Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 26.4s

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

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
  (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- 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(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp(((Vef + (Ev + (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(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp(((vef + (ev + (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(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
}

Python

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

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp(((Vef + (Ev + (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[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 71.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;EAccept \leq 7.8 \cdot 10^{-56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 2.75 \cdot 10^{-28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 34000000:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;EAccept \leq 3.9 \cdot 10^{+91}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{+128}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_2 (+ t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))))
   (if (<= EAccept 7.8e-56)
     t_2
     (if (<= EAccept 2.75e-28)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
       (if (<= EAccept 34000000.0)
         (+ t_0 (/ NdChar (- 1.0 (/ Ec KbT))))
         (if (<= EAccept 3.9e+91)
           (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
           (if (<= EAccept 3.2e+128)
             t_2
             (+ t_1 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	double tmp;
	if (EAccept <= 7.8e-56) {
		tmp = t_2;
	} else if (EAccept <= 2.75e-28) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (EAccept <= 34000000.0) {
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)));
	} else if (EAccept <= 3.9e+91) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (EAccept <= 3.2e+128) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_2 = t_1 + (nachar / (1.0d0 + exp((ev / kbt))))
    if (eaccept <= 7.8d-56) then
        tmp = t_2
    else if (eaccept <= 2.75d-28) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else if (eaccept <= 34000000.0d0) then
        tmp = t_0 + (ndchar / (1.0d0 - (ec / kbt)))
    else if (eaccept <= 3.9d+91) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (eaccept <= 3.2d+128) then
        tmp = t_2
    else
        tmp = t_1 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double tmp;
	if (EAccept <= 7.8e-56) {
		tmp = t_2;
	} else if (EAccept <= 2.75e-28) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (EAccept <= 34000000.0) {
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)));
	} else if (EAccept <= 3.9e+91) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (EAccept <= 3.2e+128) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_2 = t_1 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	tmp = 0
	if EAccept <= 7.8e-56:
		tmp = t_2
	elif EAccept <= 2.75e-28:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	elif EAccept <= 34000000.0:
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)))
	elif EAccept <= 3.9e+91:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif EAccept <= 3.2e+128:
		tmp = t_2
	else:
		tmp = t_1 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	tmp = 0.0
	if (EAccept <= 7.8e-56)
		tmp = t_2;
	elseif (EAccept <= 2.75e-28)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	elseif (EAccept <= 34000000.0)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 - Float64(Ec / KbT))));
	elseif (EAccept <= 3.9e+91)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (EAccept <= 3.2e+128)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_2 = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	tmp = 0.0;
	if (EAccept <= 7.8e-56)
		tmp = t_2;
	elseif (EAccept <= 2.75e-28)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	elseif (EAccept <= 34000000.0)
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)));
	elseif (EAccept <= 3.9e+91)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (EAccept <= 3.2e+128)
		tmp = t_2;
	else
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, 7.8e-56], t$95$2, If[LessEqual[EAccept, 2.75e-28], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 34000000.0], N[(t$95$0 + N[(NdChar / N[(1.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.9e+91], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.2e+128], t$95$2, N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if EAccept < 7.8e-56 or 3.89999999999999968e91 < EAccept < 3.19999999999999986e128

   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 72.9%

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

   if 7.8e-56 < EAccept < 2.74999999999999984e-28

   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 35.9%

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

   6. Taylor expanded in Ec around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. associate-/l* 52.5%

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

      3. distribute-lft-neg-in 52.5%

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

   8. Simplified 52.5%

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

   9. Taylor expanded in KbT around 0 83.8%

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

   if 2.74999999999999984e-28 < EAccept < 3.4e7

   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 100.0%

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

   6. Taylor expanded in Ec around inf 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac2 100.0%

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

   8. Simplified 100.0%

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

   if 3.4e7 < EAccept < 3.89999999999999968e91

   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 EDonor around inf 80.2%

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

   if 3.19999999999999986e128 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 85.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 7.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 2.75 \cdot 10^{-28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 34000000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;EAccept \leq 3.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{+128}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := NdChar + t\_1\\ \mathbf{if}\;KbT \leq -1.75 \cdot 10^{+128}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + Vef \cdot \left(\frac{1}{KbT} + \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq -0.0285:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 9.5 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;KbT \leq 3 \cdot 10^{-151}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.7 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_2 (+ NdChar t_1)))
   (if (<= KbT -1.75e+128)
     (+
      t_1
      (/
       NdChar
       (+
        1.0
        (-
         (+ 1.0 (+ (/ EDonor KbT) (* Vef (+ (/ 1.0 KbT) (/ mu (* Vef KbT))))))
         (/ Ec KbT)))))
     (if (<= KbT -0.0285)
       t_0
       (if (<= KbT 9.5e-231)
         t_2
         (if (<= KbT 3e-151)
           t_0
           (if (<= KbT 1.7e+103)
             t_2
             (+
              (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
              (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = NdChar + t_1;
	double tmp;
	if (KbT <= -1.75e+128) {
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT))));
	} else if (KbT <= -0.0285) {
		tmp = t_0;
	} else if (KbT <= 9.5e-231) {
		tmp = t_2;
	} else if (KbT <= 3e-151) {
		tmp = t_0;
	} else if (KbT <= 1.7e+103) {
		tmp = t_2;
	} else {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_2 = ndchar + t_1
    if (kbt <= (-1.75d+128)) then
        tmp = t_1 + (ndchar / (1.0d0 + ((1.0d0 + ((edonor / kbt) + (vef * ((1.0d0 / kbt) + (mu / (vef * kbt)))))) - (ec / kbt))))
    else if (kbt <= (-0.0285d0)) then
        tmp = t_0
    else if (kbt <= 9.5d-231) then
        tmp = t_2
    else if (kbt <= 3d-151) then
        tmp = t_0
    else if (kbt <= 1.7d+103) then
        tmp = t_2
    else
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = NdChar + t_1;
	double tmp;
	if (KbT <= -1.75e+128) {
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT))));
	} else if (KbT <= -0.0285) {
		tmp = t_0;
	} else if (KbT <= 9.5e-231) {
		tmp = t_2;
	} else if (KbT <= 3e-151) {
		tmp = t_0;
	} else if (KbT <= 1.7e+103) {
		tmp = t_2;
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_2 = NdChar + t_1
	tmp = 0
	if KbT <= -1.75e+128:
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT))))
	elif KbT <= -0.0285:
		tmp = t_0
	elif KbT <= 9.5e-231:
		tmp = t_2
	elif KbT <= 3e-151:
		tmp = t_0
	elif KbT <= 1.7e+103:
		tmp = t_2
	else:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_2 = Float64(NdChar + t_1)
	tmp = 0.0
	if (KbT <= -1.75e+128)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(mu / Float64(Vef * KbT)))))) - Float64(Ec / KbT)))));
	elseif (KbT <= -0.0285)
		tmp = t_0;
	elseif (KbT <= 9.5e-231)
		tmp = t_2;
	elseif (KbT <= 3e-151)
		tmp = t_0;
	elseif (KbT <= 1.7e+103)
		tmp = t_2;
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_2 = NdChar + t_1;
	tmp = 0.0;
	if (KbT <= -1.75e+128)
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT))));
	elseif (KbT <= -0.0285)
		tmp = t_0;
	elseif (KbT <= 9.5e-231)
		tmp = t_2;
	elseif (KbT <= 3e-151)
		tmp = t_0;
	elseif (KbT <= 1.7e+103)
		tmp = t_2;
	else
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar + t$95$1), $MachinePrecision]}, If[LessEqual[KbT, -1.75e+128], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(mu / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -0.0285], t$95$0, If[LessEqual[KbT, 9.5e-231], t$95$2, If[LessEqual[KbT, 3e-151], t$95$0, If[LessEqual[KbT, 1.7e+103], t$95$2, N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -1.74999999999999984e128

