Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 34.1s

Alternatives: 25

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 67.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ t_1 := \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + t\_0\\ t_2 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ t_3 := \frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + t\_0\\ \mathbf{if}\;Ec \leq -5 \cdot 10^{+117}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;Ec \leq -8.4 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Ec \leq -5.4 \cdot 10^{-128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Ec \leq 8.5 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Ec \leq 2.35 \cdot 10^{-63}:\\ \;\;\;\;t\_2 + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq 3.5 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0)))
        (t_1 (+ (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) t_0))
        (t_2 (/ NdChar (+ (exp (/ mu KbT)) 1.0)))
        (t_3 (+ (/ NdChar (+ (exp (- (/ Ec KbT))) 1.0)) t_0)))
   (if (<= Ec -5e+117)
     t_3
     (if (<= Ec -8.4e-75)
       t_1
       (if (<= Ec -5.4e-128)
         t_2
         (if (<= Ec 8.5e-248)
           t_1
           (if (<= Ec 2.35e-63)
             (+ t_2 (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)))
             (if (<= Ec 3.5e+94) t_1 t_3))))))))

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 / (exp((((Vef + Ev) - mu) / KbT)) + 1.0);
	double t_1 = (NdChar / (exp((Vef / KbT)) + 1.0)) + t_0;
	double t_2 = NdChar / (exp((mu / KbT)) + 1.0);
	double t_3 = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + t_0;
	double tmp;
	if (Ec <= -5e+117) {
		tmp = t_3;
	} else if (Ec <= -8.4e-75) {
		tmp = t_1;
	} else if (Ec <= -5.4e-128) {
		tmp = t_2;
	} else if (Ec <= 8.5e-248) {
		tmp = t_1;
	} else if (Ec <= 2.35e-63) {
		tmp = t_2 + (NaChar / (exp((EAccept / KbT)) + 1.0));
	} else if (Ec <= 3.5e+94) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0)
    t_1 = (ndchar / (exp((vef / kbt)) + 1.0d0)) + t_0
    t_2 = ndchar / (exp((mu / kbt)) + 1.0d0)
    t_3 = (ndchar / (exp(-(ec / kbt)) + 1.0d0)) + t_0
    if (ec <= (-5d+117)) then
        tmp = t_3
    else if (ec <= (-8.4d-75)) then
        tmp = t_1
    else if (ec <= (-5.4d-128)) then
        tmp = t_2
    else if (ec <= 8.5d-248) then
        tmp = t_1
    else if (ec <= 2.35d-63) then
        tmp = t_2 + (nachar / (exp((eaccept / kbt)) + 1.0d0))
    else if (ec <= 3.5d+94) then
        tmp = t_1
    else
        tmp = t_3
    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 / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0);
	double t_1 = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + t_0;
	double t_2 = NdChar / (Math.exp((mu / KbT)) + 1.0);
	double t_3 = (NdChar / (Math.exp(-(Ec / KbT)) + 1.0)) + t_0;
	double tmp;
	if (Ec <= -5e+117) {
		tmp = t_3;
	} else if (Ec <= -8.4e-75) {
		tmp = t_1;
	} else if (Ec <= -5.4e-128) {
		tmp = t_2;
	} else if (Ec <= 8.5e-248) {
		tmp = t_1;
	} else if (Ec <= 2.35e-63) {
		tmp = t_2 + (NaChar / (Math.exp((EAccept / KbT)) + 1.0));
	} else if (Ec <= 3.5e+94) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)
	t_1 = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + t_0
	t_2 = NdChar / (math.exp((mu / KbT)) + 1.0)
	t_3 = (NdChar / (math.exp(-(Ec / KbT)) + 1.0)) + t_0
	tmp = 0
	if Ec <= -5e+117:
		tmp = t_3
	elif Ec <= -8.4e-75:
		tmp = t_1
	elif Ec <= -5.4e-128:
		tmp = t_2
	elif Ec <= 8.5e-248:
		tmp = t_1
	elif Ec <= 2.35e-63:
		tmp = t_2 + (NaChar / (math.exp((EAccept / KbT)) + 1.0))
	elif Ec <= 3.5e+94:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + t_0)
	t_2 = Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0))
	t_3 = Float64(Float64(NdChar / Float64(exp(Float64(-Float64(Ec / KbT))) + 1.0)) + t_0)
	tmp = 0.0
	if (Ec <= -5e+117)
		tmp = t_3;
	elseif (Ec <= -8.4e-75)
		tmp = t_1;
	elseif (Ec <= -5.4e-128)
		tmp = t_2;
	elseif (Ec <= 8.5e-248)
		tmp = t_1;
	elseif (Ec <= 2.35e-63)
		tmp = Float64(t_2 + Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)));
	elseif (Ec <= 3.5e+94)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0);
	t_1 = (NdChar / (exp((Vef / KbT)) + 1.0)) + t_0;
	t_2 = NdChar / (exp((mu / KbT)) + 1.0);
	t_3 = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + t_0;
	tmp = 0.0;
	if (Ec <= -5e+117)
		tmp = t_3;
	elseif (Ec <= -8.4e-75)
		tmp = t_1;
	elseif (Ec <= -5.4e-128)
		tmp = t_2;
	elseif (Ec <= 8.5e-248)
		tmp = t_1;
	elseif (Ec <= 2.35e-63)
		tmp = t_2 + (NaChar / (exp((EAccept / KbT)) + 1.0));
	elseif (Ec <= 3.5e+94)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NdChar / N[(N[Exp[(-N[(Ec / KbT), $MachinePrecision])], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]}, If[LessEqual[Ec, -5e+117], t$95$3, If[LessEqual[Ec, -8.4e-75], t$95$1, If[LessEqual[Ec, -5.4e-128], t$95$2, If[LessEqual[Ec, 8.5e-248], t$95$1, If[LessEqual[Ec, 2.35e-63], N[(t$95$2 + N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 3.5e+94], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ec < -4.99999999999999983e117 or 3.4999999999999997e94 < Ec

   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 Ec around inf 93.4%

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

      1. associate-*r/ 93.4%

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

      2. mul-1-neg 93.4%

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

   7. Simplified 93.4%

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

   8. Taylor expanded in EAccept around 0 88.8%

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

   if -4.99999999999999983e117 < Ec < -8.4000000000000004e-75 or -5.40000000000000011e-128 < Ec < 8.5000000000000003e-248 or 2.35e-63 < Ec < 3.4999999999999997e94

   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 Vef around inf 84.1%

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

   6. Taylor expanded in EAccept around 0 81.2%

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

   if -8.4000000000000004e-75 < Ec < -5.40000000000000011e-128

   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 mu around inf 88.4%

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

   6. Taylor expanded in KbT around inf 59.8%

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

   7. Taylor expanded in Vef around inf 2.6%

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

   8. Taylor expanded in NdChar around inf 81.6%

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

   if 8.5000000000000003e-248 < Ec < 2.35e-63

   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 mu around inf 87.4%

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

   6. Taylor expanded in EAccept around inf 69.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -5 \cdot 10^{+117}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq -8.4 \cdot 10^{-75}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq -5.4 \cdot 10^{-128}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq 8.5 \cdot 10^{-248}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq 2.35 \cdot 10^{-63}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq 3.5 \cdot 10^{+94}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ t_1 := \frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Ec \leq -1.52 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Ec \leq -1.12 \cdot 10^{-92}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Ec \leq -1.16 \cdot 10^{-127}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ec \leq 2.5 \cdot 10^{+87}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)) 1.0))
          (/ NdChar (+ (exp (/ Vef KbT)) 1.0))))
        (t_1
         (+
          (/ NdChar (+ (exp (- (/ Ec KbT))) 1.0))
          (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0)))))
   (if (<= Ec -1.52e+121)
     t_1
     (if (<= Ec -1.12e-92)
       t_0
       (if (<= Ec -1.16e-127)
         (-
          (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
          (/ NdChar (- -1.0 (exp (/ mu KbT)))))
         (if (<= Ec 2.5e+87) t_0 t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	double t_1 = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	double tmp;
	if (Ec <= -1.52e+121) {
		tmp = t_1;
	} else if (Ec <= -1.12e-92) {
		tmp = t_0;
	} else if (Ec <= -1.16e-127) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - exp((mu / KbT))));
	} else if (Ec <= 2.5e+87) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / (exp(((vef - ((mu - eaccept) - ev)) / kbt)) + 1.0d0)) + (ndchar / (exp((vef / kbt)) + 1.0d0))
    t_1 = (ndchar / (exp(-(ec / kbt)) + 1.0d0)) + (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0))
    if (ec <= (-1.52d+121)) then
        tmp = t_1
    else if (ec <= (-1.12d-92)) then
        tmp = t_0
    else if (ec <= (-1.16d-127)) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) - (ndchar / ((-1.0d0) - exp((mu / kbt))))
    else if (ec <= 2.5d+87) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0)) + (NdChar / (Math.exp((Vef / KbT)) + 1.0));
	double t_1 = (NdChar / (Math.exp(-(Ec / KbT)) + 1.0)) + (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	double tmp;
	if (Ec <= -1.52e+121) {
		tmp = t_1;
	} else if (Ec <= -1.12e-92) {
		tmp = t_0;
	} else if (Ec <= -1.16e-127) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp((mu / KbT))));
	} else if (Ec <= 2.5e+87) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0)) + (NdChar / (math.exp((Vef / KbT)) + 1.0))
	t_1 = (NdChar / (math.exp(-(Ec / KbT)) + 1.0)) + (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0))
	tmp = 0
	if Ec <= -1.52e+121:
		tmp = t_1
	elif Ec <= -1.12e-92:
		tmp = t_0
	elif Ec <= -1.16e-127:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - math.exp((mu / KbT))))
	elif Ec <= 2.5e+87:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(-Float64(Ec / KbT))) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)))
	tmp = 0.0
	if (Ec <= -1.52e+121)
		tmp = t_1;
	elseif (Ec <= -1.12e-92)
		tmp = t_0;
	elseif (Ec <= -1.16e-127)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(mu / KbT)))));
	elseif (Ec <= 2.5e+87)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	t_1 = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	tmp = 0.0;
	if (Ec <= -1.52e+121)
		tmp = t_1;
	elseif (Ec <= -1.12e-92)
		tmp = t_0;
	elseif (Ec <= -1.16e-127)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - exp((mu / KbT))));
	elseif (Ec <= 2.5e+87)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[(-N[(Ec / KbT), $MachinePrecision])], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ec, -1.52e+121], t$95$1, If[LessEqual[Ec, -1.12e-92], t$95$0, If[LessEqual[Ec, -1.16e-127], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 2.5e+87], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if Ec < -1.5199999999999999e121 or 2.4999999999999999e87 < Ec

