Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 8.6s

Alternatives: 14

Speedup: N/A×

Specification

Math

\[\begin{array}{l} \\ \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
  (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
  (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{1}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} - -1}, NdChar, \frac{NaChar}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}} - -1}\right) \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (fma
  (/ 1.0 (- (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) -1.0))
  NdChar
  (/ NaChar (- (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)) -1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return fma((1.0 / (exp(((mu - ((Ec - Vef) - EDonor)) / KbT)) - -1.0)), NdChar, (NaChar / (exp((((EAccept + (Ev + Vef)) - mu) / KbT)) - -1.0)));
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return fma(Float64(1.0 / Float64(exp(Float64(Float64(mu - Float64(Float64(Ec - Vef) - EDonor)) / KbT)) - -1.0)), NdChar, Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT)) - -1.0)))
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(1.0 / N[(N[Exp[N[(N[(mu - N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] * NdChar + N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}} \]

   2. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. div-flip N/A

      \[\leadsto \color{blue}{\frac{1}{\frac{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}{NdChar}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   4. associate-/r/ N/A

      \[\leadsto \color{blue}{\frac{1}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   5. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}, NdChar, \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\right)} \]

3. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} - -1}, NdChar, \frac{NaChar}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}} - -1}\right)} \]
4. Add Preprocessing

Alternative 2: 93.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -2.4 \cdot 10^{+139}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq 1.75 \cdot 10^{+143}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= mu -2.4e+139)
     t_0
     (if (<= mu 1.75e+143)
       (+
        (/ NaChar (+ 1.0 (exp (/ (+ EAccept (+ Ev Vef)) KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- (+ EDonor Vef) Ec) KbT)))))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (mu <= -2.4e+139) {
		tmp = t_0;
	} else if (mu <= 1.75e+143) {
		tmp = (NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (mu <= (-2.4d+139)) then
        tmp = t_0
    else if (mu <= 1.75d+143) then
        tmp = (nachar / (1.0d0 + exp(((eaccept + (ev + vef)) / kbt)))) + (ndchar / (1.0d0 + exp((((edonor + vef) - ec) / kbt))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (mu <= -2.4e+139) {
		tmp = t_0;
	} else if (mu <= 1.75e+143) {
		tmp = (NaChar / (1.0 + Math.exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + Math.exp((((EDonor + Vef) - Ec) / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if mu <= -2.4e+139:
		tmp = t_0
	elif mu <= 1.75e+143:
		tmp = (NaChar / (1.0 + math.exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + math.exp((((EDonor + Vef) - Ec) / KbT))))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
	tmp = 0.0
	if (mu <= -2.4e+139)
		tmp = t_0;
	elseif (mu <= 1.75e+143)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(EAccept + Float64(Ev + Vef)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(EDonor + Vef) - Ec) / KbT)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (mu <= -2.4e+139)
		tmp = t_0;
	elseif (mu <= 1.75e+143)
		tmp = (NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -2.4e+139], t$95$0, If[LessEqual[mu, 1.75e+143], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(EDonor + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if mu < -2.40000000000000008e139 or 1.75000000000000004e143 < mu

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in mu around inf

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 68.8

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{\color{blue}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   4. Applied rewrites 68.8%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   if -2.40000000000000008e139 < mu < 1.75000000000000004e143

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in mu around 0

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \color{blue}{\frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{\color{blue}{NdChar}}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}} \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}} \]

      4. lower-exp.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}} \]

      7. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}} \]

      8. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{\color{blue}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}} \]

      9. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + \color{blue}{e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}} \]

      10. lower-exp.f64 N/A

          \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}} \]

   4. Applied rewrites 84.3%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 80.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(Ec - Vef\right) - EDonor\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{-\left(t\_0 - mu\right)}{KbT}}} + t\_1\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-170}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{e^{\frac{mu - t\_0}{KbT}} - -1}, NdChar, \frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (- (- Ec Vef) EDonor))
        (t_1
         (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
        (t_2 (+ (/ NdChar (+ 1.0 (exp (/ (- (- t_0 mu)) KbT)))) t_1)))
   (if (<= t_2 -2e-170)
     (fma
      (/ 1.0 (- (exp (/ (- mu t_0) KbT)) -1.0))
      NdChar
      (/ NaChar (- (exp (/ EAccept KbT)) -1.0)))
     (if (<= t_2 0.0)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))
       (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (Ec - Vef) - EDonor;
	double t_1 = NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	double t_2 = (NdChar / (1.0 + exp((-(t_0 - mu) / KbT)))) + t_1;
	double tmp;
	if (t_2 <= -2e-170) {
		tmp = fma((1.0 / (exp(((mu - t_0) / KbT)) - -1.0)), NdChar, (NaChar / (exp((EAccept / KbT)) - -1.0)));
	} else if (t_2 <= 0.0) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(Ec - Vef) - EDonor)
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(t_0 - mu)) / KbT)))) + t_1)
	tmp = 0.0
	if (t_2 <= -2e-170)
		tmp = fma(Float64(1.0 / Float64(exp(Float64(Float64(mu - t_0) / KbT)) - -1.0)), NdChar, Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) - -1.0)));
	elseif (t_2 <= 0.0)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_1);
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(t$95$0 - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-170], N[(N[(1.0 / N[(N[Exp[N[(N[(mu - t$95$0), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] * NdChar + N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999997e-170

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

      3. div-flip N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}{NdChar}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

      4. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{1}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}, NdChar, \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\right)} \]

   3. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} - -1}, NdChar, \frac{NaChar}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}} - -1}\right)} \]