   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 83.9%

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

   6. Taylor expanded in Vef around inf 86.3%

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

   if -1.74999999999999984e128 < KbT < -0.028500000000000001 or 9.4999999999999995e-231 < KbT < 3e-151

   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 53.1%

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

   6. Taylor expanded in Ec around inf 37.4%

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

      1. mul-1-neg 37.4%

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

      2. associate-/l* 39.5%

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

      3. distribute-lft-neg-in 39.5%

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

   8. Simplified 39.5%

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

   9. Taylor expanded in KbT around 0 77.6%

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

   if -0.028500000000000001 < KbT < 9.4999999999999995e-231 or 3e-151 < KbT < 1.6999999999999999e103

   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 41.4%

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

   6. Taylor expanded in Ec around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

      3. +-commutative 42.3%

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

      4. mul-1-neg 42.3%

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

      5. unsub-neg 42.3%

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

      6. associate-+r+ 42.3%

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

      7. +-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in mu around inf 47.3%

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

       1. associate-/r* 46.7%

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

   11. Simplified 46.7%

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

   12. Taylor expanded in KbT around inf 78.9%

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

   if 1.6999999999999999e103 < 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 Vef around inf 87.1%

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

   6. Taylor expanded in EAccept around 0 77.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.75 \cdot 10^{+128}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + Vef \cdot \left(\frac{1}{KbT} + \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq -0.0285:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 9.5 \cdot 10^{-231}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;KbT \leq 3 \cdot 10^{-151}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.7 \cdot 10^{+103}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_2 := t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -5.9 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq 2 \cdot 10^{-19}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 9.8 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT))))))
        (t_2 (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -5.9e+85)
     t_2
     (if (<= Vef 3.2e-144)
       t_1
       (if (<= Vef 2e-19)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
         (if (<= Vef 9.8e+51) t_1 t_2))))))

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 + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -5.9e+85) {
		tmp = t_2;
	} else if (Vef <= 3.2e-144) {
		tmp = t_1;
	} else if (Vef <= 2e-19) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (Vef <= 9.8e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    t_2 = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-5.9d+85)) then
        tmp = t_2
    else if (vef <= 3.2d-144) then
        tmp = t_1
    else if (vef <= 2d-19) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (vef <= 9.8d+51) then
        tmp = t_1
    else
        tmp = t_2
    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 + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -5.9e+85) {
		tmp = t_2;
	} else if (Vef <= 3.2e-144) {
		tmp = t_1;
	} else if (Vef <= 2e-19) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (Vef <= 9.8e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	t_2 = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -5.9e+85:
		tmp = t_2
	elif Vef <= 3.2e-144:
		tmp = t_1
	elif Vef <= 2e-19:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif Vef <= 9.8e+51:
		tmp = t_1
	else:
		tmp = t_2
	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(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	t_2 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -5.9e+85)
		tmp = t_2;
	elseif (Vef <= 3.2e-144)
		tmp = t_1;
	elseif (Vef <= 2e-19)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (Vef <= 9.8e+51)
		tmp = t_1;
	else
		tmp = t_2;
	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 + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	t_2 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -5.9e+85)
		tmp = t_2;
	elseif (Vef <= 3.2e-144)
		tmp = t_1;
	elseif (Vef <= 2e-19)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (Vef <= 9.8e+51)
		tmp = t_1;
	else
		tmp = t_2;
	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[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -5.9e+85], t$95$2, If[LessEqual[Vef, 3.2e-144], t$95$1, If[LessEqual[Vef, 2e-19], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 9.8e+51], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -5.9e85 or 9.79999999999999967e51 < 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 84.9%

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

   if -5.9e85 < Vef < 3.19999999999999973e-144 or 2e-19 < Vef < 9.79999999999999967e51

   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 81.0%

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

   if 3.19999999999999973e-144 < Vef < 2e-19

   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 EDonor around inf 88.2%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -5.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2 \cdot 10^{-19}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 9.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;Vef \leq -3.5 \cdot 10^{+85}:\\ \;\;\;\;t\_1 + t\_0\\ \mathbf{elif}\;Vef \leq 1.5 \cdot 10^{-253}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.5 \cdot 10^{+145}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
   (if (<= Vef -3.5e+85)
     (+ t_1 t_0)
     (if (<= Vef 1.5e-253)
       (+ t_1 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
       (if (<= Vef 8.5e+145)
         (+ t_1 (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
         (+ t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((Vef / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double tmp;
	if (Vef <= -3.5e+85) {
		tmp = t_1 + t_0;
	} else if (Vef <= 1.5e-253) {
		tmp = t_1 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= 8.5e+145) {
		tmp = t_1 + (NdChar / (1.0 + exp((-Ec / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((vef / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    if (vef <= (-3.5d+85)) then
        tmp = t_1 + t_0
    else if (vef <= 1.5d-253) then
        tmp = t_1 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= 8.5d+145) then
        tmp = t_1 + (ndchar / (1.0d0 + exp((-ec / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((Vef / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double tmp;
	if (Vef <= -3.5e+85) {
		tmp = t_1 + t_0;
	} else if (Vef <= 1.5e-253) {
		tmp = t_1 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= 8.5e+145) {
		tmp = t_1 + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((Vef / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	tmp = 0
	if Vef <= -3.5e+85:
		tmp = t_1 + t_0
	elif Vef <= 1.5e-253:
		tmp = t_1 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= 8.5e+145:
		tmp = t_1 + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	tmp = 0.0
	if (Vef <= -3.5e+85)
		tmp = Float64(t_1 + t_0);
	elseif (Vef <= 1.5e-253)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= 8.5e+145)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((Vef / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	tmp = 0.0;
	if (Vef <= -3.5e+85)
		tmp = t_1 + t_0;
	elseif (Vef <= 1.5e-253)
		tmp = t_1 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= 8.5e+145)
		tmp = t_1 + (NdChar / (1.0 + exp((-Ec / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -3.5e+85], N[(t$95$1 + t$95$0), $MachinePrecision], If[LessEqual[Vef, 1.5e-253], N[(t$95$1 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 8.5e+145], N[(t$95$1 + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -3.50000000000000005e85

   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 85.1%

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

   if -3.50000000000000005e85 < Vef < 1.5000000000000001e-253

   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 80.7%

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

   if 1.5000000000000001e-253 < Vef < 8.49999999999999977e145

   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 85.5%

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

      1. associate-*r/ 85.5%

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

      2. mul-1-neg 85.5%

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

   7. Simplified 85.5%

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

   if 8.49999999999999977e145 < 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 91.6%

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

   6. Taylor expanded in EAccept around 0 91.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -2.7 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq 2.6 \cdot 10^{-144}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.7 \cdot 10^{+109}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -2.7e+86)
     t_1
     (if (<= Vef 2.6e-144)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
       (if (<= Vef 1.7e+109)
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
         t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -2.7e+86) {
		tmp = t_1;
	} else if (Vef <= 2.6e-144) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= 1.7e+109) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-2.7d+86)) then
        tmp = t_1
    else if (vef <= 2.6d-144) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= 1.7d+109) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -2.7e+86) {
		tmp = t_1;
	} else if (Vef <= 2.6e-144) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= 1.7e+109) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -2.7e+86:
		tmp = t_1
	elif Vef <= 2.6e-144:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= 1.7e+109:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -2.7e+86)
		tmp = t_1;
	elseif (Vef <= 2.6e-144)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= 1.7e+109)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -2.7e+86)
		tmp = t_1;
	elseif (Vef <= 2.6e-144)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= 1.7e+109)
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -2.7e+86], t$95$1, If[LessEqual[Vef, 2.6e-144], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.7e+109], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -2.70000000000000018e86 or 1.70000000000000003e109 < 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 85.9%

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

   if -2.70000000000000018e86 < Vef < 2.6000000000000001e-144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 81.1%