   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 Ec around inf 93.4%

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

      1. associate-*r/ 93.4%

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

      2. mul-1-neg 93.4%

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

   7. Simplified 93.4%

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

   8. Taylor expanded in EAccept around 0 88.8%

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

   if -1.5199999999999999e121 < Ec < -1.11999999999999999e-92 or -1.16e-127 < Ec < 2.4999999999999999e87

   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 Vef around inf 80.1%

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

   if -1.11999999999999999e-92 < Ec < -1.16e-127

   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 mu around inf 92.6%

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

   6. Taylor expanded in Ev around inf 74.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -1.52 \cdot 10^{+121}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq -1.12 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq -1.16 \cdot 10^{-127}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ec \leq 2.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := \frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} - t\_0\\ \mathbf{if}\;Ec \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Ec \leq -3.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq 1.55 \cdot 10^{+149}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (- -1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1 (- (/ NdChar (+ (exp (- (/ Ec KbT))) 1.0)) t_0)))
   (if (<= Ec -1.6e+119)
     t_1
     (if (<= Ec -3.9e-69)
       (+
        (/ NdChar (+ (exp (/ Vef KbT)) 1.0))
        (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0)))
       (if (<= Ec 1.55e+149)
         (- (/ NdChar (+ (exp (/ mu KbT)) 1.0)) t_0)
         t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = (NdChar / (exp(-(Ec / KbT)) + 1.0)) - t_0;
	double tmp;
	if (Ec <= -1.6e+119) {
		tmp = t_1;
	} else if (Ec <= -3.9e-69) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else if (Ec <= 1.55e+149) {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) - t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / ((-1.0d0) - exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = (ndchar / (exp(-(ec / kbt)) + 1.0d0)) - t_0
    if (ec <= (-1.6d+119)) then
        tmp = t_1
    else if (ec <= (-3.9d-69)) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0))
    else if (ec <= 1.55d+149) then
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) - t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (-1.0 - Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = (NdChar / (Math.exp(-(Ec / KbT)) + 1.0)) - t_0;
	double tmp;
	if (Ec <= -1.6e+119) {
		tmp = t_1;
	} else if (Ec <= -3.9e-69) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else if (Ec <= 1.55e+149) {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) - t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (-1.0 - math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = (NdChar / (math.exp(-(Ec / KbT)) + 1.0)) - t_0
	tmp = 0
	if Ec <= -1.6e+119:
		tmp = t_1
	elif Ec <= -3.9e-69:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0))
	elif Ec <= 1.55e+149:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) - t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(-Float64(Ec / KbT))) + 1.0)) - t_0)
	tmp = 0.0
	if (Ec <= -1.6e+119)
		tmp = t_1;
	elseif (Ec <= -3.9e-69)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)));
	elseif (Ec <= 1.55e+149)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) - t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = (NdChar / (exp(-(Ec / KbT)) + 1.0)) - t_0;
	tmp = 0.0;
	if (Ec <= -1.6e+119)
		tmp = t_1;
	elseif (Ec <= -3.9e-69)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	elseif (Ec <= 1.55e+149)
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) - t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[(-N[(Ec / KbT), $MachinePrecision])], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[Ec, -1.6e+119], t$95$1, If[LessEqual[Ec, -3.9e-69], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 1.55e+149], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if Ec < -1.59999999999999995e119 or 1.54999999999999993e149 < Ec

   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 Ec around inf 96.1%

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

      1. associate-*r/ 96.1%

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

      2. mul-1-neg 96.1%

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

   7. Simplified 96.1%

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

   if -1.59999999999999995e119 < Ec < -3.89999999999999981e-69

   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 Vef around inf 84.3%

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

   6. Taylor expanded in EAccept around 0 84.3%

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

   if -3.89999999999999981e-69 < Ec < 1.54999999999999993e149

   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 mu around inf 83.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{elif}\;Ec \leq -3.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ec \leq 1.55 \cdot 10^{+149}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef}{KbT}} + 1\\ t_1 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ t_2 := \frac{NdChar}{2 + \frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -6 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq 5.8 \cdot 10^{-264}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq 6.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{NdChar}{t\_0} + \frac{NaChar}{t\_0}\\ \mathbf{elif}\;mu \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (exp (/ Vef KbT)) 1.0))
        (t_1
         (+
          (/ NdChar (+ (exp (/ mu KbT)) 1.0))
          (/ NaChar (+ (exp (/ mu (- KbT))) 1.0))))
        (t_2
         (-
          (/ NdChar (+ 2.0 (/ (- EDonor (- (- Ec Vef) mu)) KbT)))
          (/ NaChar (- -1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))))
   (if (<= mu -6e+52)
     t_1
     (if (<= mu 5.8e-264)
       t_2
       (if (<= mu 6.4e-55)
         (+ (/ NdChar t_0) (/ NaChar t_0))
         (if (<= mu 4.5e+150) t_2 t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp((Vef / KbT)) + 1.0;
	double t_1 = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / (exp((mu / -KbT)) + 1.0));
	double t_2 = (NdChar / (2.0 + ((EDonor - ((Ec - Vef) - mu)) / KbT))) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	double tmp;
	if (mu <= -6e+52) {
		tmp = t_1;
	} else if (mu <= 5.8e-264) {
		tmp = t_2;
	} else if (mu <= 6.4e-55) {
		tmp = (NdChar / t_0) + (NaChar / t_0);
	} else if (mu <= 4.5e+150) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = exp((vef / kbt)) + 1.0d0
    t_1 = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (nachar / (exp((mu / -kbt)) + 1.0d0))
    t_2 = (ndchar / (2.0d0 + ((edonor - ((ec - vef) - mu)) / kbt))) - (nachar / ((-1.0d0) - exp(((vef - ((mu - eaccept) - ev)) / kbt))))
    if (mu <= (-6d+52)) then
        tmp = t_1
    else if (mu <= 5.8d-264) then
        tmp = t_2
    else if (mu <= 6.4d-55) then
        tmp = (ndchar / t_0) + (nachar / t_0)
    else if (mu <= 4.5d+150) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp((Vef / KbT)) + 1.0;
	double t_1 = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar / (Math.exp((mu / -KbT)) + 1.0));
	double t_2 = (NdChar / (2.0 + ((EDonor - ((Ec - Vef) - mu)) / KbT))) - (NaChar / (-1.0 - Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	double tmp;
	if (mu <= -6e+52) {
		tmp = t_1;
	} else if (mu <= 5.8e-264) {
		tmp = t_2;
	} else if (mu <= 6.4e-55) {
		tmp = (NdChar / t_0) + (NaChar / t_0);
	} else if (mu <= 4.5e+150) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp((Vef / KbT)) + 1.0
	t_1 = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar / (math.exp((mu / -KbT)) + 1.0))
	t_2 = (NdChar / (2.0 + ((EDonor - ((Ec - Vef) - mu)) / KbT))) - (NaChar / (-1.0 - math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))))
	tmp = 0
	if mu <= -6e+52:
		tmp = t_1
	elif mu <= 5.8e-264:
		tmp = t_2
	elif mu <= 6.4e-55:
		tmp = (NdChar / t_0) + (NaChar / t_0)
	elif mu <= 4.5e+150:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(exp(Float64(Vef / KbT)) + 1.0)
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0)))
	t_2 = Float64(Float64(NdChar / Float64(2.0 + Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))))
	tmp = 0.0
	if (mu <= -6e+52)
		tmp = t_1;
	elseif (mu <= 5.8e-264)
		tmp = t_2;
	elseif (mu <= 6.4e-55)
		tmp = Float64(Float64(NdChar / t_0) + Float64(NaChar / t_0));
	elseif (mu <= 4.5e+150)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp((Vef / KbT)) + 1.0;
	t_1 = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / (exp((mu / -KbT)) + 1.0));
	t_2 = (NdChar / (2.0 + ((EDonor - ((Ec - Vef) - mu)) / KbT))) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	tmp = 0.0;
	if (mu <= -6e+52)
		tmp = t_1;
	elseif (mu <= 5.8e-264)
		tmp = t_2;
	elseif (mu <= 6.4e-55)
		tmp = (NdChar / t_0) + (NaChar / t_0);
	elseif (mu <= 4.5e+150)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(2.0 + N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -6e+52], t$95$1, If[LessEqual[mu, 5.8e-264], t$95$2, If[LessEqual[mu, 6.4e-55], N[(N[(NdChar / t$95$0), $MachinePrecision] + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 4.5e+150], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -6e52 or 4.5e150 < mu

   1. Initial program 100.0%

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

   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 mu around inf 88.9%

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

   6. Taylor expanded in mu around inf 77.1%

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

      1. associate-*r/ 77.1%

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

      2. mul-1-neg 77.1%

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

   8. Simplified 77.1%

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

   if -6e52 < mu < 5.7999999999999997e-264 or 6.4000000000000003e-55 < mu < 4.5e150

   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 60.8%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + -1 \cdot \frac{-1 \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right) + -1 \cdot \frac{0.16666666666666666 \cdot \frac{{\left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}^{3}}{KbT} + 0.5 \cdot {\left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}^{2}}{KbT}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 73.6%