   4. Taylor expanded in EAccept around inf

      \[\leadsto \mathsf{fma}\left(\frac{1}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} - -1}, NdChar, \frac{NaChar}{e^{\color{blue}{\frac{EAccept}{KbT}}} - -1}\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 68.3

         \[\leadsto \mathsf{fma}\left(\frac{1}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} - -1}, NdChar, \frac{NaChar}{e^{\frac{EAccept}{\color{blue}{KbT}}} - -1}\right) \]

   6. Applied rewrites 68.3%

      \[\leadsto \mathsf{fma}\left(\frac{1}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} - -1}, NdChar, \frac{NaChar}{e^{\color{blue}{\frac{EAccept}{KbT}}} - -1}\right) \]

   if -1.99999999999999997e-170 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 0.0

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in NdChar around 0

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{\color{blue}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + \color{blue}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      7. lower-+.f64 61.1

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

   if 0.0 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in mu around inf

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 68.8

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{\color{blue}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   4. Applied rewrites 68.8%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 80.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ t_2 := t\_0 + t\_1\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-170}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
        (t_1
         (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
        (t_2 (+ t_0 t_1)))
   (if (<= t_2 -2e-170)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
     (if (<= t_2 0.0)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))
       (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	double t_2 = t_0 + t_1;
	double tmp;
	if (t_2 <= -2e-170) {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (t_2 <= 0.0) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt)))
    t_2 = t_0 + t_1
    if (t_2 <= (-2d-170)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (t_2 <= 0.0d0) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	double t_2 = t_0 + t_1;
	double tmp;
	if (t_2 <= -2e-170) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (t_2 <= 0.0) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT)))
	t_2 = t_0 + t_1
	tmp = 0
	if t_2 <= -2e-170:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif t_2 <= 0.0:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT))))
	t_2 = Float64(t_0 + t_1)
	tmp = 0.0
	if (t_2 <= -2e-170)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (t_2 <= 0.0)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	t_1 = NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	t_2 = t_0 + t_1;
	tmp = 0.0;
	if (t_2 <= -2e-170)
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (t_2 <= 0.0)
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	else
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-170], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999997e-170

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 68.3

         \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{\color{blue}{KbT}}}} \]

   4. Applied rewrites 68.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   if -1.99999999999999997e-170 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 0.0

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in NdChar around 0

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{\color{blue}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + \color{blue}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      7. lower-+.f64 61.1

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

   if 0.0 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in mu around inf

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 68.8

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{\color{blue}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   4. Applied rewrites 68.8%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_2 := t\_0 + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-150}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
        (t_2
         (+
          t_0
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_2 -2e-170)
     t_1
     (if (<= t_2 5e-150)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))
       t_1))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	double t_2 = t_0 + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_2 <= -2e-170) {
		tmp = t_1;
	} else if (t_2 <= 5e-150) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))
    t_1 = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    t_2 = t_0 + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (t_2 <= (-2d-170)) then
        tmp = t_1
    else if (t_2 <= 5d-150) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	double t_2 = t_0 + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_2 <= -2e-170) {
		tmp = t_1;
	} else if (t_2 <= 5e-150) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))
	t_1 = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	t_2 = t_0 + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if t_2 <= -2e-170:
		tmp = t_1
	elif t_2 <= 5e-150:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))))
	t_2 = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
	tmp = 0.0
	if (t_2 <= -2e-170)
		tmp = t_1;
	elseif (t_2 <= 5e-150)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	t_1 = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	t_2 = t_0 + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (t_2 <= -2e-170)
		tmp = t_1;
	elseif (t_2 <= 5e-150)
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-170], t$95$1, If[LessEqual[t$95$2, 5e-150], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999997e-170 or 4.9999999999999999e-150 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 68.3

         \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{\color{blue}{KbT}}}} \]

   4. Applied rewrites 68.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   if -1.99999999999999997e-170 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 4.9999999999999999e-150

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in NdChar around 0

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{\color{blue}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + \color{blue}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      7. lower-+.f64 61.1

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-170}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-150}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT))))
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -2e-170)
     t_0
     (if (<= t_1 5e-150)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	double t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -2e-170) {
		tmp = t_0;
	} else if (t_1 <= 5e-150) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    t_1 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (t_1 <= (-2d-170)) then
        tmp = t_0
    else if (t_1 <= 5d-150) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	double t_1 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -2e-170) {
		tmp = t_0;
	} else if (t_1 <= 5e-150) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	t_1 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if t_1 <= -2e-170:
		tmp = t_0
	elif t_1 <= 5e-150:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
	tmp = 0.0
	if (t_1 <= -2e-170)
		tmp = t_0;
	elseif (t_1 <= 5e-150)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (t_1 <= -2e-170)
		tmp = t_0;
	elseif (t_1 <= 5e-150)
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-170], t$95$0, If[LessEqual[t$95$1, 5e-150], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999997e-170 or 4.9999999999999999e-150 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 68.3

         \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{\color{blue}{KbT}}}} \]

   4. Applied rewrites 68.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   5. Taylor expanded in EDonor around 0

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{NdChar}{\color{blue}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{NdChar}{1 + \color{blue}{e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      6. lower-+.f64 61.9

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   7. Applied rewrites 61.9%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   if -1.99999999999999997e-170 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 4.9999999999999999e-150

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in NdChar around 0

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{\color{blue}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + \color{blue}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      7. lower-+.f64 61.1

