Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 29.2s

Alternatives: 27

Speedup: 1.0×

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

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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

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

FPCore

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

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - 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(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 56.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;EAccept \leq -1 \cdot 10^{-195}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.9 \cdot 10^{-165}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 6.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 6.1 \cdot 10^{-61}:\\ \;\;\;\;t_0 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;EAccept \leq 3.7 \cdot 10^{+113}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))))
   (if (<= EAccept -1e-195)
     (+
      (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
      (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= EAccept 1.9e-165)
       (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0)))
       (if (<= EAccept 6.8e-102)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
         (if (<= EAccept 6.1e-61)
           (+
            t_0
            (/
             NaChar
             (-
              (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
              (/ mu KbT))))
           (if (<= EAccept 3.7e+113)
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
              (/ NdChar (+ (/ mu KbT) 2.0)))
             (+
              (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
              (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))))

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 + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (EAccept <= -1e-195) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (EAccept <= 1.9e-165) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 6.8e-102) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (EAccept <= 6.1e-61) {
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (EAccept <= 3.7e+113) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 + (edonor + (vef - ec))) / kbt)))
    if (eaccept <= (-1d-195)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (eaccept <= 1.9d-165) then
        tmp = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    else if (eaccept <= 6.8d-102) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (eaccept <= 6.1d-61) then
        tmp = t_0 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (eaccept <= 3.7d+113) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    else
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / 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 t_0 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (EAccept <= -1e-195) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (EAccept <= 1.9e-165) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 6.8e-102) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (EAccept <= 6.1e-61) {
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (EAccept <= 3.7e+113) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	tmp = 0
	if EAccept <= -1e-195:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif EAccept <= 1.9e-165:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	elif EAccept <= 6.8e-102:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif EAccept <= 6.1e-61:
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif EAccept <= 3.7e+113:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	else:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (EAccept <= -1e-195)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (EAccept <= 1.9e-165)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (EAccept <= 6.8e-102)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (EAccept <= 6.1e-61)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (EAccept <= 3.7e+113)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	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 + (EDonor + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (EAccept <= -1e-195)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (EAccept <= 1.9e-165)
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	elseif (EAccept <= 6.8e-102)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (EAccept <= 6.1e-61)
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (EAccept <= 3.7e+113)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	else
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	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[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -1e-195], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.9e-165], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 6.8e-102], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 6.1e-61], N[(t$95$0 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.7e+113], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if EAccept < -1.0000000000000001e-195

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Ev around inf 68.3%

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

   5. Taylor expanded in EDonor around inf 55.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -1.0000000000000001e-195 < EAccept < 1.90000000000000009e-165

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 85.2%

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

   5. Taylor expanded in Vef around 0 64.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]

   if 1.90000000000000009e-165 < EAccept < 6.80000000000000026e-102

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 75.1%

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

   5. Taylor expanded in mu around inf 55.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{-1 \cdot \frac{mu}{KbT}}}} \]
   6. Step-by-step derivation

      1. associate-*r/ 38.7%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{\frac{-1 \cdot mu}{KbT}}}} \]

      2. mul-1-neg 38.7%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\color{blue}{-mu}}{KbT}}} \]

   7. Simplified 55.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{-mu}{KbT}}}} \]

   if 6.80000000000000026e-102 < EAccept < 6.1000000000000001e-61

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 80.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   if 6.1000000000000001e-61 < EAccept < 3.6999999999999998e113

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 75.5%

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

   5. Taylor expanded in mu around 0 65.9%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if 3.6999999999999998e113 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 91.3%

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

   5. Taylor expanded in EDonor around 0 82.3%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -1 \cdot 10^{-195}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.9 \cdot 10^{-165}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 6.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 6.1 \cdot 10^{-61}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;EAccept \leq 3.7 \cdot 10^{+113}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 3: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;EDonor \leq -70000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq -2.2 \cdot 10^{-170}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 2.1 \cdot 10^{+45}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= EDonor -70000000000000.0)
     t_1
     (if (<= EDonor -2.2e-170)
       (+
        (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
       (if (<= EDonor 2.1e+45)
         (+ t_0 (/ 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 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -70000000000000.0) {
		tmp = t_1;
	} else if (EDonor <= -2.2e-170) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else if (EDonor <= 2.1e+45) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (edonor <= (-70000000000000.0d0)) then
        tmp = t_1
    else if (edonor <= (-2.2d-170)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else if (edonor <= 2.1d+45) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((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 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -70000000000000.0) {
		tmp = t_1;
	} else if (EDonor <= -2.2e-170) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else if (EDonor <= 2.1e+45) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if EDonor <= -70000000000000.0:
		tmp = t_1
	elif EDonor <= -2.2e-170:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	elif EDonor <= 2.1e+45:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (EDonor <= -70000000000000.0)
		tmp = t_1;
	elseif (EDonor <= -2.2e-170)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	elseif (EDonor <= 2.1e+45)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(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 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (EDonor <= -70000000000000.0)
		tmp = t_1;
	elseif (EDonor <= -2.2e-170)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	elseif (EDonor <= 2.1e+45)
		tmp = t_0 + (NdChar / (1.0 + exp((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[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -70000000000000.0], t$95$1, If[LessEqual[EDonor, -2.2e-170], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 2.1e+45], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if EDonor < -7e13 or 2.09999999999999995e45 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EDonor around inf 85.1%

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

   if -7e13 < EDonor < -2.20000000000000015e-170

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 84.1%

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

   5. Taylor expanded in EDonor around 0 84.1%

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

   if -2.20000000000000015e-170 < EDonor < 2.09999999999999995e45

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 79.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -70000000000000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -2.2 \cdot 10^{-170}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 2.1 \cdot 10^{+45}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]

Alternative 4: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;EDonor \leq -37000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -7.5 \cdot 10^{-171}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (<= EDonor -37000.0)
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
      (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= EDonor -7.5e-171)
       (+
        (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
       (if (<= EDonor 2.1e+44)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))))))

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(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (EDonor <= -37000.0) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (EDonor <= -7.5e-171) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else if (EDonor <= 2.1e+44) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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(((vef + (eaccept + (ev - mu))) / kbt)))
    if (edonor <= (-37000.0d0)) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (edonor <= (-7.5d-171)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else if (edonor <= 2.1d+44) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / 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 t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (EDonor <= -37000.0) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (EDonor <= -7.5e-171) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else if (EDonor <= 2.1e+44) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	tmp = 0
	if EDonor <= -37000.0:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif EDonor <= -7.5e-171:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	elif EDonor <= 2.1e+44:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	tmp = 0.0
	if (EDonor <= -37000.0)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (EDonor <= -7.5e-171)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	elseif (EDonor <= 2.1e+44)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if (EDonor <= -37000.0)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (EDonor <= -7.5e-171)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	elseif (EDonor <= 2.1e+44)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	else
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	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[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -37000.0], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, -7.5e-171], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 2.1e+44], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if EDonor < -37000

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Ev around inf 79.8%

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

   if -37000 < EDonor < -7.50000000000000033e-171

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 86.5%

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

   5. Taylor expanded in EDonor around 0 86.5%

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

   if -7.50000000000000033e-171 < EDonor < 2.09999999999999987e44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 79.7%

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

   if 2.09999999999999987e44 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EDonor around inf 85.4%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -37000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -7.5 \cdot 10^{-171}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]

Alternative 5: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;EDonor \leq -2.55 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq -1.25 \cdot 10^{-169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= EDonor -2.55e+92)
     t_1
     (if (<= EDonor -1.25e-169)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
        (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))
       (if (<= EDonor 2.3e+44)
         (+ t_0 (/ 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 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -2.55e+92) {
		tmp = t_1;
	} else if (EDonor <= -1.25e-169) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((Vef / KbT))));
	} else if (EDonor <= 2.3e+44) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (edonor <= (-2.55d+92)) then
        tmp = t_1
    else if (edonor <= (-1.25d-169)) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp((vef / kbt))))
    else if (edonor <= 2.3d+44) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((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 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -2.55e+92) {
		tmp = t_1;
	} else if (EDonor <= -1.25e-169) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	} else if (EDonor <= 2.3e+44) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if EDonor <= -2.55e+92:
		tmp = t_1
	elif EDonor <= -1.25e-169:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.exp((Vef / KbT))))
	elif EDonor <= 2.3e+44:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (EDonor <= -2.55e+92)
		tmp = t_1;
	elseif (EDonor <= -1.25e-169)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	elseif (EDonor <= 2.3e+44)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(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 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (EDonor <= -2.55e+92)
		tmp = t_1;
	elseif (EDonor <= -1.25e-169)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((Vef / KbT))));
	elseif (EDonor <= 2.3e+44)
		tmp = t_0 + (NdChar / (1.0 + exp((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[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -2.55e+92], t$95$1, If[LessEqual[EDonor, -1.25e-169], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 2.3e+44], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if EDonor < -2.5500000000000001e92 or 2.30000000000000004e44 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EDonor around inf 88.7%

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

   if -2.5500000000000001e92 < EDonor < -1.2500000000000001e-169

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 78.4%

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

   if -1.2500000000000001e-169 < EDonor < 2.30000000000000004e44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 79.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -2.55 \cdot 10^{+92}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -1.25 \cdot 10^{-169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]

