fec39"},
 ]
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-    {file = "typing_extensions-4.3.0.tar.gz", hash = "sha256:e6d2677a32f47fc7eb2795db1dd15c1f34eff616bcaf2cfb5e997f854fa1c4a6"},
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-    {file = "urllib3-1.26.12.tar.gz", hash = "sha256:3fa96cf423e6987997fc326ae8df396db2a8b7c667747d47ddd8ecba91f4a74e"},
-]
+typing-extensions = []
+urllib3 = []
 virtualenv = [
     {file = "virtualenv-20.16.5-py3-none-any.whl", hash = "sha256:d07dfc5df5e4e0dbc92862350ad87a36ed505b978f6c39609dc489eadd5b0d27"},
     {file = "virtualenv-20.16.5.tar.gz", hash = "sha256:227ea1b9994fdc5ea31977ba3383ef296d7472ea85be9d6732e42a91c04e80da"},
@@ -3240,7 +2831,4 @@ wrapt = [
     {file = "wrapt-1.14.1-cp39-cp39-win_amd64.whl", hash = "sha256:dee60e1de1898bde3b238f18340eec6148986da0455d8ba7848d50470a7a32fb"},
     {file = "wrapt-1.14.1.tar.gz", hash = "sha256:380a85cf89e0e69b7cfbe2ea9f765f004ff419f34194018a6827ac0e3edfed4d"},
 ]
-zipp = [
-    {file = "zipp-3.8.1-py3-none-any.whl", hash = "sha256:47c40d7fe183a6f21403a199b3e4192cca5774656965b0a4988ad2f8feb5f009"},
-    {file = "zipp-3.8.1.tar.gz", hash = "sha256:05b45f1ee8f807d0cc928485ca40a07cb491cf092ff587c0df9cb1fd154848d2"},
-]
+zipp = []
diff --git a/src/yadism/esf/scale_variations.py b/src/yadism/esf/scale_variations.py
index dde2aa035..9e5027dfa 100644
--- a/src/yadism/esf/scale_variations.py
+++ b/src/yadism/esf/scale_variations.py
@@ -1,4 +1,5 @@
 # -*- coding: utf-8 -*-
+"""Implementation of factorization and renormalization scale variations."""
 import logging
 import time
 
@@ -36,18 +37,22 @@ def build_orders(order):
 
 
 class ScaleVariations:
-    """
-    Apply scale variations.
+    """Manager for scale variations."""
 
-    Parameters
-    ----------
+    def __init__(self, order, interpolator, activate_ren, activate_fact):
+        """Inizialize manager.
+
+        Parameters
+        ----------
         order : int
             perturbative order
         interpolator : eko.interpolation.InterpolationDispatcher
             interpolation basis functions
-    """
-
-    def __init__(self, order, interpolator, activate_ren, activate_fact):
+        activate_ren : bool
+            activate renormalization scale variation
+        activate_fact : bool
+            activate factorization scale variation
+        """
         self.order = order
         self.interpolator = interpolator
         self.activate_ren = activate_ren
@@ -82,19 +87,17 @@ def compute_raw(self, nf):
                 )
 
     def fact_matrices(self, nf):
-        r"""
-        Compute all matrices related to factorization scale variation,
-        i.e. :math:`\ln(Q^2/\mu_F^2)`.
+        r"""Compute all matrices related to factorization scale variation, i.e. :math:`\ln(Q^2/\mu_F^2)`.
 
         Parameters
         ----------
-            nf : int
-                number of active flavors
+        nf : int
+            number of active flavors
 
         Returns
         -------
-            dict :
-                map with `(target, lnf, src) -> np.ndarray`
+        dict :
+            map with `(target, lnf, src) -> np.ndarray`
         """
         self.compute_raw(nf)
         # load mappings
@@ -111,20 +114,17 @@ def fact_matrices(self, nf):
         return fact_matrices
 
     def ren_coeffs(self, nf):
-        r"""
-        Provide the renormalization scale variation coefficients,
-        i.e. :math:`\ln(\mu_F^2/\mu_R^2)`.
+        r"""Provide the renormalization scale variation coefficients, i.e. :math:`\ln(\mu_F^2/\mu_R^2)`.
 