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 70.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2800000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 2.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))))
   (if (<= NaChar -2800000.0)
     t_0
     (if (<= NaChar 2.3e-48)
       (/ NdChar (+ 1.0 (exp (/ (- (+ EDonor (+ Vef mu)) Ec) KbT))))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	double tmp;
	if (NaChar <= -2800000.0) {
		tmp = t_0;
	} else if (NaChar <= 2.3e-48) {
		tmp = NdChar / (1.0 + exp((((EDonor + (Vef + mu)) - Ec) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    if (nachar <= (-2800000.0d0)) then
        tmp = t_0
    else if (nachar <= 2.3d-48) then
        tmp = ndchar / (1.0d0 + exp((((edonor + (vef + mu)) - ec) / kbt)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	double tmp;
	if (NaChar <= -2800000.0) {
		tmp = t_0;
	} else if (NaChar <= 2.3e-48) {
		tmp = NdChar / (1.0 + Math.exp((((EDonor + (Vef + mu)) - Ec) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	tmp = 0
	if NaChar <= -2800000.0:
		tmp = t_0
	elif NaChar <= 2.3e-48:
		tmp = NdChar / (1.0 + math.exp((((EDonor + (Vef + mu)) - Ec) / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))))
	tmp = 0.0
	if (NaChar <= -2800000.0)
		tmp = t_0;
	elseif (NaChar <= 2.3e-48)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(EDonor + Float64(Vef + mu)) - Ec) / KbT))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2800000.0)
		tmp = t_0;
	elseif (NaChar <= 2.3e-48)
		tmp = NdChar / (1.0 + exp((((EDonor + (Vef + mu)) - Ec) / KbT)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2800000.0], t$95$0, If[LessEqual[NaChar, 2.3e-48], N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(EDonor + N[(Vef + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.8e6 or 2.3000000000000001e-48 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in NdChar around 0

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{\color{blue}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + \color{blue}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      7. lower-+.f64 61.1

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

   if -2.8e6 < NaChar < 2.3000000000000001e-48

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in NaChar around inf

      \[\leadsto \color{blue}{NaChar \cdot \left(\frac{1}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} + \frac{NdChar}{NaChar \cdot \left(1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}\right)}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto NaChar \cdot \color{blue}{\left(\frac{1}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} + \frac{NdChar}{NaChar \cdot \left(1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}\right)}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto NaChar \cdot \left(\frac{1}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} + \color{blue}{\frac{NdChar}{NaChar \cdot \left(1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}\right)}}\right) \]

   4. Applied rewrites 91.0%

      \[\leadsto \color{blue}{NaChar \cdot \left(\frac{1}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} + \frac{NdChar}{NaChar \cdot \left(1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}\right)}\right)} \]

   6. Applied rewrites 99.9%

      \[\leadsto \mathsf{fma}\left(NdChar, \color{blue}{\frac{1}{\mathsf{fma}\left(e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}, NaChar, NaChar\right)} \cdot NaChar}, \frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} - -1}\right) \]

   7. Taylor expanded in NdChar around inf

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{NdChar}{\color{blue}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{NdChar}{1 + \color{blue}{e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}} \]

      7. lower-+.f64 60.3

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}} \]

   9. Applied rewrites 60.3%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 61.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -9 \cdot 10^{+120}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -9e+120)
   (* 0.5 (+ NdChar NaChar))
   (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -9e+120) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-9d+120)) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -9e+120) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -9e+120:
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -9e+120)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -9e+120)
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -9e+120], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -8.99999999999999953e120

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. +-commutative N/A

         \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2} \cdot NaChar} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2}} \cdot NaChar \]

      4. *-commutative N/A

         \[\leadsto NdChar \cdot \frac{1}{2} + \color{blue}{\frac{1}{2}} \cdot NaChar \]

      5. *-commutative N/A

         \[\leadsto NdChar \cdot \frac{1}{2} + NaChar \cdot \color{blue}{\frac{1}{2}} \]

      6. distribute-rgt-out N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

      8. lower-+.f64 26.8

         \[\leadsto 0.5 \cdot \left(NdChar + \color{blue}{NaChar}\right) \]

   6. Applied rewrites 26.8%

      \[\leadsto \color{blue}{0.5 \cdot \left(NdChar + NaChar\right)} \]

   if -8.99999999999999953e120 < KbT

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in NdChar around 0

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{\color{blue}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + \color{blue}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