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

      1. associate-*r/ 73.6%

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

      2. mul-1-neg 73.6%

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

      3. +-commutative 73.6%

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

      4. associate-+r- 73.6%

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

      5. +-commutative 73.6%

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

      6. associate--l+ 73.6%

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

   8. Simplified 73.6%

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

   if 5.7999999999999997e-264 < mu < 6.4000000000000003e-55

   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 Vef around inf 88.5%

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

   6. Taylor expanded in EAccept around 0 83.6%

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

   7. Taylor expanded in Vef around inf 83.6%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -6 \cdot 10^{+52}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{elif}\;mu \leq 5.8 \cdot 10^{-264}:\\ \;\;\;\;\frac{NdChar}{2 + \frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 6.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;mu \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{NdChar}{2 + \frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}\\ \mathbf{if}\;Vef \leq -2.45 \cdot 10^{+126} \lor \neg \left(Vef \leq 1.02 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{NaChar}{t\_0 + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
   (if (or (<= Vef -2.45e+126) (not (<= Vef 1.02e+102)))
     (+ (/ NaChar (+ t_0 1.0)) (/ NdChar (+ (exp (/ Vef KbT)) 1.0)))
     (- (/ NdChar (+ (exp (/ mu KbT)) 1.0)) (/ NaChar (- -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 = exp(((Vef - ((mu - EAccept) - Ev)) / KbT));
	double tmp;
	if ((Vef <= -2.45e+126) || !(Vef <= 1.02e+102)) {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-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 = exp(((vef - ((mu - eaccept) - ev)) / kbt))
    if ((vef <= (-2.45d+126)) .or. (.not. (vef <= 1.02d+102))) then
        tmp = (nachar / (t_0 + 1.0d0)) + (ndchar / (exp((vef / kbt)) + 1.0d0))
    else
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) - (nachar / ((-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 = Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT));
	double tmp;
	if ((Vef <= -2.45e+126) || !(Vef <= 1.02e+102)) {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (Math.exp((Vef / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))
	tmp = 0
	if (Vef <= -2.45e+126) or not (Vef <= 1.02e+102):
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (math.exp((Vef / KbT)) + 1.0))
	else:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))
	tmp = 0.0
	if ((Vef <= -2.45e+126) || !(Vef <= 1.02e+102))
		tmp = Float64(Float64(NaChar / Float64(t_0 + 1.0)) + Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) - Float64(NaChar / Float64(-1.0 - t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((Vef - ((mu - EAccept) - Ev)) / KbT));
	tmp = 0.0;
	if ((Vef <= -2.45e+126) || ~((Vef <= 1.02e+102)))
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	else
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-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[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[Vef, -2.45e+126], N[Not[LessEqual[Vef, 1.02e+102]], $MachinePrecision]], N[(N[(NaChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if Vef < -2.45e126 or 1.01999999999999999e102 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 89.0%

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

   if -2.45e126 < Vef < 1.01999999999999999e102

   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 mu around inf 83.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.45 \cdot 10^{+126} \lor \neg \left(Vef \leq 1.02 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -3.3 \cdot 10^{-171} \lor \neg \left(Vef \leq 4.8 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Vef -3.3e-171) (not (<= Vef 4.8e-67)))
   (+
    (/ NdChar (+ (exp (/ Vef KbT)) 1.0))
    (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0)))
   (+
    (/ NdChar (+ (exp (/ mu KbT)) 1.0))
    (/ NaChar (+ (exp (/ 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 ((Vef <= -3.3e-171) || !(Vef <= 4.8e-67)) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / (exp((mu / -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 ((vef <= (-3.3d-171)) .or. (.not. (vef <= 4.8d-67))) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0))
    else
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (nachar / (exp((mu / -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 ((Vef <= -3.3e-171) || !(Vef <= 4.8e-67)) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar / (Math.exp((mu / -KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Vef <= -3.3e-171) or not (Vef <= 4.8e-67):
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0))
	else:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar / (math.exp((mu / -KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Vef <= -3.3e-171) || !(Vef <= 4.8e-67))
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(mu / Float64(-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 ((Vef <= -3.3e-171) || ~((Vef <= 4.8e-67)))
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	else
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / (exp((mu / -KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Vef, -3.3e-171], N[Not[LessEqual[Vef, 4.8e-67]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -3.3000000000000002e-171 or 4.8e-67 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 81.0%

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

   6. Taylor expanded in EAccept around 0 76.0%

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

   if -3.3000000000000002e-171 < Vef < 4.8e-67

   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 mu around inf 85.3%

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

   6. Taylor expanded in mu around inf 75.2%

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

      1. associate-*r/ 75.2%

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

      2. mul-1-neg 75.2%

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

   8. Simplified 75.2%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.3 \cdot 10^{-171} \lor \neg \left(Vef \leq 4.8 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}\\ \mathbf{if}\;NdChar \leq -1.6 \cdot 10^{-56}:\\ \;\;\;\;\frac{NdChar}{e^{t\_0} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;\frac{NdChar}{2 + t\_0} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ (- EDonor (- (- Ec Vef) mu)) KbT)))
   (if (<= NdChar -1.6e-56)
     (+ (/ NdChar (+ (exp t_0) 1.0)) (/ NaChar (+ (/ Ev KbT) 2.0)))
     (if (<= NdChar 1.1e+79)
       (-
        (/ NdChar (+ 2.0 t_0))
        (/ NaChar (- -1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
       (+
        (/ NdChar (+ (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 t_0 = (EDonor - ((Ec - Vef) - mu)) / KbT;
	double tmp;
	if (NdChar <= -1.6e-56) {
		tmp = (NdChar / (exp(t_0) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= 1.1e+79) {
		tmp = (NdChar / (2.0 + t_0)) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	} else {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (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) :: t_0
    real(8) :: tmp
    t_0 = (edonor - ((ec - vef) - mu)) / kbt
    if (ndchar <= (-1.6d-56)) then
        tmp = (ndchar / (exp(t_0) + 1.0d0)) + (nachar / ((ev / kbt) + 2.0d0))
    else if (ndchar <= 1.1d+79) then
        tmp = (ndchar / (2.0d0 + t_0)) - (nachar / ((-1.0d0) - exp(((vef - ((mu - eaccept) - ev)) / kbt))))
    else
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (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 t_0 = (EDonor - ((Ec - Vef) - mu)) / KbT;
	double tmp;
	if (NdChar <= -1.6e-56) {
		tmp = (NdChar / (Math.exp(t_0) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= 1.1e+79) {
		tmp = (NdChar / (2.0 + t_0)) - (NaChar / (-1.0 - Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	} else {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar / (Math.exp((EAccept / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (EDonor - ((Ec - Vef) - mu)) / KbT
	tmp = 0
	if NdChar <= -1.6e-56:
		tmp = (NdChar / (math.exp(t_0) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0))
	elif NdChar <= 1.1e+79:
		tmp = (NdChar / (2.0 + t_0)) - (NaChar / (-1.0 - math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))))
	else:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar / (math.exp((EAccept / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)
	tmp = 0.0
	if (NdChar <= -1.6e-56)
		tmp = Float64(Float64(NdChar / Float64(exp(t_0) + 1.0)) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (NdChar <= 1.1e+79)
		tmp = Float64(Float64(NdChar / Float64(2.0 + t_0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + 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)
	t_0 = (EDonor - ((Ec - Vef) - mu)) / KbT;
	tmp = 0.0;
	if (NdChar <= -1.6e-56)
		tmp = (NdChar / (exp(t_0) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	elseif (NdChar <= 1.1e+79)
		tmp = (NdChar / (2.0 + t_0)) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	else
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / (exp((EAccept / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]}, If[LessEqual[NdChar, -1.6e-56], N[(N[(NdChar / N[(N[Exp[t$95$0], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.1e+79], N[(N[(NdChar / N[(2.0 + t$95$0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 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]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -1.59999999999999993e-56

   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 75.4%

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

   6. Taylor expanded in Ev around 0 67.2%

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

   if -1.59999999999999993e-56 < NdChar < 1.0999999999999999e79

   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 62.3%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + -1 \cdot \frac{-1 \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right) + -1 \cdot \frac{0.16666666666666666 \cdot \frac{{\left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}^{3}}{KbT} + 0.5 \cdot {\left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}^{2}}{KbT}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 77.1%

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

      1. associate-*r/ 77.1%

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

      2. mul-1-neg 77.1%

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

      3. +-commutative 77.1%

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

      4. associate-+r- 77.1%

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

      5. +-commutative 77.1%

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

      6. associate--l+ 77.1%

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

   8. Simplified 77.1%

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

   if 1.0999999999999999e79 < NdChar

   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 mu around inf 68.2%

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

   6. Taylor expanded in EAccept around inf 50.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.6 \cdot 10^{-56}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;\frac{NdChar}{2 + \frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{mu}{KbT}}\\ t_1 := \frac{NdChar}{t\_0 + 1}\\ \mathbf{if}\;NdChar \leq -2.1 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -1.15 \cdot 10^{+194}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 1} - \frac{NdChar}{-1 - t\_0}\\ \mathbf{elif}\;NdChar \leq 6.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ mu KbT))) (t_1 (/ NdChar (+ t_0 1.0))))
   (if (<= NdChar -2.1e+220)
     t_1
     (if (<= NdChar -1.15e+194)
       (+
        (/ NdChar (+ (exp (- (/ Ec KbT))) 1.0))
        (/ NaChar (+ (/ Vef KbT) 1.0)))
       (if (<= NdChar -5.8e-43)
         (- (/ NaChar (+ (/ Ev KbT) 1.0)) (/ NdChar (- -1.0 t_0)))
         (if (<= NdChar 6.1e+32)
           (-
            (/ NdChar 2.0)
            (/ NaChar (- -1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
           (+ t_1 (/ NaChar (+ (/ 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 t_0 = exp((mu / KbT));
	double t_1 = NdChar / (t_0 + 1.0);
	double tmp;
	if (NdChar <= -2.1e+220) {
		tmp = t_1;
	} else if (NdChar <= -1.15e+194) {
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= -5.8e-43) {
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0));
	} else if (NdChar <= 6.1e+32) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	} else {
		tmp = t_1 + (NaChar / ((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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = exp((mu / kbt))
    t_1 = ndchar / (t_0 + 1.0d0)
    if (ndchar <= (-2.1d+220)) then
        tmp = t_1
    else if (ndchar <= (-1.15d+194)) then
        tmp = (ndchar / (exp(-(ec / kbt)) + 1.0d0)) + (nachar / ((vef / kbt) + 1.0d0))
    else if (ndchar <= (-5.8d-43)) then
        tmp = (nachar / ((ev / kbt) + 1.0d0)) - (ndchar / ((-1.0d0) - t_0))
    else if (ndchar <= 6.1d+32) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef - ((mu - eaccept) - ev)) / kbt))))
    else
        tmp = t_1 + (nachar / ((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 t_0 = Math.exp((mu / KbT));
	double t_1 = NdChar / (t_0 + 1.0);
	double tmp;
	if (NdChar <= -2.1e+220) {
		tmp = t_1;
	} else if (NdChar <= -1.15e+194) {
		tmp = (NdChar / (Math.exp(-(Ec / KbT)) + 1.0)) + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= -5.8e-43) {
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0));
	} else if (NdChar <= 6.1e+32) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	} else {
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp((mu / KbT))
	t_1 = NdChar / (t_0 + 1.0)
	tmp = 0
	if NdChar <= -2.1e+220:
		tmp = t_1
	elif NdChar <= -1.15e+194:
		tmp = (NdChar / (math.exp(-(Ec / KbT)) + 1.0)) + (NaChar / ((Vef / KbT) + 1.0))
	elif NdChar <= -5.8e-43:
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0))
	elif NdChar <= 6.1e+32:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))))
	else:
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(mu / KbT))
	t_1 = Float64(NdChar / Float64(t_0 + 1.0))
	tmp = 0.0
	if (NdChar <= -2.1e+220)
		tmp = t_1;
	elseif (NdChar <= -1.15e+194)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(-Float64(Ec / KbT))) + 1.0)) + Float64(NaChar / Float64(Float64(Vef / KbT) + 1.0)));
	elseif (NdChar <= -5.8e-43)
		tmp = Float64(Float64(NaChar / Float64(Float64(Ev / KbT) + 1.0)) - Float64(NdChar / Float64(-1.0 - t_0)));
	elseif (NdChar <= 6.1e+32)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))));
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp((mu / KbT));
	t_1 = NdChar / (t_0 + 1.0);
	tmp = 0.0;
	if (NdChar <= -2.1e+220)
		tmp = t_1;
	elseif (NdChar <= -1.15e+194)
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + (NaChar / ((Vef / KbT) + 1.0));
	elseif (NdChar <= -5.8e-43)
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0));
	elseif (NdChar <= 6.1e+32)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	else
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -2.1e+220], t$95$1, If[LessEqual[NdChar, -1.15e+194], N[(N[(NdChar / N[(N[Exp[(-N[(Ec / KbT), $MachinePrecision])], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -5.8e-43], N[(N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 6.1e+32], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -2.10000000000000007e220