Alternative 6: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -2.2 \cdot 10^{+57} \lor \neg \left(Vef \leq 2 \cdot 10^{+78}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Vef -2.2e+57) (not (<= Vef 2e+78)))
   (+
    (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
    (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor 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 ((Vef <= -2.2e+57) || !(Vef <= 2e+78)) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 ((vef <= (-2.2d+57)) .or. (.not. (vef <= 2d+78))) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / 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 ((Vef <= -2.2e+57) || !(Vef <= 2e+78)) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Vef <= -2.2e+57) or not (Vef <= 2e+78):
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Vef <= -2.2e+57) || !(Vef <= 2e+78))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Vef <= -2.2e+57) || ~((Vef <= 2e+78)))
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Vef, -2.2e+57], N[Not[LessEqual[Vef, 2e+78]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -2.2000000000000001e57 or 2.00000000000000002e78 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 87.1%

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

   5. Taylor expanded in EDonor around 0 83.1%

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

   if -2.2000000000000001e57 < Vef < 2.00000000000000002e78

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EDonor around inf 76.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.2 \cdot 10^{+57} \lor \neg \left(Vef \leq 2 \cdot 10^{+78}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]

Alternative 7: 58.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{-183}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\frac{Vef}{KbT} + \left(2 - \frac{mu}{KbT}\right)\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}\\ \mathbf{elif}\;NaChar \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 2 \cdot 10^{+204}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ (/ mu KbT) 2.0)))))
   (if (<= NaChar -6.8e-183)
     t_0
     (if (<= NaChar 4.4e-51)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
        (/
         1.0
         (/
          (+ (+ (/ Vef KbT) (- 2.0 (/ mu KbT))) (+ (/ Ev KbT) (/ EAccept KbT)))
          NaChar)))
       (if (<= NaChar 5.5e+69)
         t_0
         (if (<= NaChar 2e+204)
           (+
            (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
            (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
           (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))

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(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	double tmp;
	if (NaChar <= -6.8e-183) {
		tmp = t_0;
	} else if (NaChar <= 4.4e-51) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	} else if (NaChar <= 5.5e+69) {
		tmp = t_0;
	} else if (NaChar <= 2e+204) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    if (nachar <= (-6.8d-183)) then
        tmp = t_0
    else if (nachar <= 4.4d-51) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (1.0d0 / ((((vef / kbt) + (2.0d0 - (mu / kbt))) + ((ev / kbt) + (eaccept / kbt))) / nachar))
    else if (nachar <= 5.5d+69) then
        tmp = t_0
    else if (nachar <= 2d+204) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = nachar / (1.0d0 + exp((eaccept / 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 t_0 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	double tmp;
	if (NaChar <= -6.8e-183) {
		tmp = t_0;
	} else if (NaChar <= 4.4e-51) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	} else if (NaChar <= 5.5e+69) {
		tmp = t_0;
	} else if (NaChar <= 2e+204) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	tmp = 0
	if NaChar <= -6.8e-183:
		tmp = t_0
	elif NaChar <= 4.4e-51:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar))
	elif NaChar <= 5.5e+69:
		tmp = t_0
	elif NaChar <= 2e+204:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)))
	tmp = 0.0
	if (NaChar <= -6.8e-183)
		tmp = t_0;
	elseif (NaChar <= 4.4e-51)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(1.0 / Float64(Float64(Float64(Float64(Vef / KbT) + Float64(2.0 - Float64(mu / KbT))) + Float64(Float64(Ev / KbT) + Float64(EAccept / KbT))) / NaChar)));
	elseif (NaChar <= 5.5e+69)
		tmp = t_0;
	elseif (NaChar <= 2e+204)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	tmp = 0.0;
	if (NaChar <= -6.8e-183)
		tmp = t_0;
	elseif (NaChar <= 4.4e-51)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	elseif (NaChar <= 5.5e+69)
		tmp = t_0;
	elseif (NaChar <= 2e+204)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.8e-183], t$95$0, If[LessEqual[NaChar, 4.4e-51], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(2.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 5.5e+69], t$95$0, If[LessEqual[NaChar, 2e+204], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -6.80000000000000029e-183 or 4.4e-51 < NaChar < 5.50000000000000002e69

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 74.5%

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

   5. Taylor expanded in mu around 0 59.1%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -6.80000000000000029e-183 < NaChar < 4.4e-51

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 76.4%

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

      1. clear-num 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}{NaChar}}} \]

      2. inv-pow 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{{\left(\frac{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}{NaChar}\right)}^{-1}} \]

      3. associate--l+ 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + {\left(\frac{\color{blue}{2 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{mu}{KbT}\right)}}{NaChar}\right)}^{-1} \]

      4. associate-+r+ 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + {\left(\frac{2 + \left(\color{blue}{\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)} - \frac{mu}{KbT}\right)}{NaChar}\right)}^{-1} \]

   6. Applied egg-rr 77.0%

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

      1. unpow-1 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{2 + \left(\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right) - \frac{mu}{KbT}\right)}{NaChar}}} \]

      2. sub-neg 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \color{blue}{\left(\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right) + \left(-\frac{mu}{KbT}\right)\right)}}{NaChar}} \]

      3. +-commutative 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \color{blue}{\left(\left(-\frac{mu}{KbT}\right) + \left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)\right)}}{NaChar}} \]

      4. associate-+r+ 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\color{blue}{\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)}}{NaChar}} \]

      5. +-commutative 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \color{blue}{\left(\frac{Vef}{KbT} + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)\right)}}{NaChar}} \]

      6. associate-+r+ 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\color{blue}{\left(\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \frac{Vef}{KbT}\right) + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)}}{NaChar}} \]

      7. unsub-neg 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\color{blue}{\left(2 - \frac{mu}{KbT}\right)} + \frac{Vef}{KbT}\right) + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)}{NaChar}} \]

      8. +-commutative 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\left(2 - \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right) + \color{blue}{\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}}{NaChar}} \]

   8. Simplified 77.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{\left(\left(2 - \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}} \]

   if 5.50000000000000002e69 < NaChar < 1.99999999999999998e204

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Ev around inf 69.7%

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

   5. Taylor expanded in EDonor around inf 65.9%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if 1.99999999999999998e204 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 65.8%

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

   5. Taylor expanded in EAccept around inf 49.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 45.9%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{-183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\frac{Vef}{KbT} + \left(2 - \frac{mu}{KbT}\right)\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}\\ \mathbf{elif}\;NaChar \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 2 \cdot 10^{+204}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 8: 57.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 5.9 \cdot 10^{+40}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\frac{Vef}{KbT} + \left(2 - \frac{mu}{KbT}\right)\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}\\ \mathbf{elif}\;NaChar \leq 4.9 \cdot 10^{+76}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.35 \cdot 10^{+203}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -8.5e-183)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar (+ (/ mu KbT) 2.0)))
   (if (<= NaChar 5.9e+40)
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
      (/
       1.0
       (/
        (+ (+ (/ Vef KbT) (- 2.0 (/ mu KbT))) (+ (/ Ev KbT) (/ EAccept KbT)))
        NaChar)))
     (if (<= NaChar 4.9e+76)
       (+
        (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
        (/
         NdChar
         (- (+ (+ (/ EDonor KbT) 2.0) (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
       (if (<= NaChar 1.35e+203)
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))
         (/ NaChar (+ 1.0 (exp (/ EAccept 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 (NaChar <= -8.5e-183) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else if (NaChar <= 5.9e+40) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	} else if (NaChar <= 4.9e+76) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else if (NaChar <= 1.35e+203) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Vef / KbT))));
	} else {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 <= (-8.5d-183)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    else if (nachar <= 5.9d+40) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (1.0d0 / ((((vef / kbt) + (2.0d0 - (mu / kbt))) + ((ev / kbt) + (eaccept / kbt))) / nachar))
    else if (nachar <= 4.9d+76) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / ((((edonor / kbt) + 2.0d0) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))
    else if (nachar <= 1.35d+203) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((vef / kbt))))
    else
        tmp = nachar / (1.0d0 + exp((eaccept / 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 (NaChar <= -8.5e-183) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else if (NaChar <= 5.9e+40) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	} else if (NaChar <= 4.9e+76) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else if (NaChar <= 1.35e+203) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	} else {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -8.5e-183:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	elif NaChar <= 5.9e+40:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar))
	elif NaChar <= 4.9e+76:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))
	elif NaChar <= 1.35e+203:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Vef / KbT))))
	else:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -8.5e-183)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	elseif (NaChar <= 5.9e+40)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(1.0 / Float64(Float64(Float64(Float64(Vef / KbT) + Float64(2.0 - Float64(mu / KbT))) + Float64(Float64(Ev / KbT) + Float64(EAccept / KbT))) / NaChar)));
	elseif (NaChar <= 4.9e+76)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(Float64(Float64(Float64(EDonor / KbT) + 2.0) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT))));
	elseif (NaChar <= 1.35e+203)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -8.5e-183)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	elseif (NaChar <= 5.9e+40)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	elseif (NaChar <= 4.9e+76)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	elseif (NaChar <= 1.35e+203)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Vef / KbT))));
	else
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -8.5e-183], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 5.9e+40], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(2.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.9e+76], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.35e+203], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -8.49999999999999973e-183

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 73.0%

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

   5. Taylor expanded in mu around 0 57.3%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -8.49999999999999973e-183 < NaChar < 5.8999999999999999e40

