Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 24.4s

Alternatives: 21

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NaChar / Float64((exp(1) ^ Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar / ((2.71828182845904523536 ^ ((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
end

Wolfram

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

Derivation

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%

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

   1. *-un-lft-identity 99.9%

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

   2. exp-prod 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 2: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;Ev \leq -3.7 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - t\_0\\ \mathbf{elif}\;Ev \leq -4.1 \cdot 10^{-173}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= Ev -3.7e-13)
     (- (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) t_0)
     (if (<= Ev -4.1e-173)
       (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
       (- (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) 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 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (Ev <= -3.7e-13) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - t_0;
	} else if (Ev <= -4.1e-173) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) - 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 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (ev <= (-3.7d-13)) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) - t_0
    else if (ev <= (-4.1d-173)) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (Ev <= -3.7e-13) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) - t_0;
	} else if (Ev <= -4.1e-173) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) - t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if Ev <= -3.7e-13:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) - t_0
	elif Ev <= -4.1e-173:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (Ev <= -3.7e-13)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) - t_0);
	elseif (Ev <= -4.1e-173)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (Ev <= -3.7e-13)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - t_0;
	elseif (Ev <= -4.1e-173)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) - t_0;
	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[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -3.7e-13], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[Ev, -4.1e-173], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -3.69999999999999989e-13

   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%

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

   5. Taylor expanded in Ev around inf 91.0%

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

   if -3.69999999999999989e-13 < Ev < -4.0999999999999997e-173

   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%

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

   5. Taylor expanded in NdChar around 0 78.1%

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

   if -4.0999999999999997e-173 < Ev

   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%

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

   5. Taylor expanded in EAccept around inf 63.0%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -3.7 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;Ev \leq -4.1 \cdot 10^{-173}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -8 \cdot 10^{+201}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 2.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{NaChar}{{e}^{\left(\frac{EAccept + \left(Ev + \left(Vef - mu\right)\right)}{KbT}\right)} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -8e+201)
   (+
    (/ NaChar (+ (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)) 1.0))
    (/ NdChar 2.0))
   (if (<= KbT 2.5e-17)
     (/ NaChar (+ (pow E (/ (+ EAccept (+ Ev (- Vef mu))) KbT)) 1.0))
     (-
      (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))
      (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -8e+201) {
		tmp = (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (KbT <= 2.5e-17) {
		tmp = NaChar / (pow(((double) M_E), ((EAccept + (Ev + (Vef - mu))) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

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 <= -8e+201) {
		tmp = (NaChar / (Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (KbT <= 2.5e-17) {
		tmp = NaChar / (Math.pow(Math.E, ((EAccept + (Ev + (Vef - mu))) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -8e+201:
		tmp = (NaChar / (math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / 2.0)
	elif KbT <= 2.5e-17:
		tmp = NaChar / (math.pow(math.e, ((EAccept + (Ev + (Vef - mu))) / KbT)) + 1.0)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -8e+201)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	elseif (KbT <= 2.5e-17)
		tmp = Float64(NaChar / Float64((exp(1) ^ Float64(Float64(EAccept + Float64(Ev + Float64(Vef - mu))) / KbT)) + 1.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -8e+201)
		tmp = (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / 2.0);
	elseif (KbT <= 2.5e-17)
		tmp = NaChar / ((2.71828182845904523536 ^ ((EAccept + (Ev + (Vef - mu))) / KbT)) + 1.0);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -8e+201], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.5e-17], N[(NaChar / N[(N[Power[E, N[(N[(EAccept + N[(Ev + N[(Vef - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -8.0000000000000003e201

   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%

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

   5. Taylor expanded in KbT around inf 78.6%

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

   if -8.0000000000000003e201 < KbT < 2.4999999999999999e-17

   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%

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

   5. Taylor expanded in NdChar around 0 72.3%

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

      1. frac-2neg 72.3%

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

      2. associate--l+ 72.3%

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

      3. associate-+r- 72.3%

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

      4. distribute-neg-frac2 72.3%

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

      5. *-un-lft-identity 72.3%

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

      6. exp-prod 72.3%

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

      7. distribute-neg-frac2 72.3%

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

      8. associate-+r- 72.3%

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

      9. associate--l+ 72.3%

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

      10. frac-2neg 72.3%

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

      11. associate--l+ 72.3%

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

      12. associate-+r- 72.3%

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

      13. associate-+r+ 72.3%

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

   7. Applied egg-rr 72.3%

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

      1. exp-1-e 72.3%

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

      2. associate-+l+ 72.3%

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

   9. Simplified 72.3%

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

   if 2.4999999999999999e-17 < 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%

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

   5. Taylor expanded in EAccept around inf 75.1%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -8 \cdot 10^{+201}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 2.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{NaChar}{{e}^{\left(\frac{EAccept + \left(Ev + \left(Vef - mu\right)\right)}{KbT}\right)} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar * (-1.0 / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))))) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / 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 = (nachar * ((-1.0d0) / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / 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 (NaChar * (-1.0 / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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%

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

   1. div-inv 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 5: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / 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 = (nachar / (exp(((vef + (ev - (mu - eaccept))) / kbt)) + 1.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / 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 (NaChar / (Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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%