   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 mu around inf 75.0%

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

   6. Taylor expanded in KbT around inf 58.1%

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

   7. Taylor expanded in Vef around inf 45.2%

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

   8. Taylor expanded in NdChar around inf 62.2%

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

   if -2.10000000000000007e220 < NdChar < -1.15000000000000003e194

   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 Ec around inf 86.5%

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

      1. associate-*r/ 86.5%

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

      2. mul-1-neg 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in KbT around inf 86.5%

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

   9. Taylor expanded in Vef around inf 86.5%

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

   if -1.15000000000000003e194 < NdChar < -5.8000000000000003e-43

   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 mu around inf 73.8%

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

   6. Taylor expanded in KbT around inf 47.6%

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

   7. Taylor expanded in Ev around inf 49.7%

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

   if -5.8000000000000003e-43 < NdChar < 6.10000000000000027e32

   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 64.9%

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

   if 6.10000000000000027e32 < NdChar

   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 mu around inf 72.1%

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

   6. Taylor expanded in KbT around inf 43.9%

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

   7. Taylor expanded in EAccept around inf 57.2%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.1 \cdot 10^{+220}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;NdChar \leq -1.15 \cdot 10^{+194}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 6.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}\\ \mathbf{if}\;NdChar \leq -3.8 \cdot 10^{-61} \lor \neg \left(NdChar \leq 1.75 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{NdChar}{e^{t\_0} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 + t\_0} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ (- EDonor (- (- Ec Vef) mu)) KbT)))
   (if (or (<= NdChar -3.8e-61) (not (<= NdChar 1.75e+81)))
     (+ (/ NdChar (+ (exp t_0) 1.0)) (/ NaChar (+ (/ Ev KbT) 2.0)))
     (-
      (/ NdChar (+ 2.0 t_0))
      (/ NaChar (- -1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) 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 = (EDonor - ((Ec - Vef) - mu)) / KbT;
	double tmp;
	if ((NdChar <= -3.8e-61) || !(NdChar <= 1.75e+81)) {
		tmp = (NdChar / (exp(t_0) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else {
		tmp = (NdChar / (2.0 + t_0)) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / 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 = (edonor - ((ec - vef) - mu)) / kbt
    if ((ndchar <= (-3.8d-61)) .or. (.not. (ndchar <= 1.75d+81))) then
        tmp = (ndchar / (exp(t_0) + 1.0d0)) + (nachar / ((ev / kbt) + 2.0d0))
    else
        tmp = (ndchar / (2.0d0 + t_0)) - (nachar / ((-1.0d0) - exp(((vef - ((mu - eaccept) - ev)) / 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 = (EDonor - ((Ec - Vef) - mu)) / KbT;
	double tmp;
	if ((NdChar <= -3.8e-61) || !(NdChar <= 1.75e+81)) {
		tmp = (NdChar / (Math.exp(t_0) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else {
		tmp = (NdChar / (2.0 + t_0)) - (NaChar / (-1.0 - Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (EDonor - ((Ec - Vef) - mu)) / KbT
	tmp = 0
	if (NdChar <= -3.8e-61) or not (NdChar <= 1.75e+81):
		tmp = (NdChar / (math.exp(t_0) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0))
	else:
		tmp = (NdChar / (2.0 + t_0)) - (NaChar / (-1.0 - math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)
	tmp = 0.0
	if ((NdChar <= -3.8e-61) || !(NdChar <= 1.75e+81))
		tmp = Float64(Float64(NdChar / Float64(exp(t_0) + 1.0)) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(2.0 + t_0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (EDonor - ((Ec - Vef) - mu)) / KbT;
	tmp = 0.0;
	if ((NdChar <= -3.8e-61) || ~((NdChar <= 1.75e+81)))
		tmp = (NdChar / (exp(t_0) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	else
		tmp = (NdChar / (2.0 + t_0)) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]}, If[Or[LessEqual[NdChar, -3.8e-61], N[Not[LessEqual[NdChar, 1.75e+81]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[t$95$0], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(2.0 + t$95$0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -3.7999999999999998e-61 or 1.75e81 < NdChar

   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 77.7%

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

   6. Taylor expanded in Ev around 0 65.8%

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

   if -3.7999999999999998e-61 < NdChar < 1.75e81

   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 61.8%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + -1 \cdot \frac{-1 \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right) + -1 \cdot \frac{0.16666666666666666 \cdot \frac{{\left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}^{3}}{KbT} + 0.5 \cdot {\left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}^{2}}{KbT}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 76.7%

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

      1. associate-*r/ 76.7%

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

      2. mul-1-neg 76.7%

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

      3. +-commutative 76.7%

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

      4. associate-+r- 76.7%

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

      5. +-commutative 76.7%

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

      6. associate--l+ 76.7%

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

   8. Simplified 76.7%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.8 \cdot 10^{-61} \lor \neg \left(NdChar \leq 1.75 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 + \frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -1.12 \cdot 10^{+195}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NdChar \leq -4.6 \cdot 10^{+34} \lor \neg \left(NdChar \leq 9.2 \cdot 10^{+36}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ mu KbT)) 1.0))))
   (if (<= NdChar -1.4e+220)
     t_0
     (if (<= NdChar -1.12e+195)
       (+ (/ NdChar (+ (exp (- (/ Ec KbT))) 1.0)) (/ (* KbT NaChar) Vef))
       (if (or (<= NdChar -4.6e+34) (not (<= NdChar 9.2e+36)))
         t_0
         (+
          (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) 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 t_0 = NdChar / (exp((mu / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -1.4e+220) {
		tmp = t_0;
	} else if (NdChar <= -1.12e+195) {
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef);
	} else if ((NdChar <= -4.6e+34) || !(NdChar <= 9.2e+36)) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / 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) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp((mu / kbt)) + 1.0d0)
    if (ndchar <= (-1.4d+220)) then
        tmp = t_0
    else if (ndchar <= (-1.12d+195)) then
        tmp = (ndchar / (exp(-(ec / kbt)) + 1.0d0)) + ((kbt * nachar) / vef)
    else if ((ndchar <= (-4.6d+34)) .or. (.not. (ndchar <= 9.2d+36))) then
        tmp = t_0
    else
        tmp = (nachar / (exp((((vef + ev) - mu) / 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 t_0 = NdChar / (Math.exp((mu / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -1.4e+220) {
		tmp = t_0;
	} else if (NdChar <= -1.12e+195) {
		tmp = (NdChar / (Math.exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef);
	} else if ((NdChar <= -4.6e+34) || !(NdChar <= 9.2e+36)) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp((mu / KbT)) + 1.0)
	tmp = 0
	if NdChar <= -1.4e+220:
		tmp = t_0
	elif NdChar <= -1.12e+195:
		tmp = (NdChar / (math.exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef)
	elif (NdChar <= -4.6e+34) or not (NdChar <= 9.2e+36):
		tmp = t_0
	else:
		tmp = (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0))
	tmp = 0.0
	if (NdChar <= -1.4e+220)
		tmp = t_0;
	elseif (NdChar <= -1.12e+195)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(-Float64(Ec / KbT))) + 1.0)) + Float64(Float64(KbT * NaChar) / Vef));
	elseif ((NdChar <= -4.6e+34) || !(NdChar <= 9.2e+36))
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / 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)
	t_0 = NdChar / (exp((mu / KbT)) + 1.0);
	tmp = 0.0;
	if (NdChar <= -1.4e+220)
		tmp = t_0;
	elseif (NdChar <= -1.12e+195)
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef);
	elseif ((NdChar <= -4.6e+34) || ~((NdChar <= 9.2e+36)))
		tmp = t_0;
	else
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.4e+220], t$95$0, If[LessEqual[NdChar, -1.12e+195], N[(N[(NdChar / N[(N[Exp[(-N[(Ec / KbT), $MachinePrecision])], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NdChar, -4.6e+34], N[Not[LessEqual[NdChar, 9.2e+36]], $MachinePrecision]], t$95$0, N[(N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -1.4e220 or -1.12000000000000004e195 < NdChar < -4.5999999999999996e34 or 9.19999999999999986e36 < NdChar

   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 mu around inf 74.1%

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

   6. Taylor expanded in KbT around inf 50.8%

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

   7. Taylor expanded in Vef around inf 23.4%

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

   8. Taylor expanded in NdChar around inf 54.0%

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

   if -1.4e220 < NdChar < -1.12000000000000004e195

   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 Ec around inf 86.5%

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

      1. associate-*r/ 86.5%

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

      2. mul-1-neg 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in KbT around inf 86.5%