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 73.9%

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

      1. clear-num 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}{NaChar}}} \]

      2. inv-pow 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{{\left(\frac{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}{NaChar}\right)}^{-1}} \]

      3. associate--l+ 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + {\left(\frac{\color{blue}{2 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{mu}{KbT}\right)}}{NaChar}\right)}^{-1} \]

      4. associate-+r+ 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + {\left(\frac{2 + \left(\color{blue}{\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)} - \frac{mu}{KbT}\right)}{NaChar}\right)}^{-1} \]

   6. Applied egg-rr 74.4%

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

      1. unpow-1 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{2 + \left(\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right) - \frac{mu}{KbT}\right)}{NaChar}}} \]

      2. sub-neg 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \color{blue}{\left(\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right) + \left(-\frac{mu}{KbT}\right)\right)}}{NaChar}} \]

      3. +-commutative 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \color{blue}{\left(\left(-\frac{mu}{KbT}\right) + \left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)\right)}}{NaChar}} \]

      4. associate-+r+ 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\color{blue}{\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)}}{NaChar}} \]

      5. +-commutative 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \color{blue}{\left(\frac{Vef}{KbT} + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)\right)}}{NaChar}} \]

      6. associate-+r+ 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\color{blue}{\left(\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \frac{Vef}{KbT}\right) + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)}}{NaChar}} \]

      7. unsub-neg 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\color{blue}{\left(2 - \frac{mu}{KbT}\right)} + \frac{Vef}{KbT}\right) + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)}{NaChar}} \]

      8. +-commutative 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\left(2 - \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right) + \color{blue}{\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}}{NaChar}} \]

   8. Simplified 74.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{\left(\left(2 - \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}} \]

   if 5.8999999999999999e40 < NaChar < 4.90000000000000026e76

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Ev around inf 64.4%

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

   5. Taylor expanded in KbT around inf 61.5%

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

      1. associate-+r+ 22.0%

         \[\leadsto \frac{NdChar}{\color{blue}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)} - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   7. Simplified 61.5%

      \[\leadsto \frac{NdChar}{\color{blue}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if 4.90000000000000026e76 < NaChar < 1.35e203

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 78.4%

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

   5. Taylor expanded in EDonor around inf 70.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]

   if 1.35e203 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 65.8%

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

   5. Taylor expanded in EAccept around inf 49.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 45.9%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 5.9 \cdot 10^{+40}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\frac{Vef}{KbT} + \left(2 - \frac{mu}{KbT}\right)\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}\\ \mathbf{elif}\;NaChar \leq 4.9 \cdot 10^{+76}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.35 \cdot 10^{+203}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 9: 57.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.35 \cdot 10^{-68}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\frac{Vef}{KbT} + \left(2 - \frac{mu}{KbT}\right)\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}\\ \mathbf{elif}\;NaChar \leq 4.3 \cdot 10^{+46}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_0\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{+203}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
   (if (<= NaChar -8.5e-183)
     (+
      (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
      (/ NdChar (+ (/ mu KbT) 2.0)))
     (if (<= NaChar 1.35e-68)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
        (/
         1.0
         (/
          (+ (+ (/ Vef KbT) (- 2.0 (/ mu KbT))) (+ (/ Ev KbT) (/ EAccept KbT)))
          NaChar)))
       (if (<= NaChar 4.3e+46)
         (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_0)
         (if (<= NaChar 4.1e+203)
           (+
            (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
            (/ NaChar (+ 1.0 (exp (/ Ev 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 / KbT)));
	double tmp;
	if (NaChar <= -8.5e-183) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else if (NaChar <= 1.35e-68) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	} else if (NaChar <= 4.3e+46) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_0;
	} else if (NaChar <= 4.1e+203) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 / kbt)))
    if (nachar <= (-8.5d-183)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    else if (nachar <= 1.35d-68) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (1.0d0 / ((((vef / kbt) + (2.0d0 - (mu / kbt))) + ((ev / kbt) + (eaccept / kbt))) / nachar))
    else if (nachar <= 4.3d+46) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_0
    else if (nachar <= 4.1d+203) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / 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 / KbT)));
	double tmp;
	if (NaChar <= -8.5e-183) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else if (NaChar <= 1.35e-68) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	} else if (NaChar <= 4.3e+46) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_0;
	} else if (NaChar <= 4.1e+203) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / 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 / KbT)))
	tmp = 0
	if NaChar <= -8.5e-183:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	elif NaChar <= 1.35e-68:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar))
	elif NaChar <= 4.3e+46:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_0
	elif NaChar <= 4.1e+203:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / 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(EAccept / KbT))))
	tmp = 0.0
	if (NaChar <= -8.5e-183)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	elseif (NaChar <= 1.35e-68)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(1.0 / Float64(Float64(Float64(Float64(Vef / KbT) + Float64(2.0 - Float64(mu / KbT))) + Float64(Float64(Ev / KbT) + Float64(EAccept / KbT))) / NaChar)));
	elseif (NaChar <= 4.3e+46)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_0);
	elseif (NaChar <= 4.1e+203)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / 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 / KbT)));
	tmp = 0.0;
	if (NaChar <= -8.5e-183)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	elseif (NaChar <= 1.35e-68)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((((Vef / KbT) + (2.0 - (mu / KbT))) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	elseif (NaChar <= 4.3e+46)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_0;
	elseif (NaChar <= 4.1e+203)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / 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[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -8.5e-183], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.35e-68], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(2.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.3e+46], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[NaChar, 4.1e+203], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -8.49999999999999973e-183

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 73.0%

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

   5. Taylor expanded in mu around 0 57.3%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -8.49999999999999973e-183 < NaChar < 1.3500000000000001e-68

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 76.3%

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

      1. clear-num 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}{NaChar}}} \]

      2. inv-pow 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{{\left(\frac{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}{NaChar}\right)}^{-1}} \]

      3. associate--l+ 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + {\left(\frac{\color{blue}{2 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{mu}{KbT}\right)}}{NaChar}\right)}^{-1} \]

      4. associate-+r+ 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + {\left(\frac{2 + \left(\color{blue}{\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)} - \frac{mu}{KbT}\right)}{NaChar}\right)}^{-1} \]

   6. Applied egg-rr 77.0%

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

      1. unpow-1 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{2 + \left(\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right) - \frac{mu}{KbT}\right)}{NaChar}}} \]

      2. sub-neg 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \color{blue}{\left(\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right) + \left(-\frac{mu}{KbT}\right)\right)}}{NaChar}} \]

      3. +-commutative 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \color{blue}{\left(\left(-\frac{mu}{KbT}\right) + \left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)\right)}}{NaChar}} \]

      4. associate-+r+ 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\color{blue}{\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)}}{NaChar}} \]

      5. +-commutative 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \color{blue}{\left(\frac{Vef}{KbT} + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)\right)}}{NaChar}} \]

      6. associate-+r+ 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\color{blue}{\left(\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \frac{Vef}{KbT}\right) + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)}}{NaChar}} \]

      7. unsub-neg 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\color{blue}{\left(2 - \frac{mu}{KbT}\right)} + \frac{Vef}{KbT}\right) + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)}{NaChar}} \]

      8. +-commutative 77.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\left(2 - \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right) + \color{blue}{\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}}{NaChar}} \]

   8. Simplified 77.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{\left(\left(2 - \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}} \]

   if 1.3500000000000001e-68 < NaChar < 4.30000000000000005e46

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 87.9%

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

   5. Taylor expanded in EAccept around inf 72.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   if 4.30000000000000005e46 < NaChar < 4.10000000000000016e203

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Ev around inf 64.7%

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

   5. Taylor expanded in EDonor around inf 58.7%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if 4.10000000000000016e203 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 65.8%

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

   5. Taylor expanded in EAccept around inf 49.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 45.9%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.35 \cdot 10^{-68}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\frac{Vef}{KbT} + \left(2 - \frac{mu}{KbT}\right)\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}\\ \mathbf{elif}\;NaChar \leq 4.3 \cdot 10^{+46}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{+203}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 10: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;EAccept \leq -1.05 \cdot 10^{-196}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 8 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))))
   (if (<= EAccept -1.05e-196)
     (+
      (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
      (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= EAccept 8e+86)
       (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) t_0)
       (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))))))

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 + Vef) - Ec) / KbT)));
	double tmp;
	if (EAccept <= -1.05e-196) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (EAccept <= 8e+86) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + t_0;
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 + vef) - ec) / kbt)))
    if (eaccept <= (-1.05d-196)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (eaccept <= 8d+86) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + t_0
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / 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 t_0 = NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (EAccept <= -1.05e-196) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (EAccept <= 8e+86) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + t_0;
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))
	tmp = 0
	if EAccept <= -1.05e-196:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif EAccept <= 8e+86:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + t_0
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	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(mu + Vef) - Ec) / KbT))))
	tmp = 0.0
	if (EAccept <= -1.05e-196)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (EAccept <= 8e+86)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + t_0);
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	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 + Vef) - Ec) / KbT)));
	tmp = 0.0;
	if (EAccept <= -1.05e-196)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (EAccept <= 8e+86)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + t_0;
	else
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	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[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -1.05e-196], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 8e+86], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < -1.04999999999999994e-196

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Ev around inf 68.3%

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

   5. Taylor expanded in EDonor around inf 55.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -1.04999999999999994e-196 < EAccept < 8.0000000000000001e86