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

   if 2.6000000000000001e-144 < Vef < 1.70000000000000003e109

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 81.5%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.7 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.7 \cdot 10^{+109}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -2.3 \cdot 10^{+86} \lor \neg \left(Vef \leq 8.5 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Vef -2.3e+86) (not (<= Vef 8.5e+36)))
   (+
    (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
    (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -2.3e+86) || !(Vef <= 8.5e+36)) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((vef <= (-2.3d+86)) .or. (.not. (vef <= 8.5d+36))) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -2.3e+86) || !(Vef <= 8.5e+36)) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Vef <= -2.3e+86) or not (Vef <= 8.5e+36):
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Vef <= -2.3e+86) || !(Vef <= 8.5e+36))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Vef <= -2.3e+86) || ~((Vef <= 8.5e+36)))
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Vef, -2.3e+86], N[Not[LessEqual[Vef, 8.5e+36]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -2.2999999999999999e86 or 8.50000000000000014e36 < 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 83.5%

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

   6. Taylor expanded in EAccept around 0 78.7%

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

   if -2.2999999999999999e86 < Vef < 8.50000000000000014e36

   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 EDonor around inf 76.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.3 \cdot 10^{+86} \lor \neg \left(Vef \leq 8.5 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.3 \cdot 10^{+85} \lor \neg \left(Vef \leq 4.5 \cdot 10^{+41}\right):\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
   (if (or (<= Vef -1.3e+85) (not (<= Vef 4.5e+41)))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double tmp;
	if ((Vef <= -1.3e+85) || !(Vef <= 4.5e+41)) {
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    if ((vef <= (-1.3d+85)) .or. (.not. (vef <= 4.5d+41))) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    else
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double tmp;
	if ((Vef <= -1.3e+85) || !(Vef <= 4.5e+41)) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	tmp = 0
	if (Vef <= -1.3e+85) or not (Vef <= 4.5e+41):
		tmp = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	else:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	tmp = 0.0
	if ((Vef <= -1.3e+85) || !(Vef <= 4.5e+41))
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	tmp = 0.0;
	if ((Vef <= -1.3e+85) || ~((Vef <= 4.5e+41)))
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	else
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[Vef, -1.3e+85], N[Not[LessEqual[Vef, 4.5e+41]], $MachinePrecision]], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if Vef < -1.30000000000000005e85 or 4.5000000000000001e41 < 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 83.5%

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

   if -1.30000000000000005e85 < Vef < 4.5000000000000001e41

   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 EDonor around inf 76.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1.3 \cdot 10^{+85} \lor \neg \left(Vef \leq 4.5 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := NdChar + t\_1\\ \mathbf{if}\;KbT \leq -4.2 \cdot 10^{+127}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + Vef \cdot \left(\frac{1}{KbT} + \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq -4.8:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 5 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;KbT \leq 1.9 \cdot 10^{-147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.15 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + Ec \cdot \left(\frac{1}{Ec} + \left(\left(\frac{EDonor}{Ec \cdot KbT} + \left(\frac{Vef}{Ec \cdot KbT} + \frac{\frac{mu}{Ec}}{KbT}\right)\right) + \frac{-1}{KbT}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_2 (+ NdChar t_1)))
   (if (<= KbT -4.2e+127)
     (+
      t_1
      (/
       NdChar
       (+
        1.0
        (-
         (+ 1.0 (+ (/ EDonor KbT) (* Vef (+ (/ 1.0 KbT) (/ mu (* Vef KbT))))))
         (/ Ec KbT)))))
     (if (<= KbT -4.8)
       t_0
       (if (<= KbT 5e-231)
         t_2
         (if (<= KbT 1.9e-147)
           t_0
           (if (<= KbT 1.15e+103)
             t_2
             (+
              t_1
              (/
               NdChar
               (+
                1.0
                (*
                 Ec
                 (+
                  (/ 1.0 Ec)
                  (+
                   (+
                    (/ EDonor (* Ec KbT))
                    (+ (/ Vef (* Ec KbT)) (/ (/ mu Ec) KbT)))
                   (/ -1.0 KbT))))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = NdChar + t_1;
	double tmp;
	if (KbT <= -4.2e+127) {
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT))));
	} else if (KbT <= -4.8) {
		tmp = t_0;
	} else if (KbT <= 5e-231) {
		tmp = t_2;
	} else if (KbT <= 1.9e-147) {
		tmp = t_0;
	} else if (KbT <= 1.15e+103) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((1.0 / Ec) + (((EDonor / (Ec * KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))) + (-1.0 / KbT))))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_2 = ndchar + t_1
    if (kbt <= (-4.2d+127)) then
        tmp = t_1 + (ndchar / (1.0d0 + ((1.0d0 + ((edonor / kbt) + (vef * ((1.0d0 / kbt) + (mu / (vef * kbt)))))) - (ec / kbt))))
    else if (kbt <= (-4.8d0)) then
        tmp = t_0
    else if (kbt <= 5d-231) then
        tmp = t_2
    else if (kbt <= 1.9d-147) then
        tmp = t_0
    else if (kbt <= 1.15d+103) then
        tmp = t_2
    else
        tmp = t_1 + (ndchar / (1.0d0 + (ec * ((1.0d0 / ec) + (((edonor / (ec * kbt)) + ((vef / (ec * kbt)) + ((mu / ec) / kbt))) + ((-1.0d0) / kbt))))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = NdChar + t_1;
	double tmp;
	if (KbT <= -4.2e+127) {
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT))));
	} else if (KbT <= -4.8) {
		tmp = t_0;
	} else if (KbT <= 5e-231) {
		tmp = t_2;
	} else if (KbT <= 1.9e-147) {
		tmp = t_0;
	} else if (KbT <= 1.15e+103) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((1.0 / Ec) + (((EDonor / (Ec * KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))) + (-1.0 / KbT))))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_2 = NdChar + t_1
	tmp = 0
	if KbT <= -4.2e+127:
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT))))
	elif KbT <= -4.8:
		tmp = t_0
	elif KbT <= 5e-231:
		tmp = t_2
	elif KbT <= 1.9e-147:
		tmp = t_0
	elif KbT <= 1.15e+103:
		tmp = t_2
	else:
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((1.0 / Ec) + (((EDonor / (Ec * KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))) + (-1.0 / KbT))))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_2 = Float64(NdChar + t_1)
	tmp = 0.0
	if (KbT <= -4.2e+127)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(mu / Float64(Vef * KbT)))))) - Float64(Ec / KbT)))));
	elseif (KbT <= -4.8)
		tmp = t_0;
	elseif (KbT <= 5e-231)
		tmp = t_2;
	elseif (KbT <= 1.9e-147)
		tmp = t_0;
	elseif (KbT <= 1.15e+103)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(1.0 / Ec) + Float64(Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(Float64(Vef / Float64(Ec * KbT)) + Float64(Float64(mu / Ec) / KbT))) + Float64(-1.0 / KbT)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_2 = NdChar + t_1;
	tmp = 0.0;
	if (KbT <= -4.2e+127)
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT))));
	elseif (KbT <= -4.8)
		tmp = t_0;
	elseif (KbT <= 5e-231)
		tmp = t_2;
	elseif (KbT <= 1.9e-147)
		tmp = t_0;
	elseif (KbT <= 1.15e+103)
		tmp = t_2;
	else
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((1.0 / Ec) + (((EDonor / (Ec * KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))) + (-1.0 / KbT))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar + t$95$1), $MachinePrecision]}, If[LessEqual[KbT, -4.2e+127], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(mu / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -4.8], t$95$0, If[LessEqual[KbT, 5e-231], t$95$2, If[LessEqual[KbT, 1.9e-147], t$95$0, If[LessEqual[KbT, 1.15e+103], t$95$2, N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(1.0 / Ec), $MachinePrecision] + N[(N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(mu / Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -4.19999999999999983e127