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

   9. Taylor expanded in Vef around inf 84.3%

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

   if -4.5999999999999996e34 < NdChar < 9.19999999999999986e36

   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 62.0%

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

   6. Taylor expanded in EAccept around 0 56.8%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;NdChar \leq -1.12 \cdot 10^{+195}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NdChar \leq -4.6 \cdot 10^{+34} \lor \neg \left(NdChar \leq 9.2 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{mu}{KbT}}\\ t_1 := \frac{NdChar}{t\_0 + 1}\\ \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -9 \cdot 10^{+194}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 1} - \frac{NdChar}{-1 - t\_0}\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ mu KbT))) (t_1 (/ NdChar (+ t_0 1.0))))
   (if (<= NdChar -1.4e+223)
     t_1
     (if (<= NdChar -9e+194)
       (+
        (/ NdChar (+ (exp (- (/ Ec KbT))) 1.0))
        (/ NaChar (+ (/ Vef KbT) 1.0)))
       (if (<= NdChar -3.9e-44)
         (- (/ NaChar (+ (/ Ev KbT) 1.0)) (/ NdChar (- -1.0 t_0)))
         (if (<= NdChar 2.4e+27)
           (+
            (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0))
            (/ NdChar 2.0))
           (+ t_1 (/ NaChar (+ (/ 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 t_0 = exp((mu / KbT));
	double t_1 = NdChar / (t_0 + 1.0);
	double tmp;
	if (NdChar <= -1.4e+223) {
		tmp = t_1;
	} else if (NdChar <= -9e+194) {
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= -3.9e-44) {
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0));
	} else if (NdChar <= 2.4e+27) {
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = t_1 + (NaChar / ((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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = exp((mu / kbt))
    t_1 = ndchar / (t_0 + 1.0d0)
    if (ndchar <= (-1.4d+223)) then
        tmp = t_1
    else if (ndchar <= (-9d+194)) then
        tmp = (ndchar / (exp(-(ec / kbt)) + 1.0d0)) + (nachar / ((vef / kbt) + 1.0d0))
    else if (ndchar <= (-3.9d-44)) then
        tmp = (nachar / ((ev / kbt) + 1.0d0)) - (ndchar / ((-1.0d0) - t_0))
    else if (ndchar <= 2.4d+27) then
        tmp = (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else
        tmp = t_1 + (nachar / ((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 t_0 = Math.exp((mu / KbT));
	double t_1 = NdChar / (t_0 + 1.0);
	double tmp;
	if (NdChar <= -1.4e+223) {
		tmp = t_1;
	} else if (NdChar <= -9e+194) {
		tmp = (NdChar / (Math.exp(-(Ec / KbT)) + 1.0)) + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= -3.9e-44) {
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0));
	} else if (NdChar <= 2.4e+27) {
		tmp = (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp((mu / KbT))
	t_1 = NdChar / (t_0 + 1.0)
	tmp = 0
	if NdChar <= -1.4e+223:
		tmp = t_1
	elif NdChar <= -9e+194:
		tmp = (NdChar / (math.exp(-(Ec / KbT)) + 1.0)) + (NaChar / ((Vef / KbT) + 1.0))
	elif NdChar <= -3.9e-44:
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0))
	elif NdChar <= 2.4e+27:
		tmp = (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0)
	else:
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(mu / KbT))
	t_1 = Float64(NdChar / Float64(t_0 + 1.0))
	tmp = 0.0
	if (NdChar <= -1.4e+223)
		tmp = t_1;
	elseif (NdChar <= -9e+194)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(-Float64(Ec / KbT))) + 1.0)) + Float64(NaChar / Float64(Float64(Vef / KbT) + 1.0)));
	elseif (NdChar <= -3.9e-44)
		tmp = Float64(Float64(NaChar / Float64(Float64(Ev / KbT) + 1.0)) - Float64(NdChar / Float64(-1.0 - t_0)));
	elseif (NdChar <= 2.4e+27)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp((mu / KbT));
	t_1 = NdChar / (t_0 + 1.0);
	tmp = 0.0;
	if (NdChar <= -1.4e+223)
		tmp = t_1;
	elseif (NdChar <= -9e+194)
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + (NaChar / ((Vef / KbT) + 1.0));
	elseif (NdChar <= -3.9e-44)
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0));
	elseif (NdChar <= 2.4e+27)
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	else
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.4e+223], t$95$1, If[LessEqual[NdChar, -9e+194], N[(N[(NdChar / N[(N[Exp[(-N[(Ec / KbT), $MachinePrecision])], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -3.9e-44], N[(N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.4e+27], N[(N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -1.3999999999999999e223

   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 mu around inf 75.0%

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

   6. Taylor expanded in KbT around inf 58.1%

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

   7. Taylor expanded in Vef around inf 45.2%

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

   8. Taylor expanded in NdChar around inf 62.2%

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

   if -1.3999999999999999e223 < NdChar < -8.9999999999999997e194

   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 Ec around inf 86.5%

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

      1. associate-*r/ 86.5%

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

      2. mul-1-neg 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in KbT around inf 86.5%

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

   9. Taylor expanded in Vef around inf 86.5%

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

   if -8.9999999999999997e194 < NdChar < -3.9000000000000002e-44

   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 mu around inf 73.8%

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

   6. Taylor expanded in KbT around inf 47.6%

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

   7. Taylor expanded in Ev around inf 49.7%

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

   if -3.9000000000000002e-44 < NdChar < 2.39999999999999998e27

   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 64.9%

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

   6. Taylor expanded in EAccept around 0 59.0%

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

   if 2.39999999999999998e27 < NdChar

   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 mu around inf 72.1%

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

   6. Taylor expanded in KbT around inf 43.9%

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

   7. Taylor expanded in EAccept around inf 57.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+223}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;NdChar \leq -9 \cdot 10^{+194}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{mu}{KbT}}\\ t_1 := \frac{NdChar}{t\_0 + 1}\\ \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -1.06 \cdot 10^{+195}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NdChar \leq -5.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 1} - \frac{NdChar}{-1 - t\_0}\\ \mathbf{elif}\;NdChar \leq 1.56 \cdot 10^{+32}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ mu KbT))) (t_1 (/ NdChar (+ t_0 1.0))))
   (if (<= NdChar -1.4e+220)
     t_1
     (if (<= NdChar -1.06e+195)
       (+ (/ NdChar (+ (exp (- (/ Ec KbT))) 1.0)) (/ (* KbT NaChar) Vef))
       (if (<= NdChar -5.2e-44)
         (- (/ NaChar (+ (/ Ev KbT) 1.0)) (/ NdChar (- -1.0 t_0)))
         (if (<= NdChar 1.56e+32)
           (+
            (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0))
            (/ NdChar 2.0))
           (+ t_1 (/ NaChar (+ (/ 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 t_0 = exp((mu / KbT));
	double t_1 = NdChar / (t_0 + 1.0);
	double tmp;
	if (NdChar <= -1.4e+220) {
		tmp = t_1;
	} else if (NdChar <= -1.06e+195) {
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef);
	} else if (NdChar <= -5.2e-44) {
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0));
	} else if (NdChar <= 1.56e+32) {
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = t_1 + (NaChar / ((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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = exp((mu / kbt))
    t_1 = ndchar / (t_0 + 1.0d0)
    if (ndchar <= (-1.4d+220)) then
        tmp = t_1
    else if (ndchar <= (-1.06d+195)) then
        tmp = (ndchar / (exp(-(ec / kbt)) + 1.0d0)) + ((kbt * nachar) / vef)
    else if (ndchar <= (-5.2d-44)) then
        tmp = (nachar / ((ev / kbt) + 1.0d0)) - (ndchar / ((-1.0d0) - t_0))
    else if (ndchar <= 1.56d+32) then
        tmp = (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else
        tmp = t_1 + (nachar / ((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 t_0 = Math.exp((mu / KbT));
	double t_1 = NdChar / (t_0 + 1.0);
	double tmp;
	if (NdChar <= -1.4e+220) {
		tmp = t_1;
	} else if (NdChar <= -1.06e+195) {
		tmp = (NdChar / (Math.exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef);
	} else if (NdChar <= -5.2e-44) {
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0));
	} else if (NdChar <= 1.56e+32) {
		tmp = (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp((mu / KbT))
	t_1 = NdChar / (t_0 + 1.0)
	tmp = 0
	if NdChar <= -1.4e+220:
		tmp = t_1
	elif NdChar <= -1.06e+195:
		tmp = (NdChar / (math.exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef)
	elif NdChar <= -5.2e-44:
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0))
	elif NdChar <= 1.56e+32:
		tmp = (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0)
	else:
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(mu / KbT))
	t_1 = Float64(NdChar / Float64(t_0 + 1.0))
	tmp = 0.0
	if (NdChar <= -1.4e+220)
		tmp = t_1;
	elseif (NdChar <= -1.06e+195)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(-Float64(Ec / KbT))) + 1.0)) + Float64(Float64(KbT * NaChar) / Vef));
	elseif (NdChar <= -5.2e-44)
		tmp = Float64(Float64(NaChar / Float64(Float64(Ev / KbT) + 1.0)) - Float64(NdChar / Float64(-1.0 - t_0)));
	elseif (NdChar <= 1.56e+32)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp((mu / KbT));
	t_1 = NdChar / (t_0 + 1.0);
	tmp = 0.0;
	if (NdChar <= -1.4e+220)
		tmp = t_1;
	elseif (NdChar <= -1.06e+195)
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef);
	elseif (NdChar <= -5.2e-44)
		tmp = (NaChar / ((Ev / KbT) + 1.0)) - (NdChar / (-1.0 - t_0));
	elseif (NdChar <= 1.56e+32)
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	else
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.4e+220], t$95$1, If[LessEqual[NdChar, -1.06e+195], N[(N[(NdChar / N[(N[Exp[(-N[(Ec / KbT), $MachinePrecision])], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -5.2e-44], N[(N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.56e+32], N[(N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -1.4e220

   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 mu around inf 75.0%

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

   6. Taylor expanded in KbT around inf 58.1%

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

   7. Taylor expanded in Vef around inf 45.2%

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

   8. Taylor expanded in NdChar around inf 62.2%

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

   if -1.4e220 < NdChar < -1.06000000000000001e195

   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 Ec around inf 86.5%

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

      1. associate-*r/ 86.5%

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

      2. mul-1-neg 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in KbT around inf 86.5%