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 79.9%

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

   5. Taylor expanded in EDonor around 0 74.0%

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

   if 8.0000000000000001e86 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 89.4%

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

   5. Taylor expanded in EDonor around 0 80.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -1.05 \cdot 10^{-196}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 8 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 11: 57.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -7.5 \cdot 10^{-144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{-145}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.82 \cdot 10^{+204}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -7.5e-144)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar (+ (/ mu KbT) 2.0)))
   (if (<= NaChar 4.1e-145)
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
      (/ NaChar (+ (/ Vef KbT) 2.0)))
     (if (<= NaChar 1.82e+204)
       (+
        (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
       (/ NaChar (+ 1.0 (exp (/ EAccept 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 (NaChar <= -7.5e-144) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else if (NaChar <= 4.1e-145) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 1.82e+204) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	} else {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 <= (-7.5d-144)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    else if (nachar <= 4.1d-145) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else if (nachar <= 1.82d+204) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    else
        tmp = nachar / (1.0d0 + exp((eaccept / 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 (NaChar <= -7.5e-144) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else if (NaChar <= 4.1e-145) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 1.82e+204) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	} else {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -7.5e-144:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	elif NaChar <= 4.1e-145:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	elif NaChar <= 1.82e+204:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	else:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -7.5e-144)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	elseif (NaChar <= 4.1e-145)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NaChar <= 1.82e+204)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -7.5e-144)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	elseif (NaChar <= 4.1e-145)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	elseif (NaChar <= 1.82e+204)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	else
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -7.5e-144], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.1e-145], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.82e+204], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -7.49999999999999963e-144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 74.7%

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

   5. Taylor expanded in mu around 0 57.8%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -7.49999999999999963e-144 < NaChar < 4.0999999999999997e-145

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 80.8%

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

   5. Taylor expanded in Vef around 0 77.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]

   if 4.0999999999999997e-145 < NaChar < 1.82000000000000002e204

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Ev around inf 72.7%

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

   5. Taylor expanded in Ec around inf 61.7%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-1 \cdot \frac{Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]
   6. Step-by-step derivation

      1. associate-*r/ 44.7%

         \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-1 \cdot Ec}{KbT}}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

      2. mul-1-neg 44.7%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{-Ec}}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   7. Simplified 61.7%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if 1.82000000000000002e204 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 65.8%

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

   5. Taylor expanded in EAccept around inf 49.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 45.9%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7.5 \cdot 10^{-144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{-145}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.82 \cdot 10^{+204}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 12: 57.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \frac{mu}{KbT}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -8 \cdot 10^{-183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 2.85 \cdot 10^{+38}:\\ \;\;\;\;t_1 + \frac{1}{\frac{\left(\frac{Vef}{KbT} + t_0\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}\\ \mathbf{elif}\;NaChar \leq 2.95 \cdot 10^{+75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{+168}:\\ \;\;\;\;t_1 + \frac{NaChar}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (- 2.0 (/ mu KbT)))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))))
   (if (<= NaChar -8e-183)
     (+
      (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
      (/ NdChar (+ (/ mu KbT) 2.0)))
     (if (<= NaChar 2.85e+38)
       (+
        t_1
        (/
         1.0
         (/ (+ (+ (/ Vef KbT) t_0) (+ (/ Ev KbT) (/ EAccept KbT))) NaChar)))
       (if (<= NaChar 2.95e+75)
         (+
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
          (/
           NdChar
           (-
            (+ (+ (/ EDonor KbT) 2.0) (+ (/ Vef KbT) (/ mu KbT)))
            (/ Ec KbT))))
         (if (<= NaChar 1.9e+168)
           (+ t_1 (/ NaChar t_0))
           (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 2.0 - (mu / KbT);
	double t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (NaChar <= -8e-183) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else if (NaChar <= 2.85e+38) {
		tmp = t_1 + (1.0 / ((((Vef / KbT) + t_0) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	} else if (NaChar <= 2.95e+75) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else if (NaChar <= 1.9e+168) {
		tmp = t_1 + (NaChar / t_0);
	} else {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 = 2.0d0 - (mu / kbt)
    t_1 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    if (nachar <= (-8d-183)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    else if (nachar <= 2.85d+38) then
        tmp = t_1 + (1.0d0 / ((((vef / kbt) + t_0) + ((ev / kbt) + (eaccept / kbt))) / nachar))
    else if (nachar <= 2.95d+75) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / ((((edonor / kbt) + 2.0d0) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))
    else if (nachar <= 1.9d+168) then
        tmp = t_1 + (nachar / t_0)
    else
        tmp = nachar / (1.0d0 + exp((eaccept / 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 t_0 = 2.0 - (mu / KbT);
	double t_1 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (NaChar <= -8e-183) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	} else if (NaChar <= 2.85e+38) {
		tmp = t_1 + (1.0 / ((((Vef / KbT) + t_0) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	} else if (NaChar <= 2.95e+75) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else if (NaChar <= 1.9e+168) {
		tmp = t_1 + (NaChar / t_0);
	} else {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 2.0 - (mu / KbT)
	t_1 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	tmp = 0
	if NaChar <= -8e-183:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	elif NaChar <= 2.85e+38:
		tmp = t_1 + (1.0 / ((((Vef / KbT) + t_0) + ((Ev / KbT) + (EAccept / KbT))) / NaChar))
	elif NaChar <= 2.95e+75:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))
	elif NaChar <= 1.9e+168:
		tmp = t_1 + (NaChar / t_0)
	else:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(2.0 - Float64(mu / KbT))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NaChar <= -8e-183)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	elseif (NaChar <= 2.85e+38)
		tmp = Float64(t_1 + Float64(1.0 / Float64(Float64(Float64(Float64(Vef / KbT) + t_0) + Float64(Float64(Ev / KbT) + Float64(EAccept / KbT))) / NaChar)));
	elseif (NaChar <= 2.95e+75)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(Float64(Float64(Float64(EDonor / KbT) + 2.0) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT))));
	elseif (NaChar <= 1.9e+168)
		tmp = Float64(t_1 + Float64(NaChar / t_0));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 2.0 - (mu / KbT);
	t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -8e-183)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	elseif (NaChar <= 2.85e+38)
		tmp = t_1 + (1.0 / ((((Vef / KbT) + t_0) + ((Ev / KbT) + (EAccept / KbT))) / NaChar));
	elseif (NaChar <= 2.95e+75)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	elseif (NaChar <= 1.9e+168)
		tmp = t_1 + (NaChar / t_0);
	else
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(2.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -8e-183], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.85e+38], N[(t$95$1 + N[(1.0 / N[(N[(N[(N[(Vef / KbT), $MachinePrecision] + t$95$0), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.95e+75], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.9e+168], N[(t$95$1 + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -8.00000000000000004e-183

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 73.0%

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

   5. Taylor expanded in mu around 0 57.3%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -8.00000000000000004e-183 < NaChar < 2.8499999999999999e38

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 73.9%

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

      1. clear-num 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}{NaChar}}} \]

      2. inv-pow 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{{\left(\frac{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}{NaChar}\right)}^{-1}} \]

      3. associate--l+ 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + {\left(\frac{\color{blue}{2 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{mu}{KbT}\right)}}{NaChar}\right)}^{-1} \]

      4. associate-+r+ 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + {\left(\frac{2 + \left(\color{blue}{\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)} - \frac{mu}{KbT}\right)}{NaChar}\right)}^{-1} \]

   6. Applied egg-rr 74.4%

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

      1. unpow-1 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{2 + \left(\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right) - \frac{mu}{KbT}\right)}{NaChar}}} \]

      2. sub-neg 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \color{blue}{\left(\left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right) + \left(-\frac{mu}{KbT}\right)\right)}}{NaChar}} \]

      3. +-commutative 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \color{blue}{\left(\left(-\frac{mu}{KbT}\right) + \left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)\right)}}{NaChar}} \]

      4. associate-+r+ 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\color{blue}{\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \left(\left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right) + \frac{Vef}{KbT}\right)}}{NaChar}} \]

      5. +-commutative 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \color{blue}{\left(\frac{Vef}{KbT} + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)\right)}}{NaChar}} \]

      6. associate-+r+ 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\color{blue}{\left(\left(2 + \left(-\frac{mu}{KbT}\right)\right) + \frac{Vef}{KbT}\right) + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)}}{NaChar}} \]

      7. unsub-neg 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\color{blue}{\left(2 - \frac{mu}{KbT}\right)} + \frac{Vef}{KbT}\right) + \left(\frac{EAccept}{KbT} + \frac{Ev}{KbT}\right)}{NaChar}} \]

      8. +-commutative 74.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\left(2 - \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right) + \color{blue}{\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}}{NaChar}} \]

   8. Simplified 74.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{\frac{\left(\left(2 - \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}} \]

   if 2.8499999999999999e38 < NaChar < 2.94999999999999991e75

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Ev around inf 64.4%

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

   5. Taylor expanded in KbT around inf 61.5%

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

      1. associate-+r+ 22.0%

         \[\leadsto \frac{NdChar}{\color{blue}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)} - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   7. Simplified 61.5%

      \[\leadsto \frac{NdChar}{\color{blue}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if 2.94999999999999991e75 < NaChar < 1.9000000000000001e168