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

5. Final simplification 99.9%

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

Alternative 6: 68.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -6 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq 1.05 \cdot 10^{-133}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{{e}^{\left(\frac{EAccept + \left(Ev + \left(Vef - mu\right)\right)}{KbT}\right)} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -6e+87)
   (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
   (if (<= NaChar 1.05e-133)
     (/ NdChar (+ (exp (/ (- (+ EDonor (+ mu Vef)) Ec) KbT)) 1.0))
     (/ NaChar (+ (pow E (/ (+ EAccept (+ Ev (- Vef mu))) KbT)) 1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -6e+87) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else if (NaChar <= 1.05e-133) {
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (pow(((double) M_E), ((EAccept + (Ev + (Vef - mu))) / KbT)) + 1.0);
	}
	return tmp;
}

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 <= -6e+87) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else if (NaChar <= 1.05e-133) {
		tmp = NdChar / (Math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.pow(Math.E, ((EAccept + (Ev + (Vef - mu))) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -6e+87:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	elif NaChar <= 1.05e-133:
		tmp = NdChar / (math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.pow(math.e, ((EAccept + (Ev + (Vef - mu))) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -6e+87)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	elseif (NaChar <= 1.05e-133)
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64((exp(1) ^ Float64(Float64(EAccept + Float64(Ev + Float64(Vef - mu))) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -6e+87)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	elseif (NaChar <= 1.05e-133)
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	else
		tmp = NaChar / ((2.71828182845904523536 ^ ((EAccept + (Ev + (Vef - mu))) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -6e+87], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.05e-133], N[(NdChar / N[(N[Exp[N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Power[E, N[(N[(EAccept + N[(Ev + N[(Vef - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -5.9999999999999998e87

   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%

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

   5. Taylor expanded in NdChar around 0 78.5%

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

   if -5.9999999999999998e87 < NaChar < 1.05e-133

   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%

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

   5. Taylor expanded in NdChar around inf 76.7%

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

   if 1.05e-133 < NaChar

   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%

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

   5. Taylor expanded in NdChar around 0 71.7%

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

      1. frac-2neg 71.7%

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

      2. associate--l+ 71.7%

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

      3. associate-+r- 71.7%

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

      4. distribute-neg-frac2 71.7%

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

      5. *-un-lft-identity 71.7%

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

      6. exp-prod 71.8%

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

      7. distribute-neg-frac2 71.8%

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

      8. associate-+r- 71.8%

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

      9. associate--l+ 71.8%

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

      10. frac-2neg 71.8%

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

      11. associate--l+ 71.8%

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

      12. associate-+r- 71.8%

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

      13. associate-+r+ 71.8%

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

   7. Applied egg-rr 71.8%

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

      1. exp-1-e 71.8%

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

      2. associate-+l+ 71.8%

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

   9. Simplified 71.8%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq 1.05 \cdot 10^{-133}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{{e}^{\left(\frac{EAccept + \left(Ev + \left(Vef - mu\right)\right)}{KbT}\right)} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -4.8 \cdot 10^{+88} \lor \neg \left(NaChar \leq 8 \cdot 10^{-134}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -4.8e+88) (not (<= NaChar 8e-134)))
   (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
   (/ NdChar (+ (exp (/ (- (+ EDonor (+ mu Vef)) Ec) KbT)) 1.0))))

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 <= -4.8e+88) || !(NaChar <= 8e-134)) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	}
	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 <= (-4.8d+88)) .or. (.not. (nachar <= 8d-134))) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = ndchar / (exp((((edonor + (mu + vef)) - ec) / kbt)) + 1.0d0)
    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 <= -4.8e+88) || !(NaChar <= 8e-134)) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (Math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -4.8e+88) or not (NaChar <= 8e-134):
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = NdChar / (math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -4.8e+88) || !(NaChar <= 8e-134))
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -4.8e+88) || ~((NaChar <= 8e-134)))
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -4.8e+88], N[Not[LessEqual[NaChar, 8e-134]], $MachinePrecision]], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(N[Exp[N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.7999999999999998e88 or 8.00000000000000032e-134 < NaChar

   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%

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

   5. Taylor expanded in NdChar around 0 74.0%

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

   if -4.7999999999999998e88 < NaChar < 8.00000000000000032e-134

   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%

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

   5. Taylor expanded in NdChar around inf 76.7%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.8 \cdot 10^{+88} \lor \neg \left(NaChar \leq 8 \cdot 10^{-134}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -2.4 \cdot 10^{+114}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -8.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{2 - \frac{\left(\left(mu - Vef\right) - Ev\right) - EAccept}{KbT}}\\ \mathbf{elif}\;Ev \leq -1.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -2.4e+114)
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
   (if (<= Ev -8.6e-30)
     (+
      (/ NdChar (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)))
      (/ NaChar (- 2.0 (/ (- (- (- mu Vef) Ev) EAccept) KbT))))
     (if (<= Ev -1.2e-176)
       (/ NaChar (+ (exp (/ mu (- KbT))) 1.0))
       (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -2.4e+114) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -8.6e-30) {
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT)));
	} else if (Ev <= -1.2e-176) {
		tmp = NaChar / (exp((mu / -KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	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 (ev <= (-2.4d+114)) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else if (ev <= (-8.6d-30)) then
        tmp = (ndchar / ((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt))) + (nachar / (2.0d0 - ((((mu - vef) - ev) - eaccept) / kbt)))
    else if (ev <= (-1.2d-176)) then
        tmp = nachar / (exp((mu / -kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    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 (Ev <= -2.4e+114) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -8.6e-30) {
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT)));
	} else if (Ev <= -1.2e-176) {
		tmp = NaChar / (Math.exp((mu / -KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -2.4e+114:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	elif Ev <= -8.6e-30:
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT)))
	elif Ev <= -1.2e-176:
		tmp = NaChar / (math.exp((mu / -KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -2.4e+114)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	elseif (Ev <= -8.6e-30)
		tmp = Float64(Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT))) + Float64(NaChar / Float64(2.0 - Float64(Float64(Float64(Float64(mu - Vef) - Ev) - EAccept) / KbT))));
	elseif (Ev <= -1.2e-176)
		tmp = Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -2.4e+114)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	elseif (Ev <= -8.6e-30)
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT)));
	elseif (Ev <= -1.2e-176)
		tmp = NaChar / (exp((mu / -KbT)) + 1.0);
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -2.4e+114], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -8.6e-30], N[(N[(NdChar / N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(2.0 - N[(N[(N[(N[(mu - Vef), $MachinePrecision] - Ev), $MachinePrecision] - EAccept), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.2e-176], N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -2.4e114