   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 83.9%

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

   6. Taylor expanded in Vef around inf 86.3%

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

   if -4.19999999999999983e127 < KbT < -4.79999999999999982 or 5.00000000000000023e-231 < KbT < 1.90000000000000014e-147

   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 53.1%

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

   6. Taylor expanded in Ec around inf 37.4%

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

      1. mul-1-neg 37.4%

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

      2. associate-/l* 39.5%

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

      3. distribute-lft-neg-in 39.5%

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

   8. Simplified 39.5%

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

   9. Taylor expanded in KbT around 0 77.6%

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

   if -4.79999999999999982 < KbT < 5.00000000000000023e-231 or 1.90000000000000014e-147 < KbT < 1.15000000000000004e103

   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 41.4%

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

   6. Taylor expanded in Ec around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

      3. +-commutative 42.3%

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

      4. mul-1-neg 42.3%

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

      5. unsub-neg 42.3%

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

      6. associate-+r+ 42.3%

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

      7. +-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in mu around inf 47.3%

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

       1. associate-/r* 46.7%

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

   11. Simplified 46.7%

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

   12. Taylor expanded in KbT around inf 78.9%

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

   if 1.15000000000000004e103 < 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 76.3%

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

   6. Taylor expanded in Ec around inf 78.8%

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

      1. associate--l+ 78.8%

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

      2. associate-/r* 84.2%

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

   8. Simplified 84.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.2 \cdot 10^{+127}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + Vef \cdot \left(\frac{1}{KbT} + \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq -4.8:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 5 \cdot 10^{-231}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.9 \cdot 10^{-147}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.15 \cdot 10^{+103}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1}{Ec} + \left(\left(\frac{EDonor}{Ec \cdot KbT} + \left(\frac{Vef}{Ec \cdot KbT} + \frac{\frac{mu}{Ec}}{KbT}\right)\right) + \frac{-1}{KbT}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -5.1 \cdot 10^{+98}:\\ \;\;\;\;t\_2 + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -1.2 \cdot 10^{-28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 8 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 2 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1
         (+
          NdChar
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NdChar -5.1e+98)
     (+ t_2 (/ NaChar 2.0))
     (if (<= NdChar -1.2e-28)
       t_0
       (if (<= NdChar 8e-116)
         t_1
         (if (<= NdChar 2.3e-75)
           t_0
           (if (<= NdChar 2e+65)
             t_1
             (+ t_2 (/ NaChar (+ (/ EAccept 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 t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_2 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -5.1e+98) {
		tmp = t_2 + (NaChar / 2.0);
	} else if (NdChar <= -1.2e-28) {
		tmp = t_0;
	} else if (NdChar <= 8e-116) {
		tmp = t_1;
	} else if (NdChar <= 2.3e-75) {
		tmp = t_0;
	} else if (NdChar <= 2e+65) {
		tmp = t_1;
	} else {
		tmp = t_2 + (NaChar / ((EAccept / 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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = ndchar + (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt))))
    t_2 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (ndchar <= (-5.1d+98)) then
        tmp = t_2 + (nachar / 2.0d0)
    else if (ndchar <= (-1.2d-28)) then
        tmp = t_0
    else if (ndchar <= 8d-116) then
        tmp = t_1
    else if (ndchar <= 2.3d-75) then
        tmp = t_0
    else if (ndchar <= 2d+65) then
        tmp = t_1
    else
        tmp = t_2 + (nachar / ((eaccept / 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 t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar + (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_2 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -5.1e+98) {
		tmp = t_2 + (NaChar / 2.0);
	} else if (NdChar <= -1.2e-28) {
		tmp = t_0;
	} else if (NdChar <= 8e-116) {
		tmp = t_1;
	} else if (NdChar <= 2.3e-75) {
		tmp = t_0;
	} else if (NdChar <= 2e+65) {
		tmp = t_1;
	} else {
		tmp = t_2 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = NdChar + (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	t_2 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -5.1e+98:
		tmp = t_2 + (NaChar / 2.0)
	elif NdChar <= -1.2e-28:
		tmp = t_0
	elif NdChar <= 8e-116:
		tmp = t_1
	elif NdChar <= 2.3e-75:
		tmp = t_0
	elif NdChar <= 2e+65:
		tmp = t_1
	else:
		tmp = t_2 + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -5.1e+98)
		tmp = Float64(t_2 + Float64(NaChar / 2.0));
	elseif (NdChar <= -1.2e-28)
		tmp = t_0;
	elseif (NdChar <= 8e-116)
		tmp = t_1;
	elseif (NdChar <= 2.3e-75)
		tmp = t_0;
	elseif (NdChar <= 2e+65)
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = NdChar + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	t_2 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -5.1e+98)
		tmp = t_2 + (NaChar / 2.0);
	elseif (NdChar <= -1.2e-28)
		tmp = t_0;
	elseif (NdChar <= 8e-116)
		tmp = t_1;
	elseif (NdChar <= 2.3e-75)
		tmp = t_0;
	elseif (NdChar <= 2e+65)
		tmp = t_1;
	else
		tmp = t_2 + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -5.1e+98], N[(t$95$2 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -1.2e-28], t$95$0, If[LessEqual[NdChar, 8e-116], t$95$1, If[LessEqual[NdChar, 2.3e-75], t$95$0, If[LessEqual[NdChar, 2e+65], t$95$1, N[(t$95$2 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -5.09999999999999988e98

   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 76.5%

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

   6. Taylor expanded in Ev around 0 65.5%

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

   if -5.09999999999999988e98 < NdChar < -1.2000000000000001e-28 or 8e-116 < NdChar < 2.3e-75

   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%

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

   6. Taylor expanded in Ec around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-/l* 51.8%

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

      3. distribute-lft-neg-in 51.8%

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

   8. Simplified 51.8%

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

   9. Taylor expanded in KbT around 0 89.9%

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

   if -1.2000000000000001e-28 < NdChar < 8e-116 or 2.3e-75 < NdChar < 2e65

   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 56.5%

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

   6. Taylor expanded in Ec around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. distribute-rgt-neg-in 57.2%

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

      3. +-commutative 57.2%

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

      4. mul-1-neg 57.2%

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

      5. unsub-neg 57.2%

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

      6. associate-+r+ 57.2%

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

      7. +-commutative 57.2%

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

   8. Simplified 57.2%

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

   9. Taylor expanded in mu around inf 57.2%

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

       1. associate-/r* 58.0%

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

   11. Simplified 58.0%

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

   12. Taylor expanded in KbT around inf 80.7%

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

   if 2e65 < 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 EAccept around inf 85.2%