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

   9. Taylor expanded in Vef around inf 84.3%

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

   if -1.06000000000000001e195 < NdChar < -5.1999999999999996e-44

   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 mu around inf 73.8%

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

   6. Taylor expanded in KbT around inf 47.6%

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

   7. Taylor expanded in Ev around inf 49.7%

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

   if -5.1999999999999996e-44 < NdChar < 1.56e32

   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 64.9%

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

   6. Taylor expanded in EAccept around 0 59.0%

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

   if 1.56e32 < NdChar

   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 mu around inf 72.1%

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

   6. Taylor expanded in KbT around inf 43.9%

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

   7. Taylor expanded in EAccept around inf 57.2%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;NdChar \leq -1.06 \cdot 10^{+195}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NdChar \leq -5.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.56 \cdot 10^{+32}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -1.12 \cdot 10^{+195}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NdChar \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 5 \cdot 10^{+26}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ mu KbT)) 1.0))))
   (if (<= NdChar -1.4e+220)
     t_0
     (if (<= NdChar -1.12e+195)
       (+ (/ NdChar (+ (exp (- (/ Ec KbT))) 1.0)) (/ (* KbT NaChar) Vef))
       (if (<= NdChar -4.5e+29)
         t_0
         (if (<= NdChar 5e+26)
           (+
            (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0))
            (/ NdChar 2.0))
           (+ t_0 (/ NaChar (+ (/ 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 t_0 = NdChar / (exp((mu / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -1.4e+220) {
		tmp = t_0;
	} else if (NdChar <= -1.12e+195) {
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef);
	} else if (NdChar <= -4.5e+29) {
		tmp = t_0;
	} else if (NdChar <= 5e+26) {
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = t_0 + (NaChar / ((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) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp((mu / kbt)) + 1.0d0)
    if (ndchar <= (-1.4d+220)) then
        tmp = t_0
    else if (ndchar <= (-1.12d+195)) then
        tmp = (ndchar / (exp(-(ec / kbt)) + 1.0d0)) + ((kbt * nachar) / vef)
    else if (ndchar <= (-4.5d+29)) then
        tmp = t_0
    else if (ndchar <= 5d+26) then
        tmp = (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else
        tmp = t_0 + (nachar / ((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 t_0 = NdChar / (Math.exp((mu / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -1.4e+220) {
		tmp = t_0;
	} else if (NdChar <= -1.12e+195) {
		tmp = (NdChar / (Math.exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef);
	} else if (NdChar <= -4.5e+29) {
		tmp = t_0;
	} else if (NdChar <= 5e+26) {
		tmp = (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp((mu / KbT)) + 1.0)
	tmp = 0
	if NdChar <= -1.4e+220:
		tmp = t_0
	elif NdChar <= -1.12e+195:
		tmp = (NdChar / (math.exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef)
	elif NdChar <= -4.5e+29:
		tmp = t_0
	elif NdChar <= 5e+26:
		tmp = (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0)
	else:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0))
	tmp = 0.0
	if (NdChar <= -1.4e+220)
		tmp = t_0;
	elseif (NdChar <= -1.12e+195)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(-Float64(Ec / KbT))) + 1.0)) + Float64(Float64(KbT * NaChar) / Vef));
	elseif (NdChar <= -4.5e+29)
		tmp = t_0;
	elseif (NdChar <= 5e+26)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp((mu / KbT)) + 1.0);
	tmp = 0.0;
	if (NdChar <= -1.4e+220)
		tmp = t_0;
	elseif (NdChar <= -1.12e+195)
		tmp = (NdChar / (exp(-(Ec / KbT)) + 1.0)) + ((KbT * NaChar) / Vef);
	elseif (NdChar <= -4.5e+29)
		tmp = t_0;
	elseif (NdChar <= 5e+26)
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / 2.0);
	else
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.4e+220], t$95$0, If[LessEqual[NdChar, -1.12e+195], N[(N[(NdChar / N[(N[Exp[(-N[(Ec / KbT), $MachinePrecision])], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -4.5e+29], t$95$0, If[LessEqual[NdChar, 5e+26], N[(N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -1.4e220 or -1.12000000000000004e195 < NdChar < -4.5000000000000002e29

   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 mu around inf 76.6%

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

   6. Taylor expanded in KbT around inf 56.9%

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

   7. Taylor expanded in Vef around inf 30.1%

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

   8. Taylor expanded in NdChar around inf 59.2%

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

   if -1.4e220 < NdChar < -1.12000000000000004e195

   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 Ec around inf 86.5%

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

      1. associate-*r/ 86.5%

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

      2. mul-1-neg 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in KbT around inf 86.5%

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

   9. Taylor expanded in Vef around inf 84.3%

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

   if -4.5000000000000002e29 < NdChar < 5.0000000000000001e26

   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 61.7%

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

   6. Taylor expanded in EAccept around 0 56.5%

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

   if 5.0000000000000001e26 < NdChar

   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 mu around inf 72.1%

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

   6. Taylor expanded in KbT around inf 43.9%

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

   7. Taylor expanded in EAccept around inf 57.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;NdChar \leq -1.12 \cdot 10^{+195}:\\ \;\;\;\;\frac{NdChar}{e^{-\frac{Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NdChar \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;NdChar \leq 5 \cdot 10^{+26}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -4.5 \cdot 10^{-55} \lor \neg \left(NdChar \leq 1.2 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -4.5e-55) (not (<= NdChar 1.2e+89)))
   (+
    (/ NdChar (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1.0))
    (/ NaChar (+ (/ Ev KbT) 2.0)))
   (+
    (/ NaChar (+ (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)) 1.0))
    (/ NdChar (+ (/ Vef KbT) 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 ((NdChar <= -4.5e-55) || !(NdChar <= 1.2e+89)) {
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else {
		tmp = (NaChar / (exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 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 ((ndchar <= (-4.5d-55)) .or. (.not. (ndchar <= 1.2d+89))) then
        tmp = (ndchar / (exp(((edonor - ((ec - vef) - mu)) / kbt)) + 1.0d0)) + (nachar / ((ev / kbt) + 2.0d0))
    else
        tmp = (nachar / (exp(((vef - ((mu - eaccept) - ev)) / kbt)) + 1.0d0)) + (ndchar / ((vef / kbt) + 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 ((NdChar <= -4.5e-55) || !(NdChar <= 1.2e+89)) {
		tmp = (NdChar / (Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else {
		tmp = (NaChar / (Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -4.5e-55) or not (NdChar <= 1.2e+89):
		tmp = (NdChar / (math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0))
	else:
		tmp = (NaChar / (math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -4.5e-55) || !(NdChar <= 1.2e+89))
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Vef / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -4.5e-55) || ~((NdChar <= 1.2e+89)))
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	else
		tmp = (NaChar / (exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -4.5e-55], N[Not[LessEqual[NdChar, 1.2e+89]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -4.4999999999999997e-55 or 1.20000000000000002e89 < NdChar

   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 77.6%

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

   6. Taylor expanded in Ev around 0 65.5%

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

   if -4.4999999999999997e-55 < NdChar < 1.20000000000000002e89

   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 Vef around inf 82.8%

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

   6. Taylor expanded in Vef around 0 72.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.5 \cdot 10^{-55} \lor \neg \left(NdChar \leq 1.2 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -6.5 \cdot 10^{-55} \lor \neg \left(NdChar \leq 1.6 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -6.5e-55) (not (<= NdChar 1.6e+89)))
   (+
    (/ NdChar (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1.0))
    (/ NaChar (+ (/ Ev KbT) 2.0)))
   (+
    (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0))
    (/ NdChar (+ (/ Vef KbT) 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 ((NdChar <= -6.5e-55) || !(NdChar <= 1.6e+89)) {
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else {
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 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 ((ndchar <= (-6.5d-55)) .or. (.not. (ndchar <= 1.6d+89))) then
        tmp = (ndchar / (exp(((edonor - ((ec - vef) - mu)) / kbt)) + 1.0d0)) + (nachar / ((ev / kbt) + 2.0d0))
    else
        tmp = (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0)) + (ndchar / ((vef / kbt) + 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 ((NdChar <= -6.5e-55) || !(NdChar <= 1.6e+89)) {
		tmp = (NdChar / (Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else {
		tmp = (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -6.5e-55) or not (NdChar <= 1.6e+89):
		tmp = (NdChar / (math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0))
	else:
		tmp = (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -6.5e-55) || !(NdChar <= 1.6e+89))
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Vef / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -6.5e-55) || ~((NdChar <= 1.6e+89)))
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	else
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -6.5e-55], N[Not[LessEqual[NdChar, 1.6e+89]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -6.50000000000000006e-55 or 1.59999999999999994e89 < NdChar

   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 77.6%

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

   6. Taylor expanded in Ev around 0 65.5%

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

   if -6.50000000000000006e-55 < NdChar < 1.59999999999999994e89

   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 Vef around inf 82.8%

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

   6. Taylor expanded in EAccept around 0 76.0%

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

   7. Taylor expanded in Vef around 0 66.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6.5 \cdot 10^{-55} \lor \neg \left(NdChar \leq 1.6 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -5.5 \cdot 10^{-73} \lor \neg \left(NdChar \leq 3.6 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -5.5e-73) (not (<= NdChar 3.6e+88)))
   (+
    (/ NdChar (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1.0))
    (* NaChar 0.5))
   (+
    (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0))
    (/ NdChar (+ (/ Vef KbT) 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 ((NdChar <= -5.5e-73) || !(NdChar <= 3.6e+88)) {
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 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 ((ndchar <= (-5.5d-73)) .or. (.not. (ndchar <= 3.6d+88))) then
        tmp = (ndchar / (exp(((edonor - ((ec - vef) - mu)) / kbt)) + 1.0d0)) + (nachar * 0.5d0)
    else
        tmp = (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0)) + (ndchar / ((vef / kbt) + 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 ((NdChar <= -5.5e-73) || !(NdChar <= 3.6e+88)) {
		tmp = (NdChar / (Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -5.5e-73) or not (NdChar <= 3.6e+88):
		tmp = (NdChar / (math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar * 0.5)
	else:
		tmp = (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -5.5e-73) || !(NdChar <= 3.6e+88))
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)) + 1.0)) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Vef / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -5.5e-73) || ~((NdChar <= 3.6e+88)))
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar * 0.5);
	else
		tmp = (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -5.5e-73], N[Not[LessEqual[NdChar, 3.6e+88]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -5.50000000000000006e-73 or 3.6000000000000002e88 < NdChar