   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%

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

   5. Taylor expanded in Ev around inf 92.8%

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

   6. Taylor expanded in NdChar around 0 49.7%

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

   if -2.4e114 < Ev < -8.59999999999999932e-30

   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%

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

   5. Taylor expanded in EAccept around 0 76.4%

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

   6. Taylor expanded in KbT around -inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. distribute-lft-out 76.7%

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

      3. associate--l+ 76.7%

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

      4. mul-1-neg 76.7%

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

      5. associate--l+ 76.7%

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

      6. associate-+r- 76.7%

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

   8. Simplified 76.7%

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

   9. Taylor expanded in KbT around inf 33.7%

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

       1. associate-+r+ 33.7%

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

   11. Simplified 33.7%

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

   12. Taylor expanded in mu around 0 34.4%

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

       1. +-commutative 34.4%

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

   14. Simplified 34.4%

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

   if -8.59999999999999932e-30 < Ev < -1.20000000000000003e-176

   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%

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

   5. Taylor expanded in KbT around inf 51.9%

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

   6. Taylor expanded in mu around inf 40.0%

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

      1. associate-*r/ 40.0%

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

      2. mul-1-neg 40.0%

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

   8. Simplified 40.0%

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

   9. Taylor expanded in NdChar around 0 50.3%

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

       1. mul-1-neg 50.3%

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

       2. distribute-frac-neg 50.3%

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

   11. Simplified 50.3%

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

   if -1.20000000000000003e-176 < Ev

   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%

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

   5. Taylor expanded in EAccept around inf 63.0%

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

   6. Taylor expanded in NdChar around 0 35.2%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -2.4 \cdot 10^{+114}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -8.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{2 - \frac{\left(\left(mu - Vef\right) - Ev\right) - EAccept}{KbT}}\\ \mathbf{elif}\;Ev \leq -1.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.15 \cdot 10^{+201}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2.15e+201)
   (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ Ev KbT)))))
   (if (<= KbT 2e+216)
     (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
     (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 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 (KbT <= -2.15e+201) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	} else if (KbT <= 2e+216) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 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 (kbt <= (-2.15d+201)) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    else if (kbt <= 2d+216) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 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 (KbT <= -2.15e+201) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	} else if (KbT <= 2e+216) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -2.15e+201:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	elif KbT <= 2e+216:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -2.15e+201)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	elseif (KbT <= 2e+216)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -2.15e+201)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	elseif (KbT <= 2e+216)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -2.15e+201], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2e+216], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -2.14999999999999995e201

   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%

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

   5. Taylor expanded in Ev around inf 74.5%

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

   6. Taylor expanded in KbT around inf 66.9%

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

   if -2.14999999999999995e201 < KbT < 2e216

   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%

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

   5. Taylor expanded in NdChar around 0 67.5%

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

   if 2e216 < 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%

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

   5. Taylor expanded in KbT around inf 87.3%

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

   6. Taylor expanded in EAccept around inf 80.8%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.15 \cdot 10^{+201}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -4.2 \cdot 10^{+87} \lor \neg \left(KbT \leq 2.1 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -4.2e+87) (not (<= KbT 2.1e+122)))
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 2.0))
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -4.2e+87) || !(KbT <= 2.1e+122)) {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	}
	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 ((kbt <= (-4.2d+87)) .or. (.not. (kbt <= 2.1d+122))) then
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    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 ((KbT <= -4.2e+87) || !(KbT <= 2.1e+122)) {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -4.2e+87) or not (KbT <= 2.1e+122):
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	else:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -4.2e+87) || !(KbT <= 2.1e+122))
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -4.2e+87) || ~((KbT <= 2.1e+122)))
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	else
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -4.2e+87], N[Not[LessEqual[KbT, 2.1e+122]], $MachinePrecision]], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -4.2e87 or 2.10000000000000016e122 < KbT