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

   6. Taylor expanded in EAccept around 0 78.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -5.1 \cdot 10^{+98}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -1.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 8 \cdot 10^{-116}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 2 \cdot 10^{+65}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -6.9 \cdot 10^{+98}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.12 \cdot 10^{-28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 8 \cdot 10^{-118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NdChar \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_2
         (+
          NdChar
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))))
   (if (<= NdChar -6.9e+98)
     (+ t_1 (/ NaChar (+ (/ Ev KbT) 2.0)))
     (if (<= NdChar -1.12e-28)
       t_0
       (if (<= NdChar 8e-118)
         t_2
         (if (<= NdChar 3.8e-75)
           t_0
           (if (<= NdChar 2.4e+71)
             t_2
             (+ t_1 (/ NaChar (+ (/ EAccept 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 t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = NdChar + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double tmp;
	if (NdChar <= -6.9e+98) {
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= -1.12e-28) {
		tmp = t_0;
	} else if (NdChar <= 8e-118) {
		tmp = t_2;
	} else if (NdChar <= 3.8e-75) {
		tmp = t_0;
	} else if (NdChar <= 2.4e+71) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NaChar / ((EAccept / 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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_2 = ndchar + (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt))))
    if (ndchar <= (-6.9d+98)) then
        tmp = t_1 + (nachar / ((ev / kbt) + 2.0d0))
    else if (ndchar <= (-1.12d-28)) then
        tmp = t_0
    else if (ndchar <= 8d-118) then
        tmp = t_2
    else if (ndchar <= 3.8d-75) then
        tmp = t_0
    else if (ndchar <= 2.4d+71) then
        tmp = t_2
    else
        tmp = t_1 + (nachar / ((eaccept / 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 t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = NdChar + (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double tmp;
	if (NdChar <= -6.9e+98) {
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= -1.12e-28) {
		tmp = t_0;
	} else if (NdChar <= 8e-118) {
		tmp = t_2;
	} else if (NdChar <= 3.8e-75) {
		tmp = t_0;
	} else if (NdChar <= 2.4e+71) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_2 = NdChar + (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	tmp = 0
	if NdChar <= -6.9e+98:
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0))
	elif NdChar <= -1.12e-28:
		tmp = t_0
	elif NdChar <= 8e-118:
		tmp = t_2
	elif NdChar <= 3.8e-75:
		tmp = t_0
	elif NdChar <= 2.4e+71:
		tmp = t_2
	else:
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
	tmp = 0.0
	if (NdChar <= -6.9e+98)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (NdChar <= -1.12e-28)
		tmp = t_0;
	elseif (NdChar <= 8e-118)
		tmp = t_2;
	elseif (NdChar <= 3.8e-75)
		tmp = t_0;
	elseif (NdChar <= 2.4e+71)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_2 = NdChar + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	tmp = 0.0;
	if (NdChar <= -6.9e+98)
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0));
	elseif (NdChar <= -1.12e-28)
		tmp = t_0;
	elseif (NdChar <= 8e-118)
		tmp = t_2;
	elseif (NdChar <= 3.8e-75)
		tmp = t_0;
	elseif (NdChar <= 2.4e+71)
		tmp = t_2;
	else
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -6.9e+98], N[(t$95$1 + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -1.12e-28], t$95$0, If[LessEqual[NdChar, 8e-118], t$95$2, If[LessEqual[NdChar, 3.8e-75], t$95$0, If[LessEqual[NdChar, 2.4e+71], t$95$2, N[(t$95$1 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -6.9e98

   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 76.5%

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

   6. Taylor expanded in Ev around 0 66.1%

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

   if -6.9e98 < NdChar < -1.1200000000000001e-28 or 7.99999999999999988e-118 < NdChar < 3.79999999999999994e-75

   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%

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

   6. Taylor expanded in Ec around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-/l* 51.8%

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

      3. distribute-lft-neg-in 51.8%

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

   8. Simplified 51.8%

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

   9. Taylor expanded in KbT around 0 89.9%

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

   if -1.1200000000000001e-28 < NdChar < 7.99999999999999988e-118 or 3.79999999999999994e-75 < NdChar < 2.39999999999999981e71

   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 56.5%

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

   6. Taylor expanded in Ec around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. distribute-rgt-neg-in 57.2%

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

      3. +-commutative 57.2%

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

      4. mul-1-neg 57.2%

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

      5. unsub-neg 57.2%

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

      6. associate-+r+ 57.2%

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

      7. +-commutative 57.2%

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

   8. Simplified 57.2%

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

   9. Taylor expanded in mu around inf 57.2%

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

       1. associate-/r* 58.0%

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

   11. Simplified 58.0%

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

   12. Taylor expanded in KbT around inf 80.7%

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

   if 2.39999999999999981e71 < 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 EAccept around inf 85.2%

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

   6. Taylor expanded in EAccept around 0 78.3%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6.9 \cdot 10^{+98}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.12 \cdot 10^{-28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 8 \cdot 10^{-118}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+71}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := NdChar + t\_0\\ \mathbf{if}\;NdChar \leq -4 \cdot 10^{+101}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.05 \cdot 10^{-28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 9.2 \cdot 10^{-116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NdChar \leq 4 \cdot 10^{-75}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 4.8 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_2 (+ NdChar t_0)))
   (if (<= NdChar -4e+101)
     (+ t_1 (/ NaChar (+ (/ Ev KbT) 2.0)))
     (if (<= NdChar -1.05e-28)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
       (if (<= NdChar 9.2e-116)
         t_2
         (if (<= NdChar 4e-75)
           (+ t_0 (/ NdChar (- 2.0 (/ Ec KbT))))
           (if (<= NdChar 4.8e+72)
             t_2
             (+ t_1 (/ NaChar (+ (/ EAccept 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 t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = NdChar + t_0;
	double tmp;
	if (NdChar <= -4e+101) {
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= -1.05e-28) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (NdChar <= 9.2e-116) {
		tmp = t_2;
	} else if (NdChar <= 4e-75) {
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	} else if (NdChar <= 4.8e+72) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NaChar / ((EAccept / 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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_2 = ndchar + t_0
    if (ndchar <= (-4d+101)) then
        tmp = t_1 + (nachar / ((ev / kbt) + 2.0d0))
    else if (ndchar <= (-1.05d-28)) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else if (ndchar <= 9.2d-116) then
        tmp = t_2
    else if (ndchar <= 4d-75) then
        tmp = t_0 + (ndchar / (2.0d0 - (ec / kbt)))
    else if (ndchar <= 4.8d+72) then
        tmp = t_2
    else
        tmp = t_1 + (nachar / ((eaccept / 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 t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = NdChar + t_0;
	double tmp;
	if (NdChar <= -4e+101) {
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= -1.05e-28) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (NdChar <= 9.2e-116) {
		tmp = t_2;
	} else if (NdChar <= 4e-75) {
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	} else if (NdChar <= 4.8e+72) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_2 = NdChar + t_0
	tmp = 0
	if NdChar <= -4e+101:
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0))
	elif NdChar <= -1.05e-28:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	elif NdChar <= 9.2e-116:
		tmp = t_2
	elif NdChar <= 4e-75:
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)))
	elif NdChar <= 4.8e+72:
		tmp = t_2
	else:
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(NdChar + t_0)
	tmp = 0.0
	if (NdChar <= -4e+101)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (NdChar <= -1.05e-28)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	elseif (NdChar <= 9.2e-116)
		tmp = t_2;
	elseif (NdChar <= 4e-75)
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))));
	elseif (NdChar <= 4.8e+72)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_2 = NdChar + t_0;
	tmp = 0.0;
	if (NdChar <= -4e+101)
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0));
	elseif (NdChar <= -1.05e-28)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	elseif (NdChar <= 9.2e-116)
		tmp = t_2;
	elseif (NdChar <= 4e-75)
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	elseif (NdChar <= 4.8e+72)
		tmp = t_2;
	else
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar + t$95$0), $MachinePrecision]}, If[LessEqual[NdChar, -4e+101], N[(t$95$1 + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -1.05e-28], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 9.2e-116], t$95$2, If[LessEqual[NdChar, 4e-75], N[(t$95$0 + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 4.8e+72], t$95$2, N[(t$95$1 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -3.9999999999999999e101

   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 76.5%

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

   6. Taylor expanded in Ev around 0 66.1%

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

   if -3.9999999999999999e101 < NdChar < -1.05000000000000003e-28

   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 47.9%

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

   6. Taylor expanded in Ec around inf 44.5%

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

      1. mul-1-neg 44.5%

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

      2. associate-/l* 44.5%

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

      3. distribute-lft-neg-in 44.5%

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

   8. Simplified 44.5%

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

   9. Taylor expanded in KbT around 0 88.9%

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

   if -1.05000000000000003e-28 < NdChar < 9.20000000000000006e-116 or 3.9999999999999998e-75 < NdChar < 4.8000000000000002e72