         Parameters
         ----------
-            nf : int
-                number of active flavors
+        nf : int
+            number of active flavors
 
         Returns
         -------
-            dict :
-                map with `(target, lnf2r, src) -> np.ndarray`
-
+        dict :
+            map with `(target, lnf2r, src) -> np.ndarray`
         """
         ren_coeffs = {(2, 1, 1): -beta.beta_qcd_as2(nf)}
         return dict(filter(lambda item: item[0][0] <= self.order, ren_coeffs.items()))
diff --git a/src/yadism/output.py b/src/yadism/output.py
index 5daf1260d..a8a7d5f29 100644
--- a/src/yadism/output.py
+++ b/src/yadism/output.py
@@ -20,11 +20,11 @@
 import numpy as np
 import pandas as pd
 import yaml
+from eko import compatibility as eko_compatibility
 from eko import couplings
 
 from . import observable_name as on
 from .esf.result import ESFResult, EXSResult
-from .input import compatibility
 
 
 class MaskedPDF:
@@ -96,8 +96,8 @@ def apply_pdf_theory(self, lhapdf_like, theory):
             output dictionary with all structure functions for all x, Q2, result and error
 
         """
-        new_theory, _ = compatibility.update(theory, dict(TargetDIS="proton"))
-        sc = couplings.Couplings.from_dict(new_theory)
+        new_eko_theory = eko_compatibility.update_theory(theory)
+        sc = couplings.Couplings.from_dict(new_eko_theory)
         alpha_s = lambda muR: sc.a_s(muR**2) * 4.0 * np.pi
         alpha_qed = lambda _muR: theory["alphaqed"]
         return self.apply_pdf_alphas_alphaqed_xir_xif(
diff --git a/src/yadmark/benchmark/external/xspace_bench_utils.py b/src/yadmark/benchmark/external/xspace_bench_utils.py
index 2af4c723d..3358a2827 100644
--- a/src/yadmark/benchmark/external/xspace_bench_utils.py
+++ b/src/yadmark/benchmark/external/xspace_bench_utils.py
@@ -1,29 +1,29 @@
 # -*- coding: utf-8 -*-
-import eko.couplings as eko_sc
+"""Benchmark to xspace_bench (the original FONLL implementation)."""
 import numpy as np
+from eko import compatibility as eko_compatibility
+from eko import couplings as eko_sc
 
 from yadism import observable_name as on
-from yadism.input import compatibility
 
 
 def compute_xspace_bench_data(theory, observables, pdf):
-
     """
     Run xspace_bench to compute observables.
 
     Parameters
     ----------
-        theory : dict
-            theory runcard
-        observables : dict
-            observables runcard
-        pdf : lhapdf_like
-            PDF set
+    theory : dict
+        theory runcard
+    observables : dict
+        observables runcard
+    pdf : lhapdf_like
+        PDF set
 
     Returns
     -------
-        num_tab : dict
-            xspace_bench numbers
+    dict
+        xspace_bench numbers
     """
     import xspace_bench  # pylint:disable=import-outside-toplevel
 
@@ -65,7 +65,6 @@ def compute_xspace_bench_data(theory, observables, pdf):
 
     # select scheme
     scheme = theory["FNS"]
-    new_theory = compatibility.update(theory)
 
     if scheme == "ZM-VFNS":
         scheme = "ZMVN"
@@ -84,7 +83,8 @@ def compute_xspace_bench_data(theory, observables, pdf):
     else:
         raise NotImplementedError(f"{scheme} is not implemented in xspace_bench.")
 
-    sc = eko_sc.Couplings.from_dict(new_theory)
+    new_eko_theory = eko_compatibility.update_theory(theory)
+    sc = eko_sc.Couplings.from_dict(new_eko_theory)
 
     num_tab = {}
     # loop over functions
diff --git a/src/yadmark/benchmark/runner.py b/src/yadmark/benchmark/runner.py
index 765b7b70c..f4f017c4d 100644
--- a/src/yadmark/benchmark/runner.py
+++ b/src/yadmark/benchmark/runner.py
@@ -1,9 +1,9 @@
 # -*- coding: utf-8 -*-
-import banana.cfg
 import numpy as np
 import pandas as pd
 from banana.benchmark.runner import BenchmarkRunner
 from banana.data import dfdict
+from eko import compatibility as eko_compatibility
 from eko.couplings import Couplings
 
 import yadism
@@ -45,8 +45,8 @@ def run_me(self, theory, ocard, pdf):
 
             alpha_s = lambda muR: lhapdf.mkAlphaS(pdf.set().name).alphasQ(muR)
         else:
-            new_theory, _ = yadism.input.compatibility.update(theory, ocard)
-            sc = Couplings.from_dict(new_theory)
+            new_eko_theory = eko_compatibility.update_theory(theory)
+            sc = Couplings.from_dict(new_eko_theory)
             alpha_s = lambda muR: sc.a_s(muR**2) * 4.0 * np.pi
 
         alpha_qed = lambda _muR: theory["alphaqed"]