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 68.5%

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

      1. associate-*r/ 46.7%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{\frac{-1 \cdot mu}{KbT}}}} \]

      2. mul-1-neg 46.7%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\color{blue}{-mu}}{KbT}}} \]

   6. Simplified 68.5%

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

   7. Taylor expanded in mu around 0 68.6%

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

      1. mul-1-neg 40.3%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{2 + \color{blue}{\left(-\frac{mu}{KbT}\right)}} \]

      2. unsub-neg 40.3%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{\color{blue}{2 - \frac{mu}{KbT}}} \]

   9. Simplified 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 - \frac{mu}{KbT}}} \]

   if 1.9000000000000001e168 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 74.0%

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

   5. Taylor expanded in EAccept around inf 54.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 51.7%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8 \cdot 10^{-183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 2.85 \cdot 10^{+38}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{\left(\frac{Vef}{KbT} + \left(2 - \frac{mu}{KbT}\right)\right) + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)}{NaChar}}\\ \mathbf{elif}\;NaChar \leq 2.95 \cdot 10^{+75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{+168}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 13: 55.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.4 \cdot 10^{-153}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 3.5 \cdot 10^{-14} \lor \neg \left(NaChar \leq 3.8 \cdot 10^{+80}\right) \land NaChar \leq 6.8 \cdot 10^{+168}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -2.4e-153)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (* NdChar 0.5))
   (if (or (<= NaChar 3.5e-14)
           (and (not (<= NaChar 3.8e+80)) (<= NaChar 6.8e+168)))
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
      (/ NaChar (+ (/ Vef KbT) 2.0)))
     (/ NaChar (+ 1.0 (exp (/ EAccept 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 (NaChar <= -2.4e-153) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else if ((NaChar <= 3.5e-14) || (!(NaChar <= 3.8e+80) && (NaChar <= 6.8e+168))) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 <= (-2.4d-153)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    else if ((nachar <= 3.5d-14) .or. (.not. (nachar <= 3.8d+80)) .and. (nachar <= 6.8d+168)) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else
        tmp = nachar / (1.0d0 + exp((eaccept / 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 (NaChar <= -2.4e-153) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else if ((NaChar <= 3.5e-14) || (!(NaChar <= 3.8e+80) && (NaChar <= 6.8e+168))) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -2.4e-153:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	elif (NaChar <= 3.5e-14) or (not (NaChar <= 3.8e+80) and (NaChar <= 6.8e+168)):
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	else:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -2.4e-153)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5));
	elseif ((NaChar <= 3.5e-14) || (!(NaChar <= 3.8e+80) && (NaChar <= 6.8e+168)))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -2.4e-153)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	elseif ((NaChar <= 3.5e-14) || (~((NaChar <= 3.8e+80)) && (NaChar <= 6.8e+168)))
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	else
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -2.4e-153], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, 3.5e-14], And[N[Not[LessEqual[NaChar, 3.8e+80]], $MachinePrecision], LessEqual[NaChar, 6.8e+168]]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2.4000000000000002e-153

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 56.6%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   5. Step-by-step derivation

      1. *-commutative 56.6%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Simplified 56.6%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -2.4000000000000002e-153 < NaChar < 3.5000000000000002e-14 or 3.79999999999999997e80 < NaChar < 6.80000000000000005e168

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 81.4%

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

   5. Taylor expanded in Vef around 0 73.1%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]

   if 3.5000000000000002e-14 < NaChar < 3.79999999999999997e80 or 6.80000000000000005e168 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 73.3%

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

   5. Taylor expanded in EAccept around inf 52.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 55.3%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.4 \cdot 10^{-153}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 3.5 \cdot 10^{-14} \lor \neg \left(NaChar \leq 3.8 \cdot 10^{+80}\right) \land NaChar \leq 6.8 \cdot 10^{+168}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 14: 55.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.65 \cdot 10^{-152}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{+72} \lor \neg \left(NaChar \leq 6.8 \cdot 10^{+167}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{2 - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))))
   (if (<= NaChar -1.65e-152)
     (+
      (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
      (* NdChar 0.5))
     (if (<= NaChar 1.4e-14)
       (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0)))
       (if (or (<= NaChar 1.7e+72) (not (<= NaChar 6.8e+167)))
         (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
         (+ t_0 (/ NaChar (- 2.0 (/ mu KbT)))))))))

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 + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (NaChar <= -1.65e-152) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else if (NaChar <= 1.4e-14) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if ((NaChar <= 1.7e+72) || !(NaChar <= 6.8e+167)) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else {
		tmp = t_0 + (NaChar / (2.0 - (mu / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 + (edonor + (vef - ec))) / kbt)))
    if (nachar <= (-1.65d-152)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    else if (nachar <= 1.4d-14) then
        tmp = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    else if ((nachar <= 1.7d+72) .or. (.not. (nachar <= 6.8d+167))) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else
        tmp = t_0 + (nachar / (2.0d0 - (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 t_0 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (NaChar <= -1.65e-152) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else if (NaChar <= 1.4e-14) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if ((NaChar <= 1.7e+72) || !(NaChar <= 6.8e+167)) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else {
		tmp = t_0 + (NaChar / (2.0 - (mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	tmp = 0
	if NaChar <= -1.65e-152:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	elif NaChar <= 1.4e-14:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	elif (NaChar <= 1.7e+72) or not (NaChar <= 6.8e+167):
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	else:
		tmp = t_0 + (NaChar / (2.0 - (mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.65e-152)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5));
	elseif (NaChar <= 1.4e-14)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif ((NaChar <= 1.7e+72) || !(NaChar <= 6.8e+167))
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(2.0 - Float64(mu / KbT))));
	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 + (EDonor + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.65e-152)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	elseif (NaChar <= 1.4e-14)
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	elseif ((NaChar <= 1.7e+72) || ~((NaChar <= 6.8e+167)))
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	else
		tmp = t_0 + (NaChar / (2.0 - (mu / KbT)));
	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[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.65e-152], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.4e-14], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, 1.7e+72], N[Not[LessEqual[NaChar, 6.8e+167]], $MachinePrecision]], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(2.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.64999999999999999e-152

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 56.6%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   5. Step-by-step derivation

      1. *-commutative 56.6%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Simplified 56.6%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -1.64999999999999999e-152 < NaChar < 1.4e-14

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 81.4%

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

   5. Taylor expanded in Vef around 0 74.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]

   if 1.4e-14 < NaChar < 1.6999999999999999e72 or 6.8000000000000001e167 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 73.3%

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

   5. Taylor expanded in EAccept around inf 52.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 55.3%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]

   if 1.6999999999999999e72 < NaChar < 6.8000000000000001e167

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 68.5%

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

      1. associate-*r/ 46.7%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{\frac{-1 \cdot mu}{KbT}}}} \]

      2. mul-1-neg 46.7%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\color{blue}{-mu}}{KbT}}} \]

   6. Simplified 68.5%

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

   7. Taylor expanded in mu around 0 68.6%

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

      1. mul-1-neg 40.3%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{2 + \color{blue}{\left(-\frac{mu}{KbT}\right)}} \]

      2. unsub-neg 40.3%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{\color{blue}{2 - \frac{mu}{KbT}}} \]

   9. Simplified 68.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.65 \cdot 10^{-152}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{+72} \lor \neg \left(NaChar \leq 6.8 \cdot 10^{+167}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 - \frac{mu}{KbT}}\\ \end{array} \]

Alternative 15: 59.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ t_1 := \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{if}\;NaChar \leq -7.5 \cdot 10^{-144}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-57}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + t_1\\ \mathbf{elif}\;NaChar \leq 2.4 \cdot 10^{+162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{+170}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ (/ mu KbT) 2.0))))
        (t_1 (/ NaChar (+ (/ Vef KbT) 2.0))))
   (if (<= NaChar -7.5e-144)
     t_0
     (if (<= NaChar 1.45e-57)
       (+ (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))) t_1)
       (if (<= NaChar 2.4e+162)
         t_0
         (if (<= NaChar 1.3e+170)
           (+ t_1 (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
           (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))

