EDIT:
The wrapper first described below made its way to CTAN, so the code with a recent LaTeX distribution is
\documentclass{article} \usepackage{tikz} \usepackage{pgfplots} \usepackage{pgfmath-xfp} \usepackage{siunitx} \usepackage{expl3} \pgfmxfpdeclarefunction{functionA}{1}{#1} \pgfmxfpdeclarefunction{functionB}{1}[functionA(#1)]{ln(2) * #1} \pgfmxfpdeclarefunction{fplog}{1}{ln(#1)} % slow (but for demonstration) \pgfmxfpdeclarefunction{nlogn}{1}[#1,fplog(#1)]{#1 * #2} % faster variant of the above \pgfmxfpdeclarefunction{NlogN}{1}{#1 * ln(#1)} \pgfmxfpdeclarefunction{lognormal}{3} {exp(-((ln(#1) - #2)^2) / (2 * (#3)^2)) / (#1 * #3 * sqrt(2 * pi))} \begin{document} \begin{tikzpicture} \draw [domain=0:1, variable=\x] plot ({\x}, {functionB(\x)}); \end{tikzpicture} \begin{tikzpicture} \begin{axis}[ domain=0.01:10, samples=100 ] \addplot {lognormal(x,ln(5),0.2)}; \end{axis} \end{tikzpicture} \begin{tikzpicture} \begin{axis}[ domain=0.01:10, samples=100 ] \addplot {nlogn(x)}; \end{axis} \end{tikzpicture} \begin{tikzpicture} \begin{axis}[ domain=0.01:10, samples=100 ] \addplot {NlogN(x)}; \end{axis} \end{tikzpicture} \end{document}
Output like below.
I've created a wrapper to define pgfmath functions which use \fpeval internally. The syntax is the following:
\pgfmathdeclarefpevalfunction{<name>}{<arg-count>}[<arg-processors>]{<function>}
In this
<name> is the name of the function<arg-count> is the number of arguments the pgfmath-function will take<arg-processors> is an optional comma-separated list of processed arguments. Those processed arguments will be processed by pgfmath (so here you could use nested functions).<function> is the function how it should be parsed by \fpeval. The number of arguments inside of <function> is the number of arguments declared in the <arg-processors> list if it was used, else it is equal to the number provided as <arg-count>
Note that the functions defined this way aren't exactly fast, but should work in every pgfmath context.
\documentclass{article} \usepackage{tikz} \usepackage{pgfplots} \usepackage{siunitx} \usepackage{expl3} \ExplSyntaxOn \tl_new:N \l_pgffpeval_function_body_tl \tl_new:N \l_pgffpeval_function_definition_tl \int_new:N \l_pgffpeval_tmp_int \cs_new_protected:Npn \pgffpeval_declare_function:nnn #1#2#3 { \__pgffpeval_initialize_body: \int_step_inline:nn {#2} { \tl_put_right:Nx \l_pgffpeval_function_body_tl { \exp_not:n { \pgfmathsetmacro } \exp_not:c { __pgffpeval_arg##1 } { \exp_not:n {####} ##1 } } } \__pgffpeval_define_function:nnnn {#2} {#1} {#2} {#3} } \cs_new_protected:Npn \pgffpeval_declare_function_processed_args:nnnn #1#2#3#4 { \__pgffpeval_initialize_body: \int_zero:N \l_pgffpeval_tmp_int \clist_map_inline:nn {#3} { \int_incr:N \l_pgffpeval_tmp_int \tl_put_right:Nx \l_pgffpeval_function_body_tl { \exp_not:n { \pgfmathsetmacro } \exp_not:c { __pgffpeval_arg \int_use:N \l_pgffpeval_tmp_int } { \exp_not:n {##1} } } } \exp_args:NV \__pgffpeval_define_function:nnnn \l_pgffpeval_tmp_int {#1} {#2} {#4} } \cs_new_protected:Npn \__pgffpeval_initialize_body: { \tl_set:Nn \l_pgffpeval_function_body_tl { \group_begin: \pgfkeys{/pgf/fpu=true, /pgf/fpu/output~format=sci}% } } \cs_new:Npn \__pgffpeval_process_function_aux:n #1 { \exp_not:n {## #1} } \cs_new_protected:Npn \__pgffpeval_process_function:nnn #1#2#3 { \exp_last_unbraced:Nx \cs_set_protected:cpn { { __pgffpeval_function_ #2 _cmd } \int_step_function:nN {#1} \__pgffpeval_process_function_aux:n } { \group_end: \exp_args:Nf \pgfmathparse { \fp_eval:n {#3} } } } \cs_new_protected:Npn \__pgffpeval_define_function:nnnn #1#2#3#4 { \__pgffpeval_process_function:nnn {#1} {#2} {#4} \tl_put_right:Nx \l_pgffpeval_function_body_tl { \use:x { \exp_not:c { __pgffpeval_function_ #2 _cmd } \int_step_function:nN {#1} \__pgffpeval_define_function_aux:n } } \exp_args:Nnno \pgfmathdeclarefunction {#2} {#3} \l_pgffpeval_function_body_tl } \cs_new:Npn \__pgffpeval_define_function_aux:n #1 { { \exp_not:c { __pgffpeval_arg#1 } } } \NewDocumentCommand \pgfmathdeclarefpevalfunction { m m o m } { \IfValueTF {#3} { \pgffpeval_declare_function_processed_args:nnnn {#1} {#2} {#3} } { \pgffpeval_declare_function:nnn {#1} {#2} } {#4} } \ExplSyntaxOff \pgfmathdeclarefpevalfunction{functionA}{1}{#1} \pgfmathdeclarefpevalfunction{functionB}{1}[functionA(#1)]{ln(2) * #1} \pgfmathdeclarefpevalfunction{fplog}{1}{ln(#1)} % slow (but for demonstration) \pgfmathdeclarefpevalfunction{nlogn}{1}[#1,fplog(#1)]{#1 * #2} % faster variant of the above \pgfmathdeclarefpevalfunction{NlogN}{1}{#1 * ln(#1)} \pgfmathdeclarefpevalfunction{lognormal}{3} {exp(-((ln(#1) - #2)^2) / (2 * (#3)^2)) / (#1 * #3 * sqrt(2 * pi))} \begin{document} \begin{tikzpicture} \draw [domain=0:1, variable=\x] plot ({\x}, {functionB(\x)}); \end{tikzpicture} \begin{tikzpicture} \begin{axis}[ domain=0.01:10, samples=100 ] \addplot {lognormal(x,ln(5),0.2)}; \end{axis} \end{tikzpicture} \begin{tikzpicture} \begin{axis}[ domain=0.01:10, samples=100 ] \addplot {nlogn(x)}; \end{axis} \end{tikzpicture} \begin{tikzpicture} \begin{axis}[ domain=0.01:10, samples=100 ] \addplot {NlogN(x)}; \end{axis} \end{tikzpicture} \end{document}
\pgfmathsetmacroto evaluatefunctionA(\x)first and passing the result of that to\fpeval. Take a look at the code here where I use\pgfmathdeclarefunctionto achieve something like this.