      7. lower-+.f64 61.1

         \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 33.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-168}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;t\_0 \leq -4 \cdot 10^{-297}:\\ \;\;\;\;0.5 \cdot NaChar\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-306}:\\ \;\;\;\;\left(\left(0.25 \cdot NaChar\right) \cdot NaChar\right) \cdot \frac{1}{0.5 \cdot \left(NaChar - NdChar\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{NaChar - NdChar} \cdot \left(\left(NaChar + NdChar\right) \cdot 0.25\right)\right) \cdot \left(NaChar - NdChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_0 -5e-168)
     (* 0.5 (+ NdChar NaChar))
     (if (<= t_0 -4e-297)
       (* 0.5 NaChar)
       (if (<= t_0 2e-306)
         (* (* (* 0.25 NaChar) NaChar) (/ 1.0 (* 0.5 (- NaChar NdChar))))
         (*
          (* (/ 2.0 (- NaChar NdChar)) (* (+ NaChar NdChar) 0.25))
          (- NaChar NdChar)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_0 <= -5e-168) {
		tmp = 0.5 * (NdChar + NaChar);
	} else if (t_0 <= -4e-297) {
		tmp = 0.5 * NaChar;
	} else if (t_0 <= 2e-306) {
		tmp = ((0.25 * NaChar) * NaChar) * (1.0 / (0.5 * (NaChar - NdChar)));
	} else {
		tmp = ((2.0 / (NaChar - NdChar)) * ((NaChar + NdChar) * 0.25)) * (NaChar - NdChar);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (t_0 <= (-5d-168)) then
        tmp = 0.5d0 * (ndchar + nachar)
    else if (t_0 <= (-4d-297)) then
        tmp = 0.5d0 * nachar
    else if (t_0 <= 2d-306) then
        tmp = ((0.25d0 * nachar) * nachar) * (1.0d0 / (0.5d0 * (nachar - ndchar)))
    else
        tmp = ((2.0d0 / (nachar - ndchar)) * ((nachar + ndchar) * 0.25d0)) * (nachar - ndchar)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_0 <= -5e-168) {
		tmp = 0.5 * (NdChar + NaChar);
	} else if (t_0 <= -4e-297) {
		tmp = 0.5 * NaChar;
	} else if (t_0 <= 2e-306) {
		tmp = ((0.25 * NaChar) * NaChar) * (1.0 / (0.5 * (NaChar - NdChar)));
	} else {
		tmp = ((2.0 / (NaChar - NdChar)) * ((NaChar + NdChar) * 0.25)) * (NaChar - NdChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if t_0 <= -5e-168:
		tmp = 0.5 * (NdChar + NaChar)
	elif t_0 <= -4e-297:
		tmp = 0.5 * NaChar
	elif t_0 <= 2e-306:
		tmp = ((0.25 * NaChar) * NaChar) * (1.0 / (0.5 * (NaChar - NdChar)))
	else:
		tmp = ((2.0 / (NaChar - NdChar)) * ((NaChar + NdChar) * 0.25)) * (NaChar - NdChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
	tmp = 0.0
	if (t_0 <= -5e-168)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	elseif (t_0 <= -4e-297)
		tmp = Float64(0.5 * NaChar);
	elseif (t_0 <= 2e-306)
		tmp = Float64(Float64(Float64(0.25 * NaChar) * NaChar) * Float64(1.0 / Float64(0.5 * Float64(NaChar - NdChar))));
	else
		tmp = Float64(Float64(Float64(2.0 / Float64(NaChar - NdChar)) * Float64(Float64(NaChar + NdChar) * 0.25)) * Float64(NaChar - NdChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (t_0 <= -5e-168)
		tmp = 0.5 * (NdChar + NaChar);
	elseif (t_0 <= -4e-297)
		tmp = 0.5 * NaChar;
	elseif (t_0 <= 2e-306)
		tmp = ((0.25 * NaChar) * NaChar) * (1.0 / (0.5 * (NaChar - NdChar)));
	else
		tmp = ((2.0 / (NaChar - NdChar)) * ((NaChar + NdChar) * 0.25)) * (NaChar - NdChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-168], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -4e-297], N[(0.5 * NaChar), $MachinePrecision], If[LessEqual[t$95$0, 2e-306], N[(N[(N[(0.25 * NaChar), $MachinePrecision] * NaChar), $MachinePrecision] * N[(1.0 / N[(0.5 * N[(NaChar - NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 / N[(NaChar - NdChar), $MachinePrecision]), $MachinePrecision] * N[(N[(NaChar + NdChar), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision] * N[(NaChar - NdChar), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -5.00000000000000001e-168

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. +-commutative N/A

         \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2} \cdot NaChar} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2}} \cdot NaChar \]

      4. *-commutative N/A

         \[\leadsto NdChar \cdot \frac{1}{2} + \color{blue}{\frac{1}{2}} \cdot NaChar \]

      5. *-commutative N/A

         \[\leadsto NdChar \cdot \frac{1}{2} + NaChar \cdot \color{blue}{\frac{1}{2}} \]

      6. distribute-rgt-out N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

      8. lower-+.f64 26.8

         \[\leadsto 0.5 \cdot \left(NdChar + \color{blue}{NaChar}\right) \]

   6. Applied rewrites 26.8%

      \[\leadsto \color{blue}{0.5 \cdot \left(NdChar + NaChar\right)} \]

   if -5.00000000000000001e-168 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -4.00000000000000016e-297

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]

   5. Taylor expanded in NdChar around 0

      \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
   6. Step-by-step derivation

      1. lower-*.f64 17.7

         \[\leadsto 0.5 \cdot NaChar \]

   7. Applied rewrites 17.7%

      \[\leadsto 0.5 \cdot \color{blue}{NaChar} \]

   if -4.00000000000000016e-297 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 2.00000000000000006e-306

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. flip-+ N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar\right) - \left(\frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NdChar\right)}{\color{blue}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

      3. mult-flip N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar\right) - \left(\frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NdChar\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar\right) - \left(\frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NdChar\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

      5. difference-of-squares N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      6. lift-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(\frac{1}{2}, NaChar, \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(\frac{1}{2}, NaChar, \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      8. lift-fma.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      9. +-commutative N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NdChar + \frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot NdChar + \frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      11. *-commutative N/A

          \[\leadsto \left(\left(NdChar \cdot \frac{1}{2} + \frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      12. *-commutative N/A

          \[\leadsto \left(\left(NdChar \cdot \frac{1}{2} + NaChar \cdot \frac{1}{2}\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      13. distribute-rgt-out N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      15. lower-+.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      16. *-commutative N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(NaChar \cdot \frac{1}{2} - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      17. lift-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(NaChar \cdot \frac{1}{2} - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      18. *-commutative N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(NaChar \cdot \frac{1}{2} - NdChar \cdot \frac{1}{2}\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      19. distribute-rgt-out-- N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      20. lower-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      21. lower--.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      22. lower-/.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\color{blue}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