   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 56.5%

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

   6. Taylor expanded in Ec around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. distribute-rgt-neg-in 57.2%

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

      3. +-commutative 57.2%

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

      4. mul-1-neg 57.2%

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

      5. unsub-neg 57.2%

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

      6. associate-+r+ 57.2%

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

      7. +-commutative 57.2%

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

   8. Simplified 57.2%

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

   9. Taylor expanded in mu around inf 57.2%

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

       1. associate-/r* 58.0%

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

   11. Simplified 58.0%

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

   12. Taylor expanded in KbT around inf 80.7%

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

   if 9.20000000000000006e-116 < NdChar < 3.9999999999999998e-75

   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 92.0%

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

      1. associate-*r/ 92.0%

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

      2. mul-1-neg 92.0%

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

   7. Simplified 92.0%

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

   8. Taylor expanded in Ec around 0 100.0%

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

      1. neg-mul-1 40.7%

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

      2. unsub-neg 40.7%

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

   10. Simplified 100.0%

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

   if 4.8000000000000002e72 < 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 EAccept around inf 85.2%

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

   6. Taylor expanded in EAccept around 0 78.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{EAccept}{KbT}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4 \cdot 10^{+101}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.05 \cdot 10^{-28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 9.2 \cdot 10^{-116}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 4 \cdot 10^{-75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 4.8 \cdot 10^{+72}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ t_2 := NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -3.05 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -9.8 \cdot 10^{-29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 1.22 \cdot 10^{-117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NdChar \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 3.6 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
          (/ NaChar 2.0)))
        (t_2
         (+
          NdChar
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))))
   (if (<= NdChar -3.05e+100)
     t_1
     (if (<= NdChar -9.8e-29)
       t_0
       (if (<= NdChar 1.22e-117)
         t_2
         (if (<= NdChar 2.3e-75) t_0 (if (<= NdChar 3.6e+162) 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 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double t_2 = NdChar + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double tmp;
	if (NdChar <= -3.05e+100) {
		tmp = t_1;
	} else if (NdChar <= -9.8e-29) {
		tmp = t_0;
	} else if (NdChar <= 1.22e-117) {
		tmp = t_2;
	} else if (NdChar <= 2.3e-75) {
		tmp = t_0;
	} else if (NdChar <= 3.6e+162) {
		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 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    t_2 = ndchar + (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt))))
    if (ndchar <= (-3.05d+100)) then
        tmp = t_1
    else if (ndchar <= (-9.8d-29)) then
        tmp = t_0
    else if (ndchar <= 1.22d-117) then
        tmp = t_2
    else if (ndchar <= 2.3d-75) then
        tmp = t_0
    else if (ndchar <= 3.6d+162) 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 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double t_2 = NdChar + (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double tmp;
	if (NdChar <= -3.05e+100) {
		tmp = t_1;
	} else if (NdChar <= -9.8e-29) {
		tmp = t_0;
	} else if (NdChar <= 1.22e-117) {
		tmp = t_2;
	} else if (NdChar <= 2.3e-75) {
		tmp = t_0;
	} else if (NdChar <= 3.6e+162) {
		tmp = t_2;
	} 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((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	t_2 = NdChar + (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	tmp = 0
	if NdChar <= -3.05e+100:
		tmp = t_1
	elif NdChar <= -9.8e-29:
		tmp = t_0
	elif NdChar <= 1.22e-117:
		tmp = t_2
	elif NdChar <= 2.3e-75:
		tmp = t_0
	elif NdChar <= 3.6e+162:
		tmp = t_2
	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(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	t_2 = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
	tmp = 0.0
	if (NdChar <= -3.05e+100)
		tmp = t_1;
	elseif (NdChar <= -9.8e-29)
		tmp = t_0;
	elseif (NdChar <= 1.22e-117)
		tmp = t_2;
	elseif (NdChar <= 2.3e-75)
		tmp = t_0;
	elseif (NdChar <= 3.6e+162)
		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 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	t_2 = NdChar + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	tmp = 0.0;
	if (NdChar <= -3.05e+100)
		tmp = t_1;
	elseif (NdChar <= -9.8e-29)
		tmp = t_0;
	elseif (NdChar <= 1.22e-117)
		tmp = t_2;
	elseif (NdChar <= 2.3e-75)
		tmp = t_0;
	elseif (NdChar <= 3.6e+162)
		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[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.05e+100], t$95$1, If[LessEqual[NdChar, -9.8e-29], t$95$0, If[LessEqual[NdChar, 1.22e-117], t$95$2, If[LessEqual[NdChar, 2.3e-75], t$95$0, If[LessEqual[NdChar, 3.6e+162], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -3.05e100 or 3.59999999999999994e162 < 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 80.8%

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

   6. Taylor expanded in Ev around 0 73.2%

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

   if -3.05e100 < NdChar < -9.7999999999999997e-29 or 1.21999999999999997e-117 < NdChar < 2.3e-75

   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%

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

   6. Taylor expanded in Ec around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-/l* 51.8%

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

      3. distribute-lft-neg-in 51.8%

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

   8. Simplified 51.8%

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

   9. Taylor expanded in KbT around 0 89.9%

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

   if -9.7999999999999997e-29 < NdChar < 1.21999999999999997e-117 or 2.3e-75 < NdChar < 3.59999999999999994e162

   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 55.7%

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

   6. Taylor expanded in Ec around -inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-rgt-neg-in 56.4%

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

      3. +-commutative 56.4%

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

      4. mul-1-neg 56.4%

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

      5. unsub-neg 56.4%

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

      6. associate-+r+ 56.4%

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

      7. +-commutative 56.4%

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

   8. Simplified 56.4%

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

   9. Taylor expanded in mu around inf 55.3%

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

       1. associate-/r* 56.0%

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

   11. Simplified 56.0%

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

   12. Taylor expanded in KbT around inf 79.3%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.05 \cdot 10^{+100}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -9.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.22 \cdot 10^{-117}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 3.6 \cdot 10^{+162}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;KbT \leq -9 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -0.11:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;KbT \leq 6.2 \cdot 10^{-231}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 2.9 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          NdChar
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))
   (if (<= KbT -9e+126)
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
     (if (<= KbT -0.11)
       t_1
       (if (<= KbT 6.2e-231)
         t_0
         (if (<= KbT 2.9e-154)
           t_1
           (if (<= KbT 2.1e+103)
             t_0
             (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ 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 + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -9e+126) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= -0.11) {
		tmp = t_1;
	} else if (KbT <= 6.2e-231) {
		tmp = t_0;
	} else if (KbT <= 2.9e-154) {
		tmp = t_1;
	} else if (KbT <= 2.1e+103) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (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) :: t_1
    real(8) :: tmp
    t_0 = ndchar + (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt))))
    t_1 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    if (kbt <= (-9d+126)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= (-0.11d0)) then
        tmp = t_1
    else if (kbt <= 6.2d-231) then
        tmp = t_0
    else if (kbt <= 2.9d-154) then
        tmp = t_1
    else if (kbt <= 2.1d+103) then
        tmp = t_0
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (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 + (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -9e+126) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= -0.11) {
		tmp = t_1;
	} else if (KbT <= 6.2e-231) {
		tmp = t_0;
	} else if (KbT <= 2.9e-154) {
		tmp = t_1;
	} else if (KbT <= 2.1e+103) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar + (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	tmp = 0
	if KbT <= -9e+126:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= -0.11:
		tmp = t_1
	elif KbT <= 6.2e-231:
		tmp = t_0
	elif KbT <= 2.9e-154:
		tmp = t_1
	elif KbT <= 2.1e+103:
		tmp = t_0
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	tmp = 0.0
	if (KbT <= -9e+126)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= -0.11)
		tmp = t_1;
	elseif (KbT <= 6.2e-231)
		tmp = t_0;
	elseif (KbT <= 2.9e-154)
		tmp = t_1;
	elseif (KbT <= 2.1e+103)
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + 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 + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	tmp = 0.0;
	if (KbT <= -9e+126)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= -0.11)
		tmp = t_1;
	elseif (KbT <= 6.2e-231)
		tmp = t_0;
	elseif (KbT <= 2.9e-154)
		tmp = t_1;
	elseif (KbT <= 2.1e+103)
		tmp = t_0;
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (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[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -9e+126], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -0.11], t$95$1, If[LessEqual[KbT, 6.2e-231], t$95$0, If[LessEqual[KbT, 2.9e-154], t$95$1, If[LessEqual[KbT, 2.1e+103], t$95$0, N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -8.99999999999999947e126