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(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	double t_1 = NaChar / ((Vef / KbT) + 2.0);
	double tmp;
	if (NaChar <= -7.5e-144) {
		tmp = t_0;
	} else if (NaChar <= 1.45e-57) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + t_1;
	} else if (NaChar <= 2.4e+162) {
		tmp = t_0;
	} else if (NaChar <= 1.3e+170) {
		tmp = t_1 + (NdChar / (1.0 + exp((-Ec / KbT))));
	} else {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    t_1 = nachar / ((vef / kbt) + 2.0d0)
    if (nachar <= (-7.5d-144)) then
        tmp = t_0
    else if (nachar <= 1.45d-57) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + t_1
    else if (nachar <= 2.4d+162) then
        tmp = t_0
    else if (nachar <= 1.3d+170) then
        tmp = t_1 + (ndchar / (1.0d0 + exp((-ec / kbt))))
    else
        tmp = nachar / (1.0d0 + exp((eaccept / 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 t_0 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	double t_1 = NaChar / ((Vef / KbT) + 2.0);
	double tmp;
	if (NaChar <= -7.5e-144) {
		tmp = t_0;
	} else if (NaChar <= 1.45e-57) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + t_1;
	} else if (NaChar <= 2.4e+162) {
		tmp = t_0;
	} else if (NaChar <= 1.3e+170) {
		tmp = t_1 + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	} else {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	t_1 = NaChar / ((Vef / KbT) + 2.0)
	tmp = 0
	if NaChar <= -7.5e-144:
		tmp = t_0
	elif NaChar <= 1.45e-57:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + t_1
	elif NaChar <= 2.4e+162:
		tmp = t_0
	elif NaChar <= 1.3e+170:
		tmp = t_1 + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	else:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)))
	t_1 = Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0))
	tmp = 0.0
	if (NaChar <= -7.5e-144)
		tmp = t_0;
	elseif (NaChar <= 1.45e-57)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + t_1);
	elseif (NaChar <= 2.4e+162)
		tmp = t_0;
	elseif (NaChar <= 1.3e+170)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	t_1 = NaChar / ((Vef / KbT) + 2.0);
	tmp = 0.0;
	if (NaChar <= -7.5e-144)
		tmp = t_0;
	elseif (NaChar <= 1.45e-57)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + t_1;
	elseif (NaChar <= 2.4e+162)
		tmp = t_0;
	elseif (NaChar <= 1.3e+170)
		tmp = t_1 + (NdChar / (1.0 + exp((-Ec / KbT))));
	else
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -7.5e-144], t$95$0, If[LessEqual[NaChar, 1.45e-57], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[NaChar, 2.4e+162], t$95$0, If[LessEqual[NaChar, 1.3e+170], N[(t$95$1 + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -7.49999999999999963e-144 or 1.45000000000000013e-57 < NaChar < 2.40000000000000009e162

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 76.4%

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

   5. Taylor expanded in mu around 0 58.9%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -7.49999999999999963e-144 < NaChar < 1.45000000000000013e-57

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 81.9%

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

   5. Taylor expanded in Vef around 0 75.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]

   if 2.40000000000000009e162 < NaChar < 1.2999999999999999e170

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 100.0%

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

   5. Taylor expanded in Vef around 0 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]

   6. Taylor expanded in Ec around inf 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-1 \cdot \frac{Ec}{KbT}}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]
   7. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-1 \cdot Ec}{KbT}}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

      2. mul-1-neg 100.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{-Ec}}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   8. Simplified 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   if 1.2999999999999999e170 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 74.0%

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

   5. Taylor expanded in EAccept around inf 54.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 51.7%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7.5 \cdot 10^{-144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-57}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 2.4 \cdot 10^{+162}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 16: 54.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -4 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 6.2 \cdot 10^{-275}:\\ \;\;\;\;t_0 + \frac{KbT \cdot NaChar}{EAccept}\\ \mathbf{elif}\;NaChar \leq 1.35 \cdot 10^{-57}:\\ \;\;\;\;t_0 + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (* NdChar 0.5))))
   (if (<= NaChar -4e-162)
     t_1
     (if (<= NaChar 6.2e-275)
       (+ t_0 (/ (* KbT NaChar) EAccept))
       (if (<= NaChar 1.35e-57) (+ t_0 (/ NaChar 2.0)) 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(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -4e-162) {
		tmp = t_1;
	} else if (NaChar <= 6.2e-275) {
		tmp = t_0 + ((KbT * NaChar) / EAccept);
	} else if (NaChar <= 1.35e-57) {
		tmp = t_0 + (NaChar / 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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(((mu + (edonor + (vef - ec))) / kbt)))
    t_1 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    if (nachar <= (-4d-162)) then
        tmp = t_1
    else if (nachar <= 6.2d-275) then
        tmp = t_0 + ((kbt * nachar) / eaccept)
    else if (nachar <= 1.35d-57) then
        tmp = t_0 + (nachar / 2.0d0)
    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(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -4e-162) {
		tmp = t_1;
	} else if (NaChar <= 6.2e-275) {
		tmp = t_0 + ((KbT * NaChar) / EAccept);
	} else if (NaChar <= 1.35e-57) {
		tmp = t_0 + (NaChar / 2.0);
	} 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(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	tmp = 0
	if NaChar <= -4e-162:
		tmp = t_1
	elif NaChar <= 6.2e-275:
		tmp = t_0 + ((KbT * NaChar) / EAccept)
	elif NaChar <= 1.35e-57:
		tmp = t_0 + (NaChar / 2.0)
	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(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5))
	tmp = 0.0
	if (NaChar <= -4e-162)
		tmp = t_1;
	elseif (NaChar <= 6.2e-275)
		tmp = Float64(t_0 + Float64(Float64(KbT * NaChar) / EAccept));
	elseif (NaChar <= 1.35e-57)
		tmp = Float64(t_0 + Float64(NaChar / 2.0));
	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(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_1 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	tmp = 0.0;
	if (NaChar <= -4e-162)
		tmp = t_1;
	elseif (NaChar <= 6.2e-275)
		tmp = t_0 + ((KbT * NaChar) / EAccept);
	elseif (NaChar <= 1.35e-57)
		tmp = t_0 + (NaChar / 2.0);
	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[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4e-162], t$95$1, If[LessEqual[NaChar, 6.2e-275], N[(t$95$0 + N[(N[(KbT * NaChar), $MachinePrecision] / EAccept), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.35e-57], N[(t$95$0 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -3.99999999999999982e-162 or 1.3500000000000001e-57 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 55.3%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   5. Step-by-step derivation

      1. *-commutative 55.3%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Simplified 55.3%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -3.99999999999999982e-162 < NaChar < 6.200000000000001e-275

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 71.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   5. Taylor expanded in EAccept around inf 69.6%

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

   if 6.200000000000001e-275 < NaChar < 1.3500000000000001e-57

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 65.4%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4 \cdot 10^{-162}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 6.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{EAccept}\\ \mathbf{elif}\;NaChar \leq 1.35 \cdot 10^{-57}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]

Alternative 17: 42.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;EAccept \leq -1.65 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EAccept \leq 2.3 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 4 \cdot 10^{+47}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
   (if (<= EAccept -1.65e-75)
     t_0
     (if (<= EAccept 2.3e-193)
       (+
        (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
        (/ NaChar (+ (/ Vef KbT) 2.0)))
       (if (<= EAccept 4e+47)
         (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (/ NaChar 2.0))
         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 / KbT)));
	double tmp;
	if (EAccept <= -1.65e-75) {
		tmp = t_0;
	} else if (EAccept <= 2.3e-193) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 4e+47) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 / kbt)))
    if (eaccept <= (-1.65d-75)) then
        tmp = t_0
    else if (eaccept <= 2.3d-193) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else if (eaccept <= 4d+47) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / 2.0d0)
    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 / KbT)));
	double tmp;
	if (EAccept <= -1.65e-75) {
		tmp = t_0;
	} else if (EAccept <= 2.3e-193) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 4e+47) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	} 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 / KbT)))
	tmp = 0
	if EAccept <= -1.65e-75:
		tmp = t_0
	elif EAccept <= 2.3e-193:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	elif EAccept <= 4e+47:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0)
	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(EAccept / KbT))))
	tmp = 0.0
	if (EAccept <= -1.65e-75)
		tmp = t_0;
	elseif (EAccept <= 2.3e-193)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (EAccept <= 4e+47)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / 2.0));
	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 / KbT)));
	tmp = 0.0;
	if (EAccept <= -1.65e-75)
		tmp = t_0;
	elseif (EAccept <= 2.3e-193)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	elseif (EAccept <= 4e+47)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	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[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -1.65e-75], t$95$0, If[LessEqual[EAccept, 2.3e-193], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 4e+47], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < -1.65e-75 or 4.0000000000000002e47 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 70.9%

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

   5. Taylor expanded in EAccept around inf 61.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 53.8%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]

   if -1.65e-75 < EAccept < 2.30000000000000009e-193

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 78.5%

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

   5. Taylor expanded in Vef around 0 58.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]

   6. Taylor expanded in EDonor around inf 45.7%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   if 2.30000000000000009e-193 < EAccept < 4.0000000000000002e47

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 57.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2}} \]

   5. Taylor expanded in EDonor around 0 55.8%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -1.65 \cdot 10^{-75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 2.3 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 4 \cdot 10^{+47}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 18: 53.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5 \cdot 10^{-153} \lor \neg \left(NaChar \leq 1.6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -5e-153) (not (<= NaChar 1.6e-57)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (* NdChar 0.5))
   (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (/ NaChar 2.0))))

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 <= -5e-153) || !(NaChar <= 1.6e-57)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 <= (-5d-153)) .or. (.not. (nachar <= 1.6d-57))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / 2.0d0)
    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 <= -5e-153) || !(NaChar <= 1.6e-57)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -5e-153) or not (NaChar <= 1.6e-57):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -5e-153) || !(NaChar <= 1.6e-57))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -5e-153) || ~((NaChar <= 1.6e-57)))
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -5e-153], N[Not[LessEqual[NaChar, 1.6e-57]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -5.00000000000000033e-153 or 1.6e-57 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 55.7%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   5. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Simplified 55.7%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -5.00000000000000033e-153 < NaChar < 1.6e-57

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 63.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2}} \]

   5. Taylor expanded in EDonor around 0 56.3%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5 \cdot 10^{-153} \lor \neg \left(NaChar \leq 1.6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 19: 55.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1 \cdot 10^{-152} \lor \neg \left(NaChar \leq 1.45 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1e-152) (not (<= NaChar 1.45e-57)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (* NdChar 0.5))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ NaChar 2.0))))