   6. Applied rewrites 17.3%

      \[\leadsto \left(\left(0.5 \cdot \left(NdChar + NaChar\right)\right) \cdot \left(0.5 \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \color{blue}{\frac{1}{0.5 \cdot \left(NaChar - NdChar\right)}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(NaChar - NdChar\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(NaChar - NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      5. sub-to-mult N/A

         \[\leadsto \left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(\left(1 - \frac{NdChar}{NaChar}\right) \cdot NaChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(NdChar + NaChar\right) \cdot \frac{1}{2}\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      11. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(NdChar + NaChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(NdChar + NaChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      13. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(\left(NdChar + NaChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      14. +-commutative N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      15. lower-+.f64 N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      16. metadata-eval N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \frac{1}{4}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      17. sub-to-fraction N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \frac{1}{4}\right) \cdot \frac{1 \cdot NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      18. *-lft-identity N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \frac{1}{4}\right) \cdot \frac{NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      19. lift--.f64 N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \frac{1}{4}\right) \cdot \frac{NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      20. lower-/.f64 15.6

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot 0.25\right) \cdot \frac{NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{1}{0.5 \cdot \left(NaChar - NdChar\right)} \]

   8. Applied rewrites 15.6%

      \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot 0.25\right) \cdot \frac{NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{\color{blue}{1}}{0.5 \cdot \left(NaChar - NdChar\right)} \]

   9. Taylor expanded in NdChar around 0

      \[\leadsto \left(\left(\frac{1}{4} \cdot NaChar\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 15.5

          \[\leadsto \left(\left(0.25 \cdot NaChar\right) \cdot NaChar\right) \cdot \frac{1}{0.5 \cdot \left(NaChar - NdChar\right)} \]

   11. Applied rewrites 15.5%

       \[\leadsto \left(\left(0.25 \cdot NaChar\right) \cdot NaChar\right) \cdot \frac{1}{0.5 \cdot \left(NaChar - NdChar\right)} \]

   if 2.00000000000000006e-306 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. flip-+ N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar\right) - \left(\frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NdChar\right)}{\color{blue}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

      3. mult-flip N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar\right) - \left(\frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NdChar\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar\right) - \left(\frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NdChar\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

      5. difference-of-squares N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      6. lift-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(\frac{1}{2}, NaChar, \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(\frac{1}{2}, NaChar, \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      8. lift-fma.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      9. +-commutative N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NdChar + \frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot NdChar + \frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      11. *-commutative N/A

          \[\leadsto \left(\left(NdChar \cdot \frac{1}{2} + \frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      12. *-commutative N/A

          \[\leadsto \left(\left(NdChar \cdot \frac{1}{2} + NaChar \cdot \frac{1}{2}\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      13. distribute-rgt-out N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      15. lower-+.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      16. *-commutative N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(NaChar \cdot \frac{1}{2} - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      17. lift-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(NaChar \cdot \frac{1}{2} - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      18. *-commutative N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(NaChar \cdot \frac{1}{2} - NdChar \cdot \frac{1}{2}\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      19. distribute-rgt-out-- N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      20. lower-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      21. lower--.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      22. lower-/.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\color{blue}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

   6. Applied rewrites 17.3%

      \[\leadsto \left(\left(0.5 \cdot \left(NdChar + NaChar\right)\right) \cdot \left(0.5 \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \color{blue}{\frac{1}{0.5 \cdot \left(NaChar - NdChar\right)}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)}} \]

      2. *-commutative N/A

         \[\leadsto \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \cdot \color{blue}{\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \cdot \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \cdot \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \color{blue}{\left(NaChar - NdChar\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \cdot \left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \color{blue}{\left(NaChar - NdChar\right)}\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \cdot \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right)\right) \cdot \color{blue}{\left(NaChar - NdChar\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \cdot \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right)\right) \cdot \color{blue}{\left(NaChar - NdChar\right)} \]