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 69.0%

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

   6. Taylor expanded in EAccept around inf 59.3%

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

   if -4.2e87 < KbT < 2.10000000000000016e122

   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%

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

   5. Taylor expanded in Ev around inf 60.9%

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

   6. Taylor expanded in NdChar around 0 35.2%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.2 \cdot 10^{+87} \lor \neg \left(KbT \leq 2.1 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.4 \cdot 10^{+201}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;KbT \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2.4e+201)
   (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ Ev KbT)))))
   (if (<= KbT 4.5e+123)
     (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0))
     (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 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 (KbT <= -2.4e+201) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	} else if (KbT <= 4.5e+123) {
		tmp = NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 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 (kbt <= (-2.4d+201)) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    else if (kbt <= 4.5d+123) then
        tmp = nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 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 (KbT <= -2.4e+201) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	} else if (KbT <= 4.5e+123) {
		tmp = NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -2.4e+201:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	elif KbT <= 4.5e+123:
		tmp = NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -2.4e+201)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	elseif (KbT <= 4.5e+123)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -2.4e+201)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	elseif (KbT <= 4.5e+123)
		tmp = NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -2.4e+201], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4.5e+123], N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -2.39999999999999993e201

   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%

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

   5. Taylor expanded in Ev around inf 74.5%

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

   6. Taylor expanded in KbT around inf 66.9%

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

   if -2.39999999999999993e201 < KbT < 4.49999999999999983e123

   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%

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

   5. Taylor expanded in NdChar around 0 69.3%

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

   6. Taylor expanded in EAccept around 0 63.8%

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

   if 4.49999999999999983e123 < 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%

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

   5. Taylor expanded in KbT around inf 66.6%

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

   6. Taylor expanded in EAccept around inf 59.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.4 \cdot 10^{+201}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;KbT \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq -8.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 1.3 \cdot 10^{+133}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept -8.8e-200)
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
   (if (<= EAccept 1.3e+133)
     (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ Vef KbT)))))
     (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= -8.8e-200) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else if (EAccept <= 1.3e+133) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Vef / KbT))));
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	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 (eaccept <= (-8.8d-200)) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else if (eaccept <= 1.3d+133) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((vef / kbt))))
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    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 (EAccept <= -8.8e-200) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else if (EAccept <= 1.3e+133) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((Vef / KbT))));
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= -8.8e-200:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	elif EAccept <= 1.3e+133:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((Vef / KbT))))
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= -8.8e-200)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	elseif (EAccept <= 1.3e+133)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Vef / KbT)))));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= -8.8e-200)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	elseif (EAccept <= 1.3e+133)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Vef / KbT))));
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, -8.8e-200], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.3e+133], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < -8.80000000000000054e-200

   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%

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

   5. Taylor expanded in Ev around inf 65.9%

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

   6. Taylor expanded in NdChar around 0 36.7%

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

   if -8.80000000000000054e-200 < EAccept < 1.2999999999999999e133

   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%

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

   5. Taylor expanded in KbT around inf 50.2%

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

   6. Taylor expanded in Vef around inf 45.0%

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

   if 1.2999999999999999e133 < 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%

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

   5. Taylor expanded in EAccept around inf 76.9%

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

   6. Taylor expanded in NdChar around 0 47.0%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -8.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 1.3 \cdot 10^{+133}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.65 \cdot 10^{-177}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -8.5e-13)
   (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ Ev KbT)))))
   (if (<= Ev -1.65e-177)
     (/ NaChar (+ (exp (/ mu (- KbT))) 1.0))
     (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -8.5e-13) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	} else if (Ev <= -1.65e-177) {
		tmp = NaChar / (exp((mu / -KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	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 (ev <= (-8.5d-13)) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    else if (ev <= (-1.65d-177)) then
        tmp = nachar / (exp((mu / -kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    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 (Ev <= -8.5e-13) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	} else if (Ev <= -1.65e-177) {
		tmp = NaChar / (Math.exp((mu / -KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -8.5e-13:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	elif Ev <= -1.65e-177:
		tmp = NaChar / (math.exp((mu / -KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -8.5e-13)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	elseif (Ev <= -1.65e-177)
		tmp = Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -8.5e-13)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	elseif (Ev <= -1.65e-177)
		tmp = NaChar / (exp((mu / -KbT)) + 1.0);
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -8.5e-13], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.65e-177], N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -8.5000000000000001e-13