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 <= -1e-152) || !(NaChar <= 1.45e-57)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 <= (-1d-152)) .or. (.not. (nachar <= 1.45d-57))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    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 <= -1e-152) || !(NaChar <= 1.45e-57)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1e-152) or not (NaChar <= 1.45e-57):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1e-152) || !(NaChar <= 1.45e-57))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1e-152) || ~((NaChar <= 1.45e-57)))
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1e-152], N[Not[LessEqual[NaChar, 1.45e-57]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.00000000000000007e-152 or 1.45000000000000013e-57 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 55.7%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   5. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Simplified 55.7%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   if -1.00000000000000007e-152 < NaChar < 1.45000000000000013e-57

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 63.3%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1 \cdot 10^{-152} \lor \neg \left(NaChar \leq 1.45 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 20: 38.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;EAccept \leq -3.45 \cdot 10^{-236}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EAccept \leq 1.06 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;EAccept \leq 1.28 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EAccept \leq 1.95 \cdot 10^{+46}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT))))))
   (if (<= EAccept -3.45e-236)
     t_0
     (if (<= EAccept 1.06e-193)
       (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
       (if (<= EAccept 1.28e-170)
         t_0
         (if (<= EAccept 1.95e+46)
           (+ (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))) (* NdChar 0.5))
           (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))

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)));
	double tmp;
	if (EAccept <= -3.45e-236) {
		tmp = t_0;
	} else if (EAccept <= 1.06e-193) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (EAccept <= 1.28e-170) {
		tmp = t_0;
	} else if (EAccept <= 1.95e+46) {
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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)))
    if (eaccept <= (-3.45d-236)) then
        tmp = t_0
    else if (eaccept <= 1.06d-193) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else if (eaccept <= 1.28d-170) then
        tmp = t_0
    else if (eaccept <= 1.95d+46) then
        tmp = (nachar / (1.0d0 + exp((-mu / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = nachar / (1.0d0 + exp((eaccept / 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 t_0 = NdChar / (1.0 + Math.exp((mu / KbT)));
	double tmp;
	if (EAccept <= -3.45e-236) {
		tmp = t_0;
	} else if (EAccept <= 1.06e-193) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (EAccept <= 1.28e-170) {
		tmp = t_0;
	} else if (EAccept <= 1.95e+46) {
		tmp = (NaChar / (1.0 + Math.exp((-mu / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((mu / KbT)))
	tmp = 0
	if EAccept <= -3.45e-236:
		tmp = t_0
	elif EAccept <= 1.06e-193:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	elif EAccept <= 1.28e-170:
		tmp = t_0
	elif EAccept <= 1.95e+46:
		tmp = (NaChar / (1.0 + math.exp((-mu / KbT)))) + (NdChar * 0.5)
	else:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))))
	tmp = 0.0
	if (EAccept <= -3.45e-236)
		tmp = t_0;
	elseif (EAccept <= 1.06e-193)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	elseif (EAccept <= 1.28e-170)
		tmp = t_0;
	elseif (EAccept <= 1.95e+46)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	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)));
	tmp = 0.0;
	if (EAccept <= -3.45e-236)
		tmp = t_0;
	elseif (EAccept <= 1.06e-193)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	elseif (EAccept <= 1.28e-170)
		tmp = t_0;
	elseif (EAccept <= 1.95e+46)
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + (NdChar * 0.5);
	else
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	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[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -3.45e-236], t$95$0, If[LessEqual[EAccept, 1.06e-193], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.28e-170], t$95$0, If[LessEqual[EAccept, 1.95e+46], N[(N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if EAccept < -3.44999999999999987e-236 or 1.06e-193 < EAccept < 1.2800000000000001e-170

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 68.6%

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

   5. Taylor expanded in EAccept around inf 52.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around inf 38.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}} \]

   if -3.44999999999999987e-236 < EAccept < 1.06e-193

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 50.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2}} \]

   5. Taylor expanded in EDonor around inf 46.8%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{2} \]

   if 1.2800000000000001e-170 < EAccept < 1.94999999999999997e46

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 51.8%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   5. Step-by-step derivation

      1. *-commutative 51.8%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Simplified 51.8%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in mu around inf 45.2%

      \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{-1 \cdot \frac{mu}{KbT}}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 45.2%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{\frac{-1 \cdot mu}{KbT}}}} \]

      2. mul-1-neg 45.2%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\color{blue}{-mu}}{KbT}}} \]

   9. Simplified 45.2%

      \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{\frac{-mu}{KbT}}}} \]

   if 1.94999999999999997e46 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 74.4%

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

   5. Taylor expanded in EAccept around inf 65.1%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 62.6%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -3.45 \cdot 10^{-236}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.06 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;EAccept \leq 1.28 \cdot 10^{-170}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.95 \cdot 10^{+46}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 21: 40.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;EAccept \leq -3.6 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 6 \cdot 10^{+46}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
   (if (<= EAccept -3.6e-75)
     t_0
     (if (<= EAccept 3.2e-193)
       (+
        (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
        (/ NaChar (+ (/ Vef KbT) 2.0)))
       (if (<= EAccept 6e+46)
         (+ (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))) (* NdChar 0.5))
         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 / KbT)));
	double tmp;
	if (EAccept <= -3.6e-75) {
		tmp = t_0;
	} else if (EAccept <= 3.2e-193) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 6e+46) {
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 / kbt)))
    if (eaccept <= (-3.6d-75)) then
        tmp = t_0
    else if (eaccept <= 3.2d-193) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else if (eaccept <= 6d+46) then
        tmp = (nachar / (1.0d0 + exp((-mu / kbt)))) + (ndchar * 0.5d0)
    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 / KbT)));
	double tmp;
	if (EAccept <= -3.6e-75) {
		tmp = t_0;
	} else if (EAccept <= 3.2e-193) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 6e+46) {
		tmp = (NaChar / (1.0 + Math.exp((-mu / KbT)))) + (NdChar * 0.5);
	} 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 / KbT)))
	tmp = 0
	if EAccept <= -3.6e-75:
		tmp = t_0
	elif EAccept <= 3.2e-193:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	elif EAccept <= 6e+46:
		tmp = (NaChar / (1.0 + math.exp((-mu / KbT)))) + (NdChar * 0.5)
	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(EAccept / KbT))))
	tmp = 0.0
	if (EAccept <= -3.6e-75)
		tmp = t_0;
	elseif (EAccept <= 3.2e-193)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (EAccept <= 6e+46)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))) + Float64(NdChar * 0.5));
	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 / KbT)));
	tmp = 0.0;
	if (EAccept <= -3.6e-75)
		tmp = t_0;
	elseif (EAccept <= 3.2e-193)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	elseif (EAccept <= 6e+46)
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + (NdChar * 0.5);
	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[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -3.6e-75], t$95$0, If[LessEqual[EAccept, 3.2e-193], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 6e+46], N[(N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < -3.6e-75 or 6.00000000000000047e46 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 71.7%

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

   5. Taylor expanded in EAccept around inf 62.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 54.7%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]

   if -3.6e-75 < EAccept < 3.20000000000000006e-193

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 77.8%

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

   5. Taylor expanded in Vef around 0 58.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]

   6. Taylor expanded in EDonor around inf 44.9%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   if 3.20000000000000006e-193 < EAccept < 6.00000000000000047e46

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 48.8%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   5. Step-by-step derivation

      1. *-commutative 48.8%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Simplified 48.8%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in mu around inf 42.7%

      \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{-1 \cdot \frac{mu}{KbT}}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 42.7%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{\frac{-1 \cdot mu}{KbT}}}} \]

      2. mul-1-neg 42.7%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\color{blue}{-mu}}{KbT}}} \]

   9. Simplified 42.7%

      \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{\frac{-mu}{KbT}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -3.6 \cdot 10^{-75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 6 \cdot 10^{+46}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 22: 39.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.75 \cdot 10^{+17}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -1.9 \cdot 10^{-189} \lor \neg \left(NaChar \leq 2.3 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -1.75e+17)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (* NdChar 0.5))
   (if (or (<= NaChar -1.9e-189) (not (<= NaChar 2.3e-50)))
     (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
     (/ NdChar (+ 1.0 (exp (/ 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 (NaChar <= -1.75e+17) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar * 0.5);
	} else if ((NaChar <= -1.9e-189) || !(NaChar <= 2.3e-50)) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 <= (-1.75d+17)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar * 0.5d0)
    else if ((nachar <= (-1.9d-189)) .or. (.not. (nachar <= 2.3d-50))) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else
        tmp = ndchar / (1.0d0 + exp((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 (NaChar <= -1.75e+17) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar * 0.5);
	} else if ((NaChar <= -1.9e-189) || !(NaChar <= 2.3e-50)) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -1.75e+17:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar * 0.5)
	elif (NaChar <= -1.9e-189) or not (NaChar <= 2.3e-50):
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	else:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -1.75e+17)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar * 0.5));
	elseif ((NaChar <= -1.9e-189) || !(NaChar <= 2.3e-50))
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	else
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -1.75e+17)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar * 0.5);
	elseif ((NaChar <= -1.9e-189) || ~((NaChar <= 2.3e-50)))
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	else
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -1.75e+17], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, -1.9e-189], N[Not[LessEqual[NaChar, 2.3e-50]], $MachinePrecision]], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.75e17