   8. Applied rewrites 26.8%

      \[\leadsto \left(\frac{2}{NaChar - NdChar} \cdot \left(\left(NaChar + NdChar\right) \cdot 0.25\right)\right) \cdot \color{blue}{\left(NaChar - NdChar\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 33.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-168}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-297}:\\ \;\;\;\;0.5 \cdot NaChar\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-306}:\\ \;\;\;\;\left(\left(0.25 \cdot NaChar\right) \cdot NaChar\right) \cdot \frac{1}{0.5 \cdot \left(NaChar - NdChar\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e-168)
     t_0
     (if (<= t_1 -4e-297)
       (* 0.5 NaChar)
       (if (<= t_1 2e-306)
         (* (* (* 0.25 NaChar) NaChar) (/ 1.0 (* 0.5 (- NaChar NdChar))))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -5e-168) {
		tmp = t_0;
	} else if (t_1 <= -4e-297) {
		tmp = 0.5 * NaChar;
	} else if (t_1 <= 2e-306) {
		tmp = ((0.25 * NaChar) * NaChar) * (1.0 / (0.5 * (NaChar - NdChar)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    t_1 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (t_1 <= (-5d-168)) then
        tmp = t_0
    else if (t_1 <= (-4d-297)) then
        tmp = 0.5d0 * nachar
    else if (t_1 <= 2d-306) then
        tmp = ((0.25d0 * nachar) * nachar) * (1.0d0 / (0.5d0 * (nachar - ndchar)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -5e-168) {
		tmp = t_0;
	} else if (t_1 <= -4e-297) {
		tmp = 0.5 * NaChar;
	} else if (t_1 <= 2e-306) {
		tmp = ((0.25 * NaChar) * NaChar) * (1.0 / (0.5 * (NaChar - NdChar)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	t_1 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if t_1 <= -5e-168:
		tmp = t_0
	elif t_1 <= -4e-297:
		tmp = 0.5 * NaChar
	elif t_1 <= 2e-306:
		tmp = ((0.25 * NaChar) * NaChar) * (1.0 / (0.5 * (NaChar - NdChar)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
	tmp = 0.0
	if (t_1 <= -5e-168)
		tmp = t_0;
	elseif (t_1 <= -4e-297)
		tmp = Float64(0.5 * NaChar);
	elseif (t_1 <= 2e-306)
		tmp = Float64(Float64(Float64(0.25 * NaChar) * NaChar) * Float64(1.0 / Float64(0.5 * Float64(NaChar - NdChar))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (t_1 <= -5e-168)
		tmp = t_0;
	elseif (t_1 <= -4e-297)
		tmp = 0.5 * NaChar;
	elseif (t_1 <= 2e-306)
		tmp = ((0.25 * NaChar) * NaChar) * (1.0 / (0.5 * (NaChar - NdChar)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-168], t$95$0, If[LessEqual[t$95$1, -4e-297], N[(0.5 * NaChar), $MachinePrecision], If[LessEqual[t$95$1, 2e-306], N[(N[(N[(0.25 * NaChar), $MachinePrecision] * NaChar), $MachinePrecision] * N[(1.0 / N[(0.5 * N[(NaChar - NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -5.00000000000000001e-168 or 2.00000000000000006e-306 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. +-commutative N/A

         \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2} \cdot NaChar} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2}} \cdot NaChar \]

      4. *-commutative N/A

         \[\leadsto NdChar \cdot \frac{1}{2} + \color{blue}{\frac{1}{2}} \cdot NaChar \]

      5. *-commutative N/A

         \[\leadsto NdChar \cdot \frac{1}{2} + NaChar \cdot \color{blue}{\frac{1}{2}} \]

      6. distribute-rgt-out N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

      8. lower-+.f64 26.8

         \[\leadsto 0.5 \cdot \left(NdChar + \color{blue}{NaChar}\right) \]

   6. Applied rewrites 26.8%

      \[\leadsto \color{blue}{0.5 \cdot \left(NdChar + NaChar\right)} \]

   if -5.00000000000000001e-168 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -4.00000000000000016e-297

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]

   5. Taylor expanded in NdChar around 0

      \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
   6. Step-by-step derivation

      1. lower-*.f64 17.7

         \[\leadsto 0.5 \cdot NaChar \]

   7. Applied rewrites 17.7%

      \[\leadsto 0.5 \cdot \color{blue}{NaChar} \]

   if -4.00000000000000016e-297 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 2.00000000000000006e-306

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. flip-+ N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar\right) - \left(\frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NdChar\right)}{\color{blue}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

      3. mult-flip N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar\right) - \left(\frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NdChar\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar\right) - \left(\frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NdChar\right)\right) \cdot \color{blue}{\frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

      5. difference-of-squares N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      6. lift-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(\frac{1}{2}, NaChar, \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(\frac{1}{2}, NaChar, \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      8. lift-fma.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      9. +-commutative N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot NdChar + \frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot NdChar + \frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      11. *-commutative N/A

          \[\leadsto \left(\left(NdChar \cdot \frac{1}{2} + \frac{1}{2} \cdot NaChar\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      12. *-commutative N/A

          \[\leadsto \left(\left(NdChar \cdot \frac{1}{2} + NaChar \cdot \frac{1}{2}\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      13. distribute-rgt-out N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      15. lower-+.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      16. *-commutative N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(NaChar \cdot \frac{1}{2} - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      17. lift-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(NaChar \cdot \frac{1}{2} - \frac{1}{2} \cdot NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      18. *-commutative N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(NaChar \cdot \frac{1}{2} - NdChar \cdot \frac{1}{2}\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      19. distribute-rgt-out-- N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      20. lower-*.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      21. lower--.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar} \]

      22. lower-/.f64 N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\color{blue}{\frac{1}{2} \cdot NaChar - \frac{1}{2} \cdot NdChar}} \]

   6. Applied rewrites 17.3%

      \[\leadsto \left(\left(0.5 \cdot \left(NdChar + NaChar\right)\right) \cdot \left(0.5 \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \color{blue}{\frac{1}{0.5 \cdot \left(NaChar - NdChar\right)}} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \left(\frac{1}{2} \cdot \left(NaChar - NdChar\right)\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(NaChar - NdChar\right)\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(NaChar - NdChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      5. sub-to-mult N/A

         \[\leadsto \left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(\left(1 - \frac{NdChar}{NaChar}\right) \cdot NaChar\right)\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{\color{blue}{1}}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(NdChar + NaChar\right) \cdot \frac{1}{2}\right) \cdot \frac{1}{2}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      11. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(NdChar + NaChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(NdChar + NaChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      13. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(\left(NdChar + NaChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      14. +-commutative N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      15. lower-+.f64 N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \left(\frac{1}{2} \cdot \frac{1}{2}\right)\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      16. metadata-eval N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \frac{1}{4}\right) \cdot \left(1 - \frac{NdChar}{NaChar}\right)\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      17. sub-to-fraction N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \frac{1}{4}\right) \cdot \frac{1 \cdot NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      18. *-lft-identity N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \frac{1}{4}\right) \cdot \frac{NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      19. lift--.f64 N/A