   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%

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

   5. Taylor expanded in Ev around inf 91.0%

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

   6. Taylor expanded in KbT around inf 47.2%

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

   if -8.5000000000000001e-13 < Ev < -1.65e-177

   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%

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

   5. Taylor expanded in KbT around inf 52.3%

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

   6. Taylor expanded in mu around inf 39.0%

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

      1. associate-*r/ 39.0%

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

      2. mul-1-neg 39.0%

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

   8. Simplified 39.0%

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

   9. Taylor expanded in NdChar around 0 48.6%

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

       1. mul-1-neg 48.6%

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

       2. distribute-frac-neg 48.6%

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

   11. Simplified 48.6%

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

   if -1.65e-177 < Ev

   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%

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

   5. Taylor expanded in EAccept around inf 63.0%

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

   6. Taylor expanded in NdChar around 0 35.2%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.65 \cdot 10^{-177}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 5.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 1.1 \cdot 10^{+92}:\\ \;\;\;\;\frac{NaChar}{2 - \frac{\left(\left(mu - Vef\right) - Ev\right) - EAccept}{KbT}} + \frac{NdChar}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 5.5e-100)
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
   (if (<= EAccept 1.1e+92)
     (+
      (/ NaChar (- 2.0 (/ (- (- (- mu Vef) Ev) EAccept) KbT)))
      (/
       NdChar
       (- (+ (+ 2.0 (/ EDonor KbT)) (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
     (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 5.5e-100) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else if (EAccept <= 1.1e+92) {
		tmp = (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT))) + (NdChar / (((2.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	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 (eaccept <= 5.5d-100) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else if (eaccept <= 1.1d+92) then
        tmp = (nachar / (2.0d0 - ((((mu - vef) - ev) - eaccept) / kbt))) + (ndchar / (((2.0d0 + (edonor / kbt)) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    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 (EAccept <= 5.5e-100) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else if (EAccept <= 1.1e+92) {
		tmp = (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT))) + (NdChar / (((2.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 5.5e-100:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	elif EAccept <= 1.1e+92:
		tmp = (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT))) + (NdChar / (((2.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 5.5e-100)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	elseif (EAccept <= 1.1e+92)
		tmp = Float64(Float64(NaChar / Float64(2.0 - Float64(Float64(Float64(Float64(mu - Vef) - Ev) - EAccept) / KbT))) + Float64(NdChar / Float64(Float64(Float64(2.0 + Float64(EDonor / KbT)) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT))));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 5.5e-100)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	elseif (EAccept <= 1.1e+92)
		tmp = (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT))) + (NdChar / (((2.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 5.5e-100], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.1e+92], N[(N[(NaChar / N[(2.0 - N[(N[(N[(N[(mu - Vef), $MachinePrecision] - Ev), $MachinePrecision] - EAccept), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 5.50000000000000011e-100

   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%

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

   5. Taylor expanded in Ev around inf 65.3%

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

   6. Taylor expanded in NdChar around 0 35.4%

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

   if 5.50000000000000011e-100 < EAccept < 1.09999999999999996e92

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in EAccept around 0 83.9%

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

   6. Taylor expanded in KbT around -inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. distribute-lft-out 76.7%

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

      3. associate--l+ 76.7%

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

      4. mul-1-neg 76.7%

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

      5. associate--l+ 76.7%

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

      6. associate-+r- 76.7%

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

   8. Simplified 76.7%

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

   9. Taylor expanded in KbT around inf 46.7%

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

       1. associate-+r+ 46.7%

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

   11. Simplified 46.7%

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

   if 1.09999999999999996e92 < 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%

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

   5. Taylor expanded in EAccept around inf 77.2%

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

   6. Taylor expanded in NdChar around 0 46.8%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 5.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 1.1 \cdot 10^{+92}:\\ \;\;\;\;\frac{NaChar}{2 - \frac{\left(\left(mu - Vef\right) - Ev\right) - EAccept}{KbT}} + \frac{NdChar}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{if}\;KbT \leq -1.24 \cdot 10^{+190}:\\ \;\;\;\;t\_0 + 0.25 \cdot \left(mu \cdot \frac{NaChar - NdChar}{KbT}\right)\\ \mathbf{elif}\;KbT \leq 2.2 \cdot 10^{+214}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0 - -0.25 \cdot \frac{NdChar \cdot Ec}{KbT}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar))))
   (if (<= KbT -1.24e+190)
     (+ t_0 (* 0.25 (* mu (/ (- NaChar NdChar) KbT))))
     (if (<= KbT 2.2e+214)
       (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))
       (- t_0 (* -0.25 (/ (* NdChar Ec) 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 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -1.24e+190) {
		tmp = t_0 + (0.25 * (mu * ((NaChar - NdChar) / KbT)));
	} else if (KbT <= 2.2e+214) {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	} else {
		tmp = t_0 - (-0.25 * ((NdChar * Ec) / 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 = 0.5d0 * (ndchar + nachar)
    if (kbt <= (-1.24d+190)) then
        tmp = t_0 + (0.25d0 * (mu * ((nachar - ndchar) / kbt)))
    else if (kbt <= 2.2d+214) then
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    else
        tmp = t_0 - ((-0.25d0) * ((ndchar * ec) / 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 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -1.24e+190) {
		tmp = t_0 + (0.25 * (mu * ((NaChar - NdChar) / KbT)));
	} else if (KbT <= 2.2e+214) {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	} else {
		tmp = t_0 - (-0.25 * ((NdChar * Ec) / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	tmp = 0
	if KbT <= -1.24e+190:
		tmp = t_0 + (0.25 * (mu * ((NaChar - NdChar) / KbT)))
	elif KbT <= 2.2e+214:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	else:
		tmp = t_0 - (-0.25 * ((NdChar * Ec) / KbT))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	tmp = 0.0
	if (KbT <= -1.24e+190)
		tmp = Float64(t_0 + Float64(0.25 * Float64(mu * Float64(Float64(NaChar - NdChar) / KbT))));
	elseif (KbT <= 2.2e+214)
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	else
		tmp = Float64(t_0 - Float64(-0.25 * Float64(Float64(NdChar * Ec) / KbT)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	tmp = 0.0;
	if (KbT <= -1.24e+190)
		tmp = t_0 + (0.25 * (mu * ((NaChar - NdChar) / KbT)));
	elseif (KbT <= 2.2e+214)
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	else
		tmp = t_0 - (-0.25 * ((NdChar * Ec) / KbT));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -1.24e+190], N[(t$95$0 + N[(0.25 * N[(mu * N[(N[(NaChar - NdChar), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.2e+214], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 - N[(-0.25 * N[(N[(NdChar * Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.24e190

   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%

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

   5. Taylor expanded in KbT around inf 39.2%

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

   7. Simplified 39.2%

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

   8. Taylor expanded in mu around inf 50.0%

      \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{0.25 \cdot \frac{mu \cdot \left(NdChar + -1 \cdot NaChar\right)}{KbT}} \]
   9. Step-by-step derivation