   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 77.9%

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

   6. Taylor expanded in Ev around 0 58.5%

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

   if -5.50000000000000006e-73 < NdChar < 3.6000000000000002e88

   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 Vef around inf 82.5%

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

   6. Taylor expanded in EAccept around 0 75.7%

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

   7. Taylor expanded in Vef around 0 66.2%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -5.5 \cdot 10^{-73} \lor \neg \left(NdChar \leq 3.6 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{if}\;KbT \leq -4.8 \cdot 10^{+211}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2 + \left(\frac{Ev}{KbT} - \frac{mu - Vef}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq 10^{+65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 3.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \mathbf{elif}\;KbT \leq 4.7 \cdot 10^{+173}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ mu KbT)) 1.0))))
   (if (<= KbT -4.8e+211)
     (+ (/ NdChar 2.0) (/ NaChar (+ 2.0 (- (/ Ev KbT) (/ (- mu Vef) KbT)))))
     (if (<= KbT 1e+65)
       t_0
       (if (<= KbT 3.6e+164)
         (+ (/ NdChar 2.0) (/ NaChar (+ (/ EAccept KbT) 1.0)))
         (if (<= KbT 4.7e+173) t_0 (+ (* NaChar 0.5) (/ 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 t_0 = NdChar / (exp((mu / KbT)) + 1.0);
	double tmp;
	if (KbT <= -4.8e+211) {
		tmp = (NdChar / 2.0) + (NaChar / (2.0 + ((Ev / KbT) - ((mu - Vef) / KbT))));
	} else if (KbT <= 1e+65) {
		tmp = t_0;
	} else if (KbT <= 3.6e+164) {
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	} else if (KbT <= 4.7e+173) {
		tmp = t_0;
	} else {
		tmp = (NaChar * 0.5) + (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) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp((mu / kbt)) + 1.0d0)
    if (kbt <= (-4.8d+211)) then
        tmp = (ndchar / 2.0d0) + (nachar / (2.0d0 + ((ev / kbt) - ((mu - vef) / kbt))))
    else if (kbt <= 1d+65) then
        tmp = t_0
    else if (kbt <= 3.6d+164) then
        tmp = (ndchar / 2.0d0) + (nachar / ((eaccept / kbt) + 1.0d0))
    else if (kbt <= 4.7d+173) then
        tmp = t_0
    else
        tmp = (nachar * 0.5d0) + (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 t_0 = NdChar / (Math.exp((mu / KbT)) + 1.0);
	double tmp;
	if (KbT <= -4.8e+211) {
		tmp = (NdChar / 2.0) + (NaChar / (2.0 + ((Ev / KbT) - ((mu - Vef) / KbT))));
	} else if (KbT <= 1e+65) {
		tmp = t_0;
	} else if (KbT <= 3.6e+164) {
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	} else if (KbT <= 4.7e+173) {
		tmp = t_0;
	} else {
		tmp = (NaChar * 0.5) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp((mu / KbT)) + 1.0)
	tmp = 0
	if KbT <= -4.8e+211:
		tmp = (NdChar / 2.0) + (NaChar / (2.0 + ((Ev / KbT) - ((mu - Vef) / KbT))))
	elif KbT <= 1e+65:
		tmp = t_0
	elif KbT <= 3.6e+164:
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0))
	elif KbT <= 4.7e+173:
		tmp = t_0
	else:
		tmp = (NaChar * 0.5) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0))
	tmp = 0.0
	if (KbT <= -4.8e+211)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(2.0 + Float64(Float64(Ev / KbT) - Float64(Float64(mu - Vef) / KbT)))));
	elseif (KbT <= 1e+65)
		tmp = t_0;
	elseif (KbT <= 3.6e+164)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 1.0)));
	elseif (KbT <= 4.7e+173)
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar * 0.5) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp((mu / KbT)) + 1.0);
	tmp = 0.0;
	if (KbT <= -4.8e+211)
		tmp = (NdChar / 2.0) + (NaChar / (2.0 + ((Ev / KbT) - ((mu - Vef) / KbT))));
	elseif (KbT <= 1e+65)
		tmp = t_0;
	elseif (KbT <= 3.6e+164)
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	elseif (KbT <= 4.7e+173)
		tmp = t_0;
	else
		tmp = (NaChar * 0.5) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -4.8e+211], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(2.0 + N[(N[(Ev / KbT), $MachinePrecision] - N[(N[(mu - Vef), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1e+65], t$95$0, If[LessEqual[KbT, 3.6e+164], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4.7e+173], t$95$0, N[(N[(NaChar * 0.5), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -4.80000000000000035e211

   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 97.8%

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

   6. Taylor expanded in KbT around inf 93.1%

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

      1. div-inv 93.1%

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

   8. Applied egg-rr 93.1%

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

   9. Taylor expanded in EAccept around 0 93.9%

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

       1. associate--l+ 93.9%

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

       2. associate--l+ 93.9%

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

       3. div-sub 93.9%

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

   11. Simplified 93.9%

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

   if -4.80000000000000035e211 < KbT < 9.9999999999999999e64 or 3.5999999999999999e164 < KbT < 4.70000000000000015e173

   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 mu around inf 73.5%

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

   6. Taylor expanded in KbT around inf 34.4%

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

   7. Taylor expanded in Vef around inf 18.4%

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

   8. Taylor expanded in NdChar around inf 43.1%

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

   if 9.9999999999999999e64 < KbT < 3.5999999999999999e164

   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 69.3%

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

   6. Taylor expanded in KbT around inf 29.2%

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

   7. Taylor expanded in EAccept around inf 41.3%

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

   if 4.70000000000000015e173 < 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 73.6%

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

   6. Taylor expanded in KbT around inf 61.4%

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

   7. Taylor expanded in KbT around inf 62.5%

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

      1. *-commutative 62.5%

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

   9. Simplified 62.5%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.8 \cdot 10^{+211}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2 + \left(\frac{Ev}{KbT} - \frac{mu - Vef}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq 10^{+65}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;KbT \leq 3.6 \cdot 10^{+164}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \mathbf{elif}\;KbT \leq 4.7 \cdot 10^{+173}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -8.2 \cdot 10^{-74} \lor \neg \left(NdChar \leq 3.3 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -8.2e-74) (not (<= NdChar 3.3e+36)))
   (+
    (/ NdChar (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1.0))
    (* NaChar 0.5))
   (-
    (/ NdChar 2.0)
    (/ NaChar (- -1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) 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 ((NdChar <= -8.2e-74) || !(NdChar <= 3.3e+36)) {
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar * 0.5);
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / 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 ((ndchar <= (-8.2d-74)) .or. (.not. (ndchar <= 3.3d+36))) then
        tmp = (ndchar / (exp(((edonor - ((ec - vef) - mu)) / kbt)) + 1.0d0)) + (nachar * 0.5d0)
    else
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef - ((mu - eaccept) - ev)) / 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 ((NdChar <= -8.2e-74) || !(NdChar <= 3.3e+36)) {
		tmp = (NdChar / (Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar * 0.5);
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -8.2e-74) or not (NdChar <= 3.3e+36):
		tmp = (NdChar / (math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar * 0.5)
	else:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -8.2e-74) || !(NdChar <= 3.3e+36))
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)) + 1.0)) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -8.2e-74) || ~((NdChar <= 3.3e+36)))
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar * 0.5);
	else
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -8.2e-74], N[Not[LessEqual[NdChar, 3.3e+36]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -8.20000000000000063e-74 or 3.2999999999999999e36 < NdChar

   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 77.4%

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

   6. Taylor expanded in Ev around 0 56.9%

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

   if -8.20000000000000063e-74 < NdChar < 3.2999999999999999e36

   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 65.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -8.2 \cdot 10^{-74} \lor \neg \left(NdChar \leq 3.3 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -6.5 \cdot 10^{+105} \lor \neg \left(KbT \leq 6.6 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -6.5e+105) (not (<= KbT 6.6e+41)))
   (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (/ NdChar 2.0))
   (/ NdChar (+ (exp (/ 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 ((KbT <= -6.5e+105) || !(KbT <= 6.6e+41)) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = NdChar / (exp((mu / 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 <= (-6.5d+105)) .or. (.not. (kbt <= 6.6d+41))) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else
        tmp = ndchar / (exp((mu / 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 <= -6.5e+105) || !(KbT <= 6.6e+41)) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = NdChar / (Math.exp((mu / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -6.5e+105) or not (KbT <= 6.6e+41):
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0)
	else:
		tmp = NdChar / (math.exp((mu / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -6.5e+105) || !(KbT <= 6.6e+41))
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	else
		tmp = Float64(NdChar / Float64(exp(Float64(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 ((KbT <= -6.5e+105) || ~((KbT <= 6.6e+41)))
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	else
		tmp = NdChar / (exp((mu / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -6.5e+105], N[Not[LessEqual[KbT, 6.6e+41]], $MachinePrecision]], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -6.50000000000000049e105 or 6.6000000000000001e41 < 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 76.0%

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

   6. Taylor expanded in Ev around inf 64.1%

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

   if -6.50000000000000049e105 < KbT < 6.6000000000000001e41

   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 mu around inf 71.4%

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

   6. Taylor expanded in KbT around inf 34.9%

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

   7. Taylor expanded in Vef around inf 20.2%

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

   8. Taylor expanded in NdChar around inf 41.8%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -6.5 \cdot 10^{+105} \lor \neg \left(KbT \leq 6.6 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 40.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -7.5 \cdot 10^{+50} \lor \neg \left(mu \leq 2.1 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= mu -7.5e+50) (not (<= mu 2.1e-108)))
   (/ NdChar (+ (exp (/ 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 ((mu <= -7.5e+50) || !(mu <= 2.1e-108)) {
		tmp = NdChar / (exp((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 ((mu <= (-7.5d+50)) .or. (.not. (mu <= 2.1d-108))) then
        tmp = ndchar / (exp((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 ((mu <= -7.5e+50) || !(mu <= 2.1e-108)) {
		tmp = NdChar / (Math.exp((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 (mu <= -7.5e+50) or not (mu <= 2.1e-108):
		tmp = NdChar / (math.exp((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 ((mu <= -7.5e+50) || !(mu <= 2.1e-108))
		tmp = Float64(NdChar / Float64(exp(Float64(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 ((mu <= -7.5e+50) || ~((mu <= 2.1e-108)))
		tmp = NdChar / (exp((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[Or[LessEqual[mu, -7.5e+50], N[Not[LessEqual[mu, 2.1e-108]], $MachinePrecision]], N[(NdChar / N[(N[Exp[N[(mu / 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 2 regimes