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot \frac{1}{4}\right) \cdot \frac{NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]

      20. lower-/.f64 15.6

          \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot 0.25\right) \cdot \frac{NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{1}{0.5 \cdot \left(NaChar - NdChar\right)} \]

   8. Applied rewrites 15.6%

      \[\leadsto \left(\left(\left(\left(NaChar + NdChar\right) \cdot 0.25\right) \cdot \frac{NaChar - NdChar}{NaChar}\right) \cdot NaChar\right) \cdot \frac{\color{blue}{1}}{0.5 \cdot \left(NaChar - NdChar\right)} \]

   9. Taylor expanded in NdChar around 0

      \[\leadsto \left(\left(\frac{1}{4} \cdot NaChar\right) \cdot NaChar\right) \cdot \frac{1}{\frac{1}{2} \cdot \left(NaChar - NdChar\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 15.5

          \[\leadsto \left(\left(0.25 \cdot NaChar\right) \cdot NaChar\right) \cdot \frac{1}{0.5 \cdot \left(NaChar - NdChar\right)} \]

   11. Applied rewrites 15.5%

       \[\leadsto \left(\left(0.25 \cdot NaChar\right) \cdot NaChar\right) \cdot \frac{1}{0.5 \cdot \left(NaChar - NdChar\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 30.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-168}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-297}:\\ \;\;\;\;0.5 \cdot NaChar\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;-0.25 \cdot \frac{Ev \cdot NaChar}{KbT}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e-168)
     t_0
     (if (<= t_1 -4e-297)
       (* 0.5 NaChar)
       (if (<= t_1 0.0) (* -0.25 (/ (* Ev NaChar) KbT)) t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -5e-168) {
		tmp = t_0;
	} else if (t_1 <= -4e-297) {
		tmp = 0.5 * NaChar;
	} else if (t_1 <= 0.0) {
		tmp = -0.25 * ((Ev * NaChar) / KbT);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    t_1 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (t_1 <= (-5d-168)) then
        tmp = t_0
    else if (t_1 <= (-4d-297)) then
        tmp = 0.5d0 * nachar
    else if (t_1 <= 0.0d0) then
        tmp = (-0.25d0) * ((ev * nachar) / kbt)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -5e-168) {
		tmp = t_0;
	} else if (t_1 <= -4e-297) {
		tmp = 0.5 * NaChar;
	} else if (t_1 <= 0.0) {
		tmp = -0.25 * ((Ev * NaChar) / KbT);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	t_1 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if t_1 <= -5e-168:
		tmp = t_0
	elif t_1 <= -4e-297:
		tmp = 0.5 * NaChar
	elif t_1 <= 0.0:
		tmp = -0.25 * ((Ev * NaChar) / KbT)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
	tmp = 0.0
	if (t_1 <= -5e-168)
		tmp = t_0;
	elseif (t_1 <= -4e-297)
		tmp = Float64(0.5 * NaChar);
	elseif (t_1 <= 0.0)
		tmp = Float64(-0.25 * Float64(Float64(Ev * NaChar) / KbT));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (t_1 <= -5e-168)
		tmp = t_0;
	elseif (t_1 <= -4e-297)
		tmp = 0.5 * NaChar;
	elseif (t_1 <= 0.0)
		tmp = -0.25 * ((Ev * NaChar) / KbT);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-168], t$95$0, If[LessEqual[t$95$1, -4e-297], N[(0.5 * NaChar), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(-0.25 * N[(N[(Ev * NaChar), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -5.00000000000000001e-168 or 0.0 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. +-commutative N/A

         \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2} \cdot NaChar} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2}} \cdot NaChar \]

      4. *-commutative N/A

         \[\leadsto NdChar \cdot \frac{1}{2} + \color{blue}{\frac{1}{2}} \cdot NaChar \]

      5. *-commutative N/A

         \[\leadsto NdChar \cdot \frac{1}{2} + NaChar \cdot \color{blue}{\frac{1}{2}} \]

      6. distribute-rgt-out N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

      8. lower-+.f64 26.8

         \[\leadsto 0.5 \cdot \left(NdChar + \color{blue}{NaChar}\right) \]

   6. Applied rewrites 26.8%

      \[\leadsto \color{blue}{0.5 \cdot \left(NdChar + NaChar\right)} \]

   if -5.00000000000000001e-168 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -4.00000000000000016e-297

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]

   5. Taylor expanded in NdChar around 0

      \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
   6. Step-by-step derivation

      1. lower-*.f64 17.7

         \[\leadsto 0.5 \cdot NaChar \]

   7. Applied rewrites 17.7%

      \[\leadsto 0.5 \cdot \color{blue}{NaChar} \]

   if -4.00000000000000016e-297 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 0.0

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{1}{4} \cdot \left(NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)\right) + \frac{1}{4} \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)}{KbT} + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-1, \color{blue}{\frac{\frac{1}{4} \cdot \left(NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)\right) + \frac{1}{4} \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)}{KbT}}, \frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \]

   4. Applied rewrites 14.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{\mathsf{fma}\left(0.25, NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right), 0.25 \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)\right)}{KbT}, \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\right)} \]

   5. Taylor expanded in Ev around inf

      \[\leadsto \frac{-1}{4} \cdot \color{blue}{\frac{Ev \cdot NaChar}{KbT}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{4} \cdot \frac{Ev \cdot NaChar}{\color{blue}{KbT}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{-1}{4} \cdot \frac{Ev \cdot NaChar}{KbT} \]