      1. associate-/l* 64.5%

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

      2. +-commutative 64.5%

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

      3. mul-1-neg 64.5%

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

   10. Simplified 64.5%

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

   if -1.24e190 < KbT < 2.20000000000000023e214

   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%

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

   5. Taylor expanded in EAccept around inf 60.8%

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

   6. Taylor expanded in NdChar around 0 34.4%

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

   if 2.20000000000000023e214 < 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%

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

   5. Taylor expanded in KbT around inf 42.6%

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

   7. Simplified 42.6%

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

   8. Taylor expanded in Ec around inf 74.2%

      \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{-0.25 \cdot \frac{Ec \cdot NdChar}{KbT}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.24 \cdot 10^{+190}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) + 0.25 \cdot \left(mu \cdot \frac{NaChar - NdChar}{KbT}\right)\\ \mathbf{elif}\;KbT \leq 2.2 \cdot 10^{+214}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) - -0.25 \cdot \frac{NdChar \cdot Ec}{KbT}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.1% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{2 - \frac{\left(\left(mu - Vef\right) - Ev\right) - EAccept}{KbT}}\\ \mathbf{if}\;Ev \leq -1.5 \cdot 10^{-12}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;Ev \leq -1.02 \cdot 10^{-210}:\\ \;\;\;\;\frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef - mu}{KbT}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}} + t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (- 2.0 (/ (- (- (- mu Vef) Ev) EAccept) KbT)))))
   (if (<= Ev -1.5e-12)
     (+
      t_0
      (/
       NdChar
       (- (+ (+ 2.0 (/ EDonor KbT)) (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
     (if (<= Ev -1.02e-210)
       (/ NaChar (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ (- Vef mu) KbT)))))
       (+
        (/ NdChar (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)))
        t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT));
	double tmp;
	if (Ev <= -1.5e-12) {
		tmp = t_0 + (NdChar / (((2.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else if (Ev <= -1.02e-210) {
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))));
	} else {
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + 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 / (2.0d0 - ((((mu - vef) - ev) - eaccept) / kbt))
    if (ev <= (-1.5d-12)) then
        tmp = t_0 + (ndchar / (((2.0d0 + (edonor / kbt)) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))
    else if (ev <= (-1.02d-210)) then
        tmp = nachar / (2.0d0 + ((eaccept / kbt) + ((ev / kbt) + ((vef - mu) / kbt))))
    else
        tmp = (ndchar / ((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt))) + 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 / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT));
	double tmp;
	if (Ev <= -1.5e-12) {
		tmp = t_0 + (NdChar / (((2.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else if (Ev <= -1.02e-210) {
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))));
	} else {
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT))
	tmp = 0
	if Ev <= -1.5e-12:
		tmp = t_0 + (NdChar / (((2.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))
	elif Ev <= -1.02e-210:
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))))
	else:
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(2.0 - Float64(Float64(Float64(Float64(mu - Vef) - Ev) - EAccept) / KbT)))
	tmp = 0.0
	if (Ev <= -1.5e-12)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(Float64(2.0 + Float64(EDonor / KbT)) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT))));
	elseif (Ev <= -1.02e-210)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Float64(Vef - mu) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT))) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT));
	tmp = 0.0;
	if (Ev <= -1.5e-12)
		tmp = t_0 + (NdChar / (((2.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	elseif (Ev <= -1.02e-210)
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))));
	else
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + 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[(2.0 - N[(N[(N[(N[(mu - Vef), $MachinePrecision] - Ev), $MachinePrecision] - EAccept), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -1.5e-12], N[(t$95$0 + N[(NdChar / N[(N[(N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.02e-210], N[(NaChar / N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(N[(Vef - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -1.5000000000000001e-12

   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%

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

   5. Taylor expanded in EAccept around 0 79.6%

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

   6. Taylor expanded in KbT around -inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. distribute-lft-out 70.3%

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

      3. associate--l+ 70.3%

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

      4. mul-1-neg 70.3%

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

      5. associate--l+ 70.3%

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

      6. associate-+r- 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in KbT around inf 33.1%