2. if mu < -7.4999999999999999e50 or 2.0999999999999999e-108 < mu

   1. Initial program 100.0%

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

   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 mu around inf 82.2%

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

   6. Taylor expanded in KbT around inf 47.0%

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

   7. Taylor expanded in Vef around inf 19.1%

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

   8. Taylor expanded in NdChar around inf 49.9%

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

   if -7.4999999999999999e50 < mu < 2.0999999999999999e-108

   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 63.8%

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

   6. Taylor expanded in EAccept around inf 49.0%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -7.5 \cdot 10^{+50} \lor \neg \left(mu \leq 2.1 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.9% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.4 \cdot 10^{+208}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2 + \left(\frac{Ev}{KbT} - \frac{mu - Vef}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq 9 \cdot 10^{-191}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{Ev}{KbT} + 1}\\ \mathbf{elif}\;KbT \leq 2.6 \cdot 10^{+138}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2.4e+208)
   (+ (/ NdChar 2.0) (/ NaChar (+ 2.0 (- (/ Ev KbT) (/ (- mu Vef) KbT)))))
   (if (<= KbT 9e-191)
     (+ (/ NdChar 2.0) (/ NaChar (+ (/ Ev KbT) 1.0)))
     (if (<= KbT 2.6e+138)
       (+ (/ NdChar 2.0) (/ NaChar (+ (/ EAccept KbT) 1.0)))
       (+ (* NaChar 0.5) (/ 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+208) {
		tmp = (NdChar / 2.0) + (NaChar / (2.0 + ((Ev / KbT) - ((mu - Vef) / KbT))));
	} else if (KbT <= 9e-191) {
		tmp = (NdChar / 2.0) + (NaChar / ((Ev / KbT) + 1.0));
	} else if (KbT <= 2.6e+138) {
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	} else {
		tmp = (NaChar * 0.5) + (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+208)) then
        tmp = (ndchar / 2.0d0) + (nachar / (2.0d0 + ((ev / kbt) - ((mu - vef) / kbt))))
    else if (kbt <= 9d-191) then
        tmp = (ndchar / 2.0d0) + (nachar / ((ev / kbt) + 1.0d0))
    else if (kbt <= 2.6d+138) then
        tmp = (ndchar / 2.0d0) + (nachar / ((eaccept / kbt) + 1.0d0))
    else
        tmp = (nachar * 0.5d0) + (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+208) {
		tmp = (NdChar / 2.0) + (NaChar / (2.0 + ((Ev / KbT) - ((mu - Vef) / KbT))));
	} else if (KbT <= 9e-191) {
		tmp = (NdChar / 2.0) + (NaChar / ((Ev / KbT) + 1.0));
	} else if (KbT <= 2.6e+138) {
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	} else {
		tmp = (NaChar * 0.5) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -2.4e+208:
		tmp = (NdChar / 2.0) + (NaChar / (2.0 + ((Ev / KbT) - ((mu - Vef) / KbT))))
	elif KbT <= 9e-191:
		tmp = (NdChar / 2.0) + (NaChar / ((Ev / KbT) + 1.0))
	elif KbT <= 2.6e+138:
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0))
	else:
		tmp = (NaChar * 0.5) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -2.4e+208)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(2.0 + Float64(Float64(Ev / KbT) - Float64(Float64(mu - Vef) / KbT)))));
	elseif (KbT <= 9e-191)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(Float64(Ev / KbT) + 1.0)));
	elseif (KbT <= 2.6e+138)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 1.0)));
	else
		tmp = Float64(Float64(NaChar * 0.5) + 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+208)
		tmp = (NdChar / 2.0) + (NaChar / (2.0 + ((Ev / KbT) - ((mu - Vef) / KbT))));
	elseif (KbT <= 9e-191)
		tmp = (NdChar / 2.0) + (NaChar / ((Ev / KbT) + 1.0));
	elseif (KbT <= 2.6e+138)
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	else
		tmp = (NaChar * 0.5) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -2.4e+208], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(2.0 + N[(N[(Ev / KbT), $MachinePrecision] - N[(N[(mu - Vef), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 9e-191], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.6e+138], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar * 0.5), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -2.39999999999999987e208

   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 94.2%

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

   6. Taylor expanded in KbT around inf 89.0%

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

      1. div-inv 89.0%

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

   8. Applied egg-rr 89.0%

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

   9. Taylor expanded in EAccept around 0 89.7%

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

       1. associate--l+ 89.7%

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

       2. associate--l+ 89.7%

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

       3. div-sub 89.7%

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

   11. Simplified 89.7%

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

   if -2.39999999999999987e208 < KbT < 9.00000000000000017e-191

   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 38.5%

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

   6. Taylor expanded in KbT around inf 15.3%

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

   7. Taylor expanded in Ev around inf 19.9%

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

   if 9.00000000000000017e-191 < KbT < 2.6000000000000001e138

   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 45.6%

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

   6. Taylor expanded in KbT around inf 15.6%

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

   7. Taylor expanded in EAccept around inf 31.3%

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

   if 2.6000000000000001e138 < 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 73.2%

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

   6. Taylor expanded in KbT around inf 57.0%

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

   7. Taylor expanded in KbT around inf 58.5%

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

      1. *-commutative 58.5%

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

   9. Simplified 58.5%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.4 \cdot 10^{+208}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2 + \left(\frac{Ev}{KbT} - \frac{mu - Vef}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq 9 \cdot 10^{-191}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{Ev}{KbT} + 1}\\ \mathbf{elif}\;KbT \leq 2.6 \cdot 10^{+138}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.9% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \mathbf{if}\;KbT \leq -3.8 \cdot 10^{+205}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 9 \cdot 10^{-191}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{Ev}{KbT} + 1}\\ \mathbf{elif}\;KbT \leq 1.65 \cdot 10^{+138}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (* NaChar 0.5) (/ NdChar 2.0))))
   (if (<= KbT -3.8e+205)
     t_0
     (if (<= KbT 9e-191)
       (+ (/ NdChar 2.0) (/ NaChar (+ (/ Ev KbT) 1.0)))
       (if (<= KbT 1.65e+138)
         (+ (/ NdChar 2.0) (/ NaChar (+ (/ 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 = (NaChar * 0.5) + (NdChar / 2.0);
	double tmp;
	if (KbT <= -3.8e+205) {
		tmp = t_0;
	} else if (KbT <= 9e-191) {
		tmp = (NdChar / 2.0) + (NaChar / ((Ev / KbT) + 1.0));
	} else if (KbT <= 1.65e+138) {
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar * 0.5d0) + (ndchar / 2.0d0)
    if (kbt <= (-3.8d+205)) then
        tmp = t_0
    else if (kbt <= 9d-191) then
        tmp = (ndchar / 2.0d0) + (nachar / ((ev / kbt) + 1.0d0))
    else if (kbt <= 1.65d+138) then
        tmp = (ndchar / 2.0d0) + (nachar / ((eaccept / kbt) + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar * 0.5) + (NdChar / 2.0);
	double tmp;
	if (KbT <= -3.8e+205) {
		tmp = t_0;
	} else if (KbT <= 9e-191) {
		tmp = (NdChar / 2.0) + (NaChar / ((Ev / KbT) + 1.0));
	} else if (KbT <= 1.65e+138) {
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar * 0.5) + (NdChar / 2.0)
	tmp = 0
	if KbT <= -3.8e+205:
		tmp = t_0
	elif KbT <= 9e-191:
		tmp = (NdChar / 2.0) + (NaChar / ((Ev / KbT) + 1.0))
	elif KbT <= 1.65e+138:
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar * 0.5) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (KbT <= -3.8e+205)
		tmp = t_0;
	elseif (KbT <= 9e-191)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(Float64(Ev / KbT) + 1.0)));
	elseif (KbT <= 1.65e+138)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar * 0.5) + (NdChar / 2.0);
	tmp = 0.0;
	if (KbT <= -3.8e+205)
		tmp = t_0;
	elseif (KbT <= 9e-191)
		tmp = (NdChar / 2.0) + (NaChar / ((Ev / KbT) + 1.0));
	elseif (KbT <= 1.65e+138)
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar * 0.5), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -3.8e+205], t$95$0, If[LessEqual[KbT, 9e-191], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.65e+138], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -3.8e205 or 1.64999999999999989e138 < 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 80.1%

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

   6. Taylor expanded in KbT around inf 67.5%

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

   7. Taylor expanded in KbT around inf 68.7%

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

      1. *-commutative 68.7%

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

   9. Simplified 68.7%

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

   if -3.8e205 < KbT < 9.00000000000000017e-191

   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 38.5%

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

   6. Taylor expanded in KbT around inf 15.3%

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

   7. Taylor expanded in Ev around inf 19.9%

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

   if 9.00000000000000017e-191 < KbT < 1.64999999999999989e138

   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 45.6%

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

   6. Taylor expanded in KbT around inf 15.6%

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

   7. Taylor expanded in EAccept around inf 31.3%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.8 \cdot 10^{+205}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 9 \cdot 10^{-191}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{Ev}{KbT} + 1}\\ \mathbf{elif}\;KbT \leq 1.65 \cdot 10^{+138}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.5% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq -1.9 \cdot 10^{-139}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EDonor -1.9e-139)
   (+ (* NaChar 0.5) (/ NdChar 2.0))
   (+ (/ NdChar 2.0) (/ NaChar (+ (/ 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 (EDonor <= -1.9e-139) {
		tmp = (NaChar * 0.5) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / 2.0) + (NaChar / ((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 (edonor <= (-1.9d-139)) then
        tmp = (nachar * 0.5d0) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / 2.0d0) + (nachar / ((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 (EDonor <= -1.9e-139) {
		tmp = (NaChar * 0.5) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EDonor <= -1.9e-139:
		tmp = (NaChar * 0.5) + (NdChar / 2.0)
	else:
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EDonor <= -1.9e-139)
		tmp = Float64(Float64(NaChar * 0.5) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(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 (EDonor <= -1.9e-139)
		tmp = (NaChar * 0.5) + (NdChar / 2.0);
	else
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EDonor, -1.9e-139], N[(N[(NaChar * 0.5), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -1.90000000000000004e-139

   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 49.2%

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

   6. Taylor expanded in KbT around inf 30.9%

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

   7. Taylor expanded in KbT around inf 33.1%

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

      1. *-commutative 33.1%

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

   9. Simplified 33.1%

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

   if -1.90000000000000004e-139 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 52.0%

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

   6. Taylor expanded in KbT around inf 28.0%

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

   7. Taylor expanded in EAccept around inf 34.2%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -1.9 \cdot 10^{-139}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 27.8% accurate, 32.7× speedup

Math

\[\begin{array}{l} \\ NaChar \cdot 0.5 + \frac{NdChar}{2} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (* NaChar 0.5) (/ NdChar 2.0)))

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) + (NdChar / 2.0);
}

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) + (ndchar / 2.0d0)
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) + (NdChar / 2.0);
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NaChar * 0.5) + (NdChar / 2.0)

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NaChar * 0.5) + Float64(NdChar / 2.0))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar * 0.5) + (NdChar / 2.0);
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NaChar * 0.5), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 51.0%

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

6. Taylor expanded in KbT around inf 29.0%

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

7. Taylor expanded in KbT around inf 31.1%

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

   1. *-commutative 31.1%

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

9. Simplified 31.1%

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

10. Final simplification 31.1%

    \[\leadsto NaChar \cdot 0.5 + \frac{NdChar}{2} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024091 
(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))))))