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Ev around inf 60.7%

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

   5. Taylor expanded in KbT around inf 35.3%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]
   6. Step-by-step derivation

      1. *-commutative 59.7%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Simplified 35.3%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -1.75e17 < NaChar < -1.90000000000000011e-189 or 2.3000000000000002e-50 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 70.7%

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

   5. Taylor expanded in EAccept around inf 51.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 50.7%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]

   if -1.90000000000000011e-189 < NaChar < 2.3000000000000002e-50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 63.2%

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

   5. Taylor expanded in EAccept around inf 50.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around inf 52.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.75 \cdot 10^{+17}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -1.9 \cdot 10^{-189} \lor \neg \left(NaChar \leq 2.3 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]

Alternative 23: 39.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5.4 \cdot 10^{-191} \lor \neg \left(NaChar \leq 2.2 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -5.4e-191) (not (<= NaChar 2.2e-50)))
   (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
   (/ NdChar (+ 1.0 (exp (/ 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 ((NaChar <= -5.4e-191) || !(NaChar <= 2.2e-50)) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 <= (-5.4d-191)) .or. (.not. (nachar <= 2.2d-50))) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else
        tmp = ndchar / (1.0d0 + exp((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 ((NaChar <= -5.4e-191) || !(NaChar <= 2.2e-50)) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -5.4e-191) or not (NaChar <= 2.2e-50):
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	else:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -5.4e-191) || !(NaChar <= 2.2e-50))
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	else
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -5.4e-191) || ~((NaChar <= 2.2e-50)))
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	else
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -5.4e-191], N[Not[LessEqual[NaChar, 2.2e-50]], $MachinePrecision]], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -5.39999999999999998e-191 or 2.1999999999999999e-50 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 73.5%

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

   5. Taylor expanded in EAccept around inf 48.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 45.4%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]

   if -5.39999999999999998e-191 < NaChar < 2.1999999999999999e-50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 63.2%

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

   5. Taylor expanded in EAccept around inf 50.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around inf 52.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.4 \cdot 10^{-191} \lor \neg \left(NaChar \leq 2.2 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]

Alternative 24: 40.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -9 \cdot 10^{+152}:\\ \;\;\;\;\frac{NaChar}{2 - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.8 \cdot 10^{+101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -9e+152)
   (+ (/ NaChar (- 2.0 (/ mu KbT))) (* NdChar 0.5))
   (if (<= KbT 1.8e+101)
     (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
     (* 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) {
	double tmp;
	if (KbT <= -9e+152) {
		tmp = (NaChar / (2.0 - (mu / KbT))) + (NdChar * 0.5);
	} else if (KbT <= 1.8e+101) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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+152)) then
        tmp = (nachar / (2.0d0 - (mu / kbt))) + (ndchar * 0.5d0)
    else if (kbt <= 1.8d+101) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else
        tmp = 0.5d0 * (ndchar + 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 (KbT <= -9e+152) {
		tmp = (NaChar / (2.0 - (mu / KbT))) + (NdChar * 0.5);
	} else if (KbT <= 1.8e+101) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -9e+152:
		tmp = (NaChar / (2.0 - (mu / KbT))) + (NdChar * 0.5)
	elif KbT <= 1.8e+101:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	else:
		tmp = 0.5 * (NdChar + NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -9e+152)
		tmp = Float64(Float64(NaChar / Float64(2.0 - Float64(mu / KbT))) + Float64(NdChar * 0.5));
	elseif (KbT <= 1.8e+101)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	else
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -9e+152)
		tmp = (NaChar / (2.0 - (mu / KbT))) + (NdChar * 0.5);
	elseif (KbT <= 1.8e+101)
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	else
		tmp = 0.5 * (NdChar + NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -9e+152], N[(N[(NaChar / N[(2.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.8e+101], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -9.0000000000000002e152

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in KbT around inf 82.7%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   5. Step-by-step derivation

      1. *-commutative 82.7%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Simplified 82.7%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in mu around inf 76.9%

      \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{-1 \cdot \frac{mu}{KbT}}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 76.9%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{\frac{-1 \cdot mu}{KbT}}}} \]

      2. mul-1-neg 76.9%

         \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\color{blue}{-mu}}{KbT}}} \]

   9. Simplified 76.9%

      \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\color{blue}{\frac{-mu}{KbT}}}} \]

   10. Taylor expanded in mu around 0 74.6%

       \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{\color{blue}{2 + -1 \cdot \frac{mu}{KbT}}} \]
   11. Step-by-step derivation

       1. mul-1-neg 74.6%

          \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{2 + \color{blue}{\left(-\frac{mu}{KbT}\right)}} \]

       2. unsub-neg 74.6%

          \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{\color{blue}{2 - \frac{mu}{KbT}}} \]

   12. Simplified 74.6%

       \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{\color{blue}{2 - \frac{mu}{KbT}}} \]

   if -9.0000000000000002e152 < KbT < 1.80000000000000015e101

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 64.1%

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

   5. Taylor expanded in EAccept around inf 39.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in NdChar around 0 37.0%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}} \]

   if 1.80000000000000015e101 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 80.0%

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

   5. Taylor expanded in EAccept around inf 67.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in KbT around inf 58.5%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   7. Step-by-step derivation

      1. distribute-lft-out 58.5%

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

   8. Simplified 58.5%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -9 \cdot 10^{+152}:\\ \;\;\;\;\frac{NaChar}{2 - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.8 \cdot 10^{+101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]

Alternative 25: 27.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq 6.8 \cdot 10^{-304}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT 6.8e-304)
   (+
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT)))
    (/
     NdChar
     (- (+ (+ (/ EDonor KbT) 2.0) (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
   (* 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) {
	double tmp;
	if (KbT <= 6.8e-304) {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 <= 6.8d-304) then
        tmp = (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt))) + (ndchar / ((((edonor / kbt) + 2.0d0) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))
    else
        tmp = 0.5d0 * (ndchar + 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 (KbT <= 6.8e-304) {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= 6.8e-304:
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))
	else:
		tmp = 0.5 * (NdChar + NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= 6.8e-304)
		tmp = Float64(Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))) + Float64(NdChar / Float64(Float64(Float64(Float64(EDonor / KbT) + 2.0) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT))));
	else
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= 6.8e-304)
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	else
		tmp = 0.5 * (NdChar + NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, 6.8e-304], N[(N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < 6.7999999999999997e-304

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 59.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   5. Taylor expanded in KbT around inf 31.3%

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

      1. associate-+r+ 31.0%

         \[\leadsto \frac{NdChar}{\color{blue}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)} - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   7. Simplified 31.3%

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

   if 6.7999999999999997e-304 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 71.0%

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

   5. Taylor expanded in EAccept around inf 47.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in KbT around inf 30.1%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   7. Step-by-step derivation

      1. distribute-lft-out 30.1%

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

   8. Simplified 30.1%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 6.8 \cdot 10^{-304}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]

Alternative 26: 27.5% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq 4.8 \cdot 10^{-304}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT 4.8e-304)
   (+
    (/ NaChar (+ (/ Vef KbT) 2.0))
    (/
     NdChar
     (- (+ (+ (/ EDonor KbT) 2.0) (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
   (* 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) {
	double tmp;
	if (KbT <= 4.8e-304) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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 <= 4.8d-304) then
        tmp = (nachar / ((vef / kbt) + 2.0d0)) + (ndchar / ((((edonor / kbt) + 2.0d0) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))
    else
        tmp = 0.5d0 * (ndchar + 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 (KbT <= 4.8e-304) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= 4.8e-304:
		tmp = (NaChar / ((Vef / KbT) + 2.0)) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))
	else:
		tmp = 0.5 * (NdChar + NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= 4.8e-304)
		tmp = Float64(Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)) + Float64(NdChar / Float64(Float64(Float64(Float64(EDonor / KbT) + 2.0) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT))));
	else
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= 4.8e-304)
		tmp = (NaChar / ((Vef / KbT) + 2.0)) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	else
		tmp = 0.5 * (NdChar + NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, 4.8e-304], N[(N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < 4.8000000000000002e-304

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 73.1%

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

   5. Taylor expanded in Vef around 0 57.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]

   6. Taylor expanded in KbT around inf 31.0%

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

      1. associate-+r+ 31.0%

         \[\leadsto \frac{NdChar}{\color{blue}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)} - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   8. Simplified 31.0%

      \[\leadsto \frac{NdChar}{\color{blue}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}} \]

   if 4.8000000000000002e-304 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 71.0%

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

   5. Taylor expanded in EAccept around inf 47.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in KbT around inf 30.1%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   7. Step-by-step derivation

      1. distribute-lft-out 30.1%

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

   8. Simplified 30.1%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 4.8 \cdot 10^{-304}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]

Alternative 27: 27.5% accurate, 45.8× 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

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    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%

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

3. Simplified 100.0%

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

4. Taylor expanded in mu around inf 69.7%

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

5. Taylor expanded in EAccept around inf 49.5%

   \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

6. Taylor expanded in KbT around inf 28.9%

   \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
7. Step-by-step derivation

   1. distribute-lft-out 28.9%

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

8. Simplified 28.9%

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

9. Final simplification 28.9%

   \[\leadsto 0.5 \cdot \left(NdChar + NaChar\right) \]

Reproduce

herbie shell --seed 2023319 
(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))))))