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

       1. associate-+r+ 33.1%

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

   11. Simplified 33.1%

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

   if -1.5000000000000001e-12 < Ev < -1.02000000000000002e-210

   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%

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

   5. Taylor expanded in EAccept around 0 73.3%

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

   6. Taylor expanded in KbT around -inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-lft-out 61.1%

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

      3. associate--l+ 61.1%

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

      4. mul-1-neg 61.1%

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

      5. associate--l+ 61.1%

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

      6. associate-+r- 61.1%

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

   8. Simplified 61.1%

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

   9. Taylor expanded in NdChar around 0 42.7%

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

       1. associate--l+ 42.7%

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

       2. associate--l+ 42.7%

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

       3. associate--l+ 42.7%

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

       4. div-sub 42.7%

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

   11. Simplified 42.7%

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

   if -1.02000000000000002e-210 < Ev

   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%

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

   5. Taylor expanded in EAccept around 0 73.9%

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

   6. Taylor expanded in KbT around -inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-lft-out 56.1%

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

      3. associate--l+ 56.1%

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

      4. mul-1-neg 56.1%

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

      5. associate--l+ 56.1%

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

      6. associate-+r- 56.1%

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

   8. Simplified 56.1%

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

   9. Taylor expanded in KbT around inf 27.9%

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

       1. associate-+r+ 27.9%

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

   11. Simplified 27.9%

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

   12. Taylor expanded in mu around 0 29.5%

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

       1. +-commutative 29.5%

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

   14. Simplified 29.5%

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

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{NaChar}{2 - \frac{\left(\left(mu - Vef\right) - Ev\right) - EAccept}{KbT}} + \frac{NdChar}{\left(\left(2 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;Ev \leq -1.02 \cdot 10^{-210}:\\ \;\;\;\;\frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef - mu}{KbT}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{2 - \frac{\left(\left(mu - Vef\right) - Ev\right) - EAccept}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.2% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq -1.55 \cdot 10^{+168}:\\ \;\;\;\;\frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef - mu}{KbT}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{2 - \frac{\left(\left(mu - Vef\right) - Ev\right) - EAccept}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ec -1.55e+168)
   (/ NaChar (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ (- Vef mu) KbT)))))
   (+
    (/ NdChar (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)))
    (/ NaChar (- 2.0 (/ (- (- (- mu Vef) Ev) 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 (Ec <= -1.55e+168) {
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))));
	} else {
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + (NaChar / (2.0 - ((((mu - Vef) - Ev) - 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 (ec <= (-1.55d+168)) then
        tmp = nachar / (2.0d0 + ((eaccept / kbt) + ((ev / kbt) + ((vef - mu) / kbt))))
    else
        tmp = (ndchar / ((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt))) + (nachar / (2.0d0 - ((((mu - vef) - ev) - 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 (Ec <= -1.55e+168) {
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))));
	} else {
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ec <= -1.55e+168:
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))))
	else:
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ec <= -1.55e+168)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Float64(Vef - mu) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT))) + Float64(NaChar / Float64(2.0 - Float64(Float64(Float64(Float64(mu - Vef) - Ev) - EAccept) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ec <= -1.55e+168)
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))));
	else
		tmp = (NdChar / ((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT))) + (NaChar / (2.0 - ((((mu - Vef) - Ev) - EAccept) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ec, -1.55e+168], N[(NaChar / N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(N[(Vef - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(2.0 - N[(N[(N[(N[(mu - Vef), $MachinePrecision] - Ev), $MachinePrecision] - EAccept), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < -1.54999999999999998e168

   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%

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

   5. Taylor expanded in EAccept around 0 81.4%

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

   6. Taylor expanded in KbT around -inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. distribute-lft-out 57.5%

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

      3. associate--l+ 57.5%

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

      4. mul-1-neg 57.5%

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

      5. associate--l+ 57.5%

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

      6. associate-+r- 57.5%

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

   8. Simplified 57.5%

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

   9. Taylor expanded in NdChar around 0 27.4%

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

       1. associate--l+ 27.4%

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

       2. associate--l+ 27.4%

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

       3. associate--l+ 27.4%

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

       4. div-sub 27.5%

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

   11. Simplified 27.5%

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

   if -1.54999999999999998e168 < Ec

   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%

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

   5. Taylor expanded in EAccept around 0 74.3%

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

   6. Taylor expanded in KbT around -inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. distribute-lft-out 60.9%

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

      3. associate--l+ 60.9%

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

      4. mul-1-neg 60.9%

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

      5. associate--l+ 60.9%

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

      6. associate-+r- 60.9%

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

   8. Simplified 60.9%

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

   9. Taylor expanded in KbT around inf 32.7%

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

       1. associate-+r+ 32.7%

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

   11. Simplified 32.7%

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

   12. Taylor expanded in mu around 0 33.5%

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

       1. +-commutative 33.5%

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

   14. Simplified 33.5%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -1.55 \cdot 10^{+168}:\\ \;\;\;\;\frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef - mu}{KbT}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{2 - \frac{\left(\left(mu - Vef\right) - Ev\right) - EAccept}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.8% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{if}\;KbT \leq -6 \cdot 10^{+87}:\\ \;\;\;\;t\_0 + 0.25 \cdot \left(mu \cdot \frac{NaChar - NdChar}{KbT}\right)\\ \mathbf{elif}\;KbT \leq 2.35 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef - mu}{KbT}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar))))
   (if (<= KbT -6e+87)
     (+ t_0 (* 0.25 (* mu (/ (- NaChar NdChar) KbT))))
     (if (<= KbT 2.35e-20)
       (/ NaChar (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ (- Vef mu) KbT)))))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -6e+87) {
		tmp = t_0 + (0.25 * (mu * ((NaChar - NdChar) / KbT)));
	} else if (KbT <= 2.35e-20) {
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / 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 = 0.5d0 * (ndchar + nachar)
    if (kbt <= (-6d+87)) then
        tmp = t_0 + (0.25d0 * (mu * ((nachar - ndchar) / kbt)))
    else if (kbt <= 2.35d-20) then
        tmp = nachar / (2.0d0 + ((eaccept / kbt) + ((ev / kbt) + ((vef - mu) / kbt))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -6e+87) {
		tmp = t_0 + (0.25 * (mu * ((NaChar - NdChar) / KbT)));
	} else if (KbT <= 2.35e-20) {
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	tmp = 0
	if KbT <= -6e+87:
		tmp = t_0 + (0.25 * (mu * ((NaChar - NdChar) / KbT)))
	elif KbT <= 2.35e-20:
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	tmp = 0.0
	if (KbT <= -6e+87)
		tmp = Float64(t_0 + Float64(0.25 * Float64(mu * Float64(Float64(NaChar - NdChar) / KbT))));
	elseif (KbT <= 2.35e-20)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Float64(Vef - mu) / KbT)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	tmp = 0.0;
	if (KbT <= -6e+87)
		tmp = t_0 + (0.25 * (mu * ((NaChar - NdChar) / KbT)));
	elseif (KbT <= 2.35e-20)
		tmp = NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + ((Vef - mu) / KbT))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -6e+87], N[(t$95$0 + N[(0.25 * N[(mu * N[(N[(NaChar - NdChar), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.35e-20], N[(NaChar / N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(N[(Vef - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -5.9999999999999998e87