      3. lower-*.f64 6.4

         \[\leadsto -0.25 \cdot \frac{Ev \cdot NaChar}{KbT} \]

   7. Applied rewrites 6.4%

      \[\leadsto -0.25 \cdot \color{blue}{\frac{Ev \cdot NaChar}{KbT}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 26.8% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(NdChar + NaChar\right) \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (* 0.5 (+ NdChar NaChar)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return 0.5 * (NdChar + NaChar);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = 0.5d0 * (ndchar + nachar)
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return 0.5 * (NdChar + NaChar);
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return 0.5 * (NdChar + NaChar)

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(0.5 * Float64(NdChar + NaChar))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.5 * (NdChar + NaChar);
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

2. Taylor expanded in KbT around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
3. Step-by-step derivation

   1. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

   2. lower-*.f64 26.8

      \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

4. Applied rewrites 26.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
5. Step-by-step derivation

   1. lift-fma.f64 N/A

      \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

   2. +-commutative N/A

      \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2} \cdot NaChar} \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot NdChar + \color{blue}{\frac{1}{2}} \cdot NaChar \]

   4. *-commutative N/A

      \[\leadsto NdChar \cdot \frac{1}{2} + \color{blue}{\frac{1}{2}} \cdot NaChar \]

   5. *-commutative N/A

      \[\leadsto NdChar \cdot \frac{1}{2} + NaChar \cdot \color{blue}{\frac{1}{2}} \]

   6. distribute-rgt-out N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

   7. lower-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NdChar + NaChar\right)} \]

   8. lower-+.f64 26.8

      \[\leadsto 0.5 \cdot \left(NdChar + \color{blue}{NaChar}\right) \]

6. Applied rewrites 26.8%

   \[\leadsto \color{blue}{0.5 \cdot \left(NdChar + NaChar\right)} \]
7. Add Preprocessing

Alternative 13: 22.4% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -950000:\\ \;\;\;\;0.5 \cdot NaChar\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-121}:\\ \;\;\;\;0.5 \cdot NdChar\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NaChar\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -950000.0)
   (* 0.5 NaChar)
   (if (<= NaChar 1.45e-121) (* 0.5 NdChar) (* 0.5 NaChar))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -950000.0) {
		tmp = 0.5 * NaChar;
	} else if (NaChar <= 1.45e-121) {
		tmp = 0.5 * NdChar;
	} else {
		tmp = 0.5 * NaChar;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-950000.0d0)) then
        tmp = 0.5d0 * nachar
    else if (nachar <= 1.45d-121) then
        tmp = 0.5d0 * ndchar
    else
        tmp = 0.5d0 * nachar
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -950000.0) {
		tmp = 0.5 * NaChar;
	} else if (NaChar <= 1.45e-121) {
		tmp = 0.5 * NdChar;
	} else {
		tmp = 0.5 * NaChar;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -950000.0:
		tmp = 0.5 * NaChar
	elif NaChar <= 1.45e-121:
		tmp = 0.5 * NdChar
	else:
		tmp = 0.5 * NaChar
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -950000.0)
		tmp = Float64(0.5 * NaChar);
	elseif (NaChar <= 1.45e-121)
		tmp = Float64(0.5 * NdChar);
	else
		tmp = Float64(0.5 * NaChar);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -950000.0)
		tmp = 0.5 * NaChar;
	elseif (NaChar <= 1.45e-121)
		tmp = 0.5 * NdChar;
	else
		tmp = 0.5 * NaChar;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -950000.0], N[(0.5 * NaChar), $MachinePrecision], If[LessEqual[NaChar, 1.45e-121], N[(0.5 * NdChar), $MachinePrecision], N[(0.5 * NaChar), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -9.5e5 or 1.45e-121 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]

   5. Taylor expanded in NdChar around 0

      \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
   6. Step-by-step derivation

      1. lower-*.f64 17.7

         \[\leadsto 0.5 \cdot NaChar \]

   7. Applied rewrites 17.7%

      \[\leadsto 0.5 \cdot \color{blue}{NaChar} \]

   if -9.5e5 < NaChar < 1.45e-121

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 26.8

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 26.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]

   5. Taylor expanded in NdChar around 0

      \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
   6. Step-by-step derivation

      1. lower-*.f64 17.7

         \[\leadsto 0.5 \cdot NaChar \]

   7. Applied rewrites 17.7%

      \[\leadsto 0.5 \cdot \color{blue}{NaChar} \]

   8. Taylor expanded in NdChar around inf

      \[\leadsto \frac{1}{2} \cdot \color{blue}{NdChar} \]
   9. Step-by-step derivation

      1. lower-*.f64 18.1

         \[\leadsto 0.5 \cdot NdChar \]

   10. Applied rewrites 18.1%

       \[\leadsto 0.5 \cdot \color{blue}{NdChar} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 17.7% accurate, 15.4× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot NaChar \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (* 0.5 NaChar))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return 0.5 * NaChar;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = 0.5d0 * nachar
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return 0.5 * NaChar;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return 0.5 * NaChar

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(0.5 * NaChar)
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.5 * NaChar;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(0.5 * NaChar), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

2. Taylor expanded in KbT around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
3. Step-by-step derivation

   1. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

   2. lower-*.f64 26.8

      \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

4. Applied rewrites 26.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]

5. Taylor expanded in NdChar around 0

   \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
6. Step-by-step derivation

   1. lower-*.f64 17.7

      \[\leadsto 0.5 \cdot NaChar \]

7. Applied rewrites 17.7%

   \[\leadsto 0.5 \cdot \color{blue}{NaChar} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025140 
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  :precision binary64
  (+ (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))