   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 81.5%

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

   6. Taylor expanded in EAccept around inf 77.4%

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

   if -8.99999999999999947e126 < KbT < -0.110000000000000001 or 6.19999999999999976e-231 < KbT < 2.9e-154

   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 54.4%

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

   6. Taylor expanded in Ec around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. associate-/l* 40.3%

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

      3. distribute-lft-neg-in 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in KbT around 0 79.4%

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

   if -0.110000000000000001 < KbT < 6.19999999999999976e-231 or 2.9e-154 < KbT < 2.1000000000000002e103

   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 41.4%

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

   6. Taylor expanded in Ec around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

      3. +-commutative 42.3%

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

      4. mul-1-neg 42.3%

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

      5. unsub-neg 42.3%

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

      6. associate-+r+ 42.3%

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

      7. +-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in mu around inf 47.3%

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

       1. associate-/r* 46.7%

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

   11. Simplified 46.7%

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

   12. Taylor expanded in KbT around inf 78.9%

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

   if 2.1000000000000002e103 < 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 73.8%

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

   6. Taylor expanded in Ev around inf 67.2%

      \[\leadsto \frac{NdChar}{2} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -9 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -0.11:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 6.2 \cdot 10^{-231}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.9 \cdot 10^{-154}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;KbT \leq -8.5 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -5.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;KbT \leq 7 \cdot 10^{-231}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.75 \cdot 10^{-148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          NdChar
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))
   (if (<= KbT -8.5e+126)
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
     (if (<= KbT -5.8)
       t_1
       (if (<= KbT 7e-231)
         t_0
         (if (<= KbT 1.75e-148)
           t_1
           (if (<= KbT 2.1e+103)
             t_0
             (+
              (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))
              (/ 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 + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -8.5e+126) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= -5.8) {
		tmp = t_1;
	} else if (KbT <= 7e-231) {
		tmp = t_0;
	} else if (KbT <= 1.75e-148) {
		tmp = t_1;
	} else if (KbT <= 2.1e+103) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (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) :: t_1
    real(8) :: tmp
    t_0 = ndchar + (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt))))
    t_1 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    if (kbt <= (-8.5d+126)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= (-5.8d0)) then
        tmp = t_1
    else if (kbt <= 7d-231) then
        tmp = t_0
    else if (kbt <= 1.75d-148) then
        tmp = t_1
    else if (kbt <= 2.1d+103) then
        tmp = t_0
    else
        tmp = (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))) + (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 + (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -8.5e+126) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= -5.8) {
		tmp = t_1;
	} else if (KbT <= 7e-231) {
		tmp = t_0;
	} else if (KbT <= 1.75e-148) {
		tmp = t_1;
	} else if (KbT <= 2.1e+103) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar + (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	tmp = 0
	if KbT <= -8.5e+126:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= -5.8:
		tmp = t_1
	elif KbT <= 7e-231:
		tmp = t_0
	elif KbT <= 1.75e-148:
		tmp = t_1
	elif KbT <= 2.1e+103:
		tmp = t_0
	else:
		tmp = (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	tmp = 0.0
	if (KbT <= -8.5e+126)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= -5.8)
		tmp = t_1;
	elseif (KbT <= 7e-231)
		tmp = t_0;
	elseif (KbT <= 1.75e-148)
		tmp = t_1;
	elseif (KbT <= 2.1e+103)
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))) + 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 + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	tmp = 0.0;
	if (KbT <= -8.5e+126)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= -5.8)
		tmp = t_1;
	elseif (KbT <= 7e-231)
		tmp = t_0;
	elseif (KbT <= 1.75e-148)
		tmp = t_1;
	elseif (KbT <= 2.1e+103)
		tmp = t_0;
	else
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (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[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -8.5e+126], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -5.8], t$95$1, If[LessEqual[KbT, 7e-231], t$95$0, If[LessEqual[KbT, 1.75e-148], t$95$1, If[LessEqual[KbT, 2.1e+103], t$95$0, N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -8.49999999999999944e126

   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 81.5%

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

   6. Taylor expanded in EAccept around inf 77.4%

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

   if -8.49999999999999944e126 < KbT < -5.79999999999999982 or 7.0000000000000002e-231 < KbT < 1.75e-148

   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 54.4%

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

   6. Taylor expanded in Ec around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. associate-/l* 40.3%

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

      3. distribute-lft-neg-in 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in KbT around 0 79.4%

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

   if -5.79999999999999982 < KbT < 7.0000000000000002e-231 or 1.75e-148 < KbT < 2.1000000000000002e103

   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 41.4%

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

   6. Taylor expanded in Ec around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

      3. +-commutative 42.3%

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

      4. mul-1-neg 42.3%

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

      5. unsub-neg 42.3%

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

      6. associate-+r+ 42.3%

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

      7. +-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in mu around inf 47.3%

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

       1. associate-/r* 46.7%

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

   11. Simplified 46.7%

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

   12. Taylor expanded in KbT around inf 78.9%

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

   if 2.1000000000000002e103 < 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 73.8%

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

   6. Taylor expanded in EAccept around 0 67.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -8.5 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -5.8:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 7 \cdot 10^{-231}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.75 \cdot 10^{-148}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;KbT \leq -9 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;KbT \leq -0.085:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;KbT \leq 1.1 \cdot 10^{-230}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 3.4 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          NdChar
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))
   (if (<= KbT -9e+126)
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar (- 2.0 (/ Ec KbT))))
     (if (<= KbT -0.085)
       t_1
       (if (<= KbT 1.1e-230)
         t_0
         (if (<= KbT 3.4e-150)
           t_1
           (if (<= KbT 2.1e+103)
             t_0
             (+
              (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))
              (/ 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 + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -9e+126) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	} else if (KbT <= -0.085) {
		tmp = t_1;
	} else if (KbT <= 1.1e-230) {
		tmp = t_0;
	} else if (KbT <= 3.4e-150) {
		tmp = t_1;
	} else if (KbT <= 2.1e+103) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (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) :: t_1
    real(8) :: tmp
    t_0 = ndchar + (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt))))
    t_1 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    if (kbt <= (-9d+126)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / (2.0d0 - (ec / kbt)))
    else if (kbt <= (-0.085d0)) then
        tmp = t_1
    else if (kbt <= 1.1d-230) then
        tmp = t_0
    else if (kbt <= 3.4d-150) then
        tmp = t_1
    else if (kbt <= 2.1d+103) then
        tmp = t_0
    else
        tmp = (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))) + (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 + (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -9e+126) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	} else if (KbT <= -0.085) {
		tmp = t_1;
	} else if (KbT <= 1.1e-230) {
		tmp = t_0;
	} else if (KbT <= 3.4e-150) {
		tmp = t_1;
	} else if (KbT <= 2.1e+103) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar + (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	tmp = 0
	if KbT <= -9e+126:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (2.0 - (Ec / KbT)))
	elif KbT <= -0.085:
		tmp = t_1
	elif KbT <= 1.1e-230:
		tmp = t_0
	elif KbT <= 3.4e-150:
		tmp = t_1
	elif KbT <= 2.1e+103:
		tmp = t_0
	else:
		tmp = (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	tmp = 0.0
	if (KbT <= -9e+126)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))));
	elseif (KbT <= -0.085)
		tmp = t_1;
	elseif (KbT <= 1.1e-230)
		tmp = t_0;
	elseif (KbT <= 3.4e-150)
		tmp = t_1;
	elseif (KbT <= 2.1e+103)
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))) + 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 + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	tmp = 0.0;
	if (KbT <= -9e+126)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	elseif (KbT <= -0.085)
		tmp = t_1;
	elseif (KbT <= 1.1e-230)
		tmp = t_0;
	elseif (KbT <= 3.4e-150)
		tmp = t_1;
	elseif (KbT <= 2.1e+103)
		tmp = t_0;
	else
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (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[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -9e+126], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -0.085], t$95$1, If[LessEqual[KbT, 1.1e-230], t$95$0, If[LessEqual[KbT, 3.4e-150], t$95$1, If[LessEqual[KbT, 2.1e+103], t$95$0, N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -8.99999999999999947e126