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in KbT around inf 30.3%

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

   7. Simplified 30.3%

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

   8. Taylor expanded in mu around inf 39.9%

      \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{0.25 \cdot \frac{mu \cdot \left(NdChar + -1 \cdot NaChar\right)}{KbT}} \]
   9. Step-by-step derivation

      1. associate-/l* 49.6%

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

      2. +-commutative 49.6%

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

      3. mul-1-neg 49.6%

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

   10. Simplified 49.6%

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

   if -5.9999999999999998e87 < KbT < 2.35000000000000007e-20

   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%

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

   5. Taylor expanded in EAccept around 0 70.0%

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

   6. Taylor expanded in KbT around -inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. distribute-lft-out 56.0%

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

      3. associate--l+ 56.0%

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

      4. mul-1-neg 56.0%

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

      5. associate--l+ 56.0%

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

      6. associate-+r- 56.0%

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

   8. Simplified 56.0%

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

   9. Taylor expanded in NdChar around 0 23.4%

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

       1. associate--l+ 23.4%

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

       2. associate--l+ 23.4%

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

       3. associate--l+ 23.4%

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

       4. div-sub 23.5%

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

   11. Simplified 23.5%

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

   if 2.35000000000000007e-20 < 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%

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

   5. Taylor expanded in KbT around inf 40.6%

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

      1. distribute-lft-out 40.6%

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

   7. Simplified 40.6%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -6 \cdot 10^{+87}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) + 0.25 \cdot \left(mu \cdot \frac{NaChar - NdChar}{KbT}\right)\\ \mathbf{elif}\;KbT \leq 2.35 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef - mu}{KbT}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.1% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -3.2 \cdot 10^{+126} \lor \neg \left(NaChar \leq 7 \cdot 10^{-50}\right):\\ \;\;\;\;NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -3.2e+126) (not (<= NaChar 7e-50)))
   (* NaChar 0.5)
   (* NdChar 0.5)))

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 <= -3.2e+126) || !(NaChar <= 7e-50)) {
		tmp = NaChar * 0.5;
	} else {
		tmp = NdChar * 0.5;
	}
	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 <= (-3.2d+126)) .or. (.not. (nachar <= 7d-50))) then
        tmp = nachar * 0.5d0
    else
        tmp = ndchar * 0.5d0
    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 <= -3.2e+126) || !(NaChar <= 7e-50)) {
		tmp = NaChar * 0.5;
	} else {
		tmp = NdChar * 0.5;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -3.2e+126) or not (NaChar <= 7e-50):
		tmp = NaChar * 0.5
	else:
		tmp = NdChar * 0.5
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -3.2e+126) || !(NaChar <= 7e-50))
		tmp = Float64(NaChar * 0.5);
	else
		tmp = Float64(NdChar * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -3.2e+126) || ~((NaChar <= 7e-50)))
		tmp = NaChar * 0.5;
	else
		tmp = NdChar * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -3.2e+126], N[Not[LessEqual[NaChar, 7e-50]], $MachinePrecision]], N[(NaChar * 0.5), $MachinePrecision], N[(NdChar * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -3.1999999999999998e126 or 6.99999999999999993e-50 < NaChar

   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%

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

   5. Taylor expanded in KbT around inf 30.9%

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

      1. distribute-lft-out 30.9%

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

   7. Simplified 30.9%

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

   8. Taylor expanded in NaChar around inf 28.7%

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

   if -3.1999999999999998e126 < NaChar < 6.99999999999999993e-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%

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

   5. Taylor expanded in KbT around inf 25.4%

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

      1. distribute-lft-out 25.4%

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

   7. Simplified 25.4%

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

   8. Taylor expanded in NaChar around 0 22.6%

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

      1. *-commutative 22.6%

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

   10. Simplified 22.6%

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

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.2 \cdot 10^{+126} \lor \neg \left(NaChar \leq 7 \cdot 10^{-50}\right):\\ \;\;\;\;NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.3% 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 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%

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

5. Taylor expanded in KbT around inf 27.7%

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

   1. distribute-lft-out 27.7%

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

7. Simplified 27.7%

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

8. Final simplification 27.7%

   \[\leadsto 0.5 \cdot \left(NdChar + NaChar\right) \]
9. Add Preprocessing

Alternative 21: 18.1% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

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 = nachar * 0.5d0
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 NaChar * 0.5;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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%

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

5. Taylor expanded in KbT around inf 27.7%

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

   1. distribute-lft-out 27.7%

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

7. Simplified 27.7%

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

8. Taylor expanded in NaChar around inf 18.7%

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

9. Final simplification 18.7%

   \[\leadsto NaChar \cdot 0.5 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024188 
(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))))))