   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 86.1%

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

      1. associate-*r/ 86.1%

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

      2. mul-1-neg 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in Ec around 0 81.5%

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

      1. neg-mul-1 66.8%

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

      2. unsub-neg 66.8%

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

   10. Simplified 81.5%

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

   11. Taylor expanded in EAccept around inf 77.4%

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

   if -8.99999999999999947e126 < KbT < -0.0850000000000000061 or 1.0999999999999999e-230 < KbT < 3.39999999999999999e-150

   1. Initial program 100.0%

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

   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 54.4%

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

   6. Taylor expanded in Ec around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. associate-/l* 40.3%

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

      3. distribute-lft-neg-in 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in KbT around 0 79.4%

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

   if -0.0850000000000000061 < KbT < 1.0999999999999999e-230 or 3.39999999999999999e-150 < KbT < 2.1000000000000002e103

   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 41.4%

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

   6. Taylor expanded in Ec around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

      3. +-commutative 42.3%

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

      4. mul-1-neg 42.3%

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

      5. unsub-neg 42.3%

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

      6. associate-+r+ 42.3%

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

      7. +-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in mu around inf 47.3%

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

       1. associate-/r* 46.7%

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

   11. Simplified 46.7%

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

   12. Taylor expanded in KbT around inf 78.9%

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

   if 2.1000000000000002e103 < 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 73.8%

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

   6. Taylor expanded in EAccept around 0 67.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -9 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;KbT \leq -0.085:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.1 \cdot 10^{-230}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;KbT \leq 3.4 \cdot 10^{-150}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ t_1 := NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;KbT \leq -9 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + t\_0\\ \mathbf{elif}\;KbT \leq -0.41:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;KbT \leq 8 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;KbT \leq 1.5 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- 2.0 (/ Ec KbT))))
        (t_1
         (+
          NdChar
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))
   (if (<= KbT -9e+126)
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) t_0)
     (if (<= KbT -0.41)
       t_2
       (if (<= KbT 8e-231)
         t_1
         (if (<= KbT 1.5e-142)
           t_2
           (if (<= KbT 2.1e+103)
             t_1
             (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_0))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (2.0 - (Ec / KbT));
	double t_1 = NdChar + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_2 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -9e+126) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + t_0;
	} else if (KbT <= -0.41) {
		tmp = t_2;
	} else if (KbT <= 8e-231) {
		tmp = t_1;
	} else if (KbT <= 1.5e-142) {
		tmp = t_2;
	} else if (KbT <= 2.1e+103) {
		tmp = t_1;
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (2.0d0 - (ec / kbt))
    t_1 = ndchar + (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt))))
    t_2 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    if (kbt <= (-9d+126)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + t_0
    else if (kbt <= (-0.41d0)) then
        tmp = t_2
    else if (kbt <= 8d-231) then
        tmp = t_1
    else if (kbt <= 1.5d-142) then
        tmp = t_2
    else if (kbt <= 2.1d+103) then
        tmp = t_1
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (2.0 - (Ec / KbT));
	double t_1 = NdChar + (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_2 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -9e+126) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + t_0;
	} else if (KbT <= -0.41) {
		tmp = t_2;
	} else if (KbT <= 8e-231) {
		tmp = t_1;
	} else if (KbT <= 1.5e-142) {
		tmp = t_2;
	} else if (KbT <= 2.1e+103) {
		tmp = t_1;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (2.0 - (Ec / KbT))
	t_1 = NdChar + (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	t_2 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	tmp = 0
	if KbT <= -9e+126:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + t_0
	elif KbT <= -0.41:
		tmp = t_2
	elif KbT <= 8e-231:
		tmp = t_1
	elif KbT <= 1.5e-142:
		tmp = t_2
	elif KbT <= 2.1e+103:
		tmp = t_1
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(2.0 - Float64(Ec / KbT)))
	t_1 = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	tmp = 0.0
	if (KbT <= -9e+126)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + t_0);
	elseif (KbT <= -0.41)
		tmp = t_2;
	elseif (KbT <= 8e-231)
		tmp = t_1;
	elseif (KbT <= 1.5e-142)
		tmp = t_2;
	elseif (KbT <= 2.1e+103)
		tmp = t_1;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (2.0 - (Ec / KbT));
	t_1 = NdChar + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	t_2 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	tmp = 0.0;
	if (KbT <= -9e+126)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + t_0;
	elseif (KbT <= -0.41)
		tmp = t_2;
	elseif (KbT <= 8e-231)
		tmp = t_1;
	elseif (KbT <= 1.5e-142)
		tmp = t_2;
	elseif (KbT <= 2.1e+103)
		tmp = t_1;
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -9e+126], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[KbT, -0.41], t$95$2, If[LessEqual[KbT, 8e-231], t$95$1, If[LessEqual[KbT, 1.5e-142], t$95$2, If[LessEqual[KbT, 2.1e+103], t$95$1, N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -8.99999999999999947e126

   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 86.1%

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

      1. associate-*r/ 86.1%

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

      2. mul-1-neg 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in Ec around 0 81.5%

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

      1. neg-mul-1 66.8%

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

      2. unsub-neg 66.8%

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

   10. Simplified 81.5%

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

   11. Taylor expanded in EAccept around inf 77.4%

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

   if -8.99999999999999947e126 < KbT < -0.409999999999999976 or 7.9999999999999999e-231 < KbT < 1.5000000000000001e-142

   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 54.4%

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

   6. Taylor expanded in Ec around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. associate-/l* 40.3%

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

      3. distribute-lft-neg-in 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in KbT around 0 79.4%

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

   if -0.409999999999999976 < KbT < 7.9999999999999999e-231 or 1.5000000000000001e-142 < KbT < 2.1000000000000002e103

   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 41.4%

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

   6. Taylor expanded in Ec around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

      3. +-commutative 42.3%

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

      4. mul-1-neg 42.3%

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

      5. unsub-neg 42.3%

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

      6. associate-+r+ 42.3%

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

      7. +-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in mu around inf 47.3%

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

       1. associate-/r* 46.7%

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

   11. Simplified 46.7%

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

   12. Taylor expanded in KbT around inf 78.9%

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

   if 2.1000000000000002e103 < 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 Ec around inf 84.1%

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

      1. associate-*r/ 84.1%

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

      2. mul-1-neg 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in Ec around 0 76.2%

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

      1. neg-mul-1 63.0%

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

      2. unsub-neg 63.0%

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

   10. Simplified 76.2%

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

   11. Taylor expanded in Ev around inf 69.6%

       \[\leadsto \frac{NdChar}{2 - \frac{Ec}{KbT}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -9 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;KbT \leq -0.41:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 8 \cdot 10^{-231}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.5 \cdot 10^{-142}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := NdChar + t\_1\\ \mathbf{if}\;KbT \leq -1 \cdot 10^{+124}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -0.065:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 5.6 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;KbT \leq 3.8 \cdot 10^{-150}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_2 (+ NdChar t_1)))
   (if (<= KbT -1e+124)
     (+ t_1 (/ NdChar 2.0))
     (if (<= KbT -0.065)
       t_0
       (if (<= KbT 5.6e-231)
         t_2
         (if (<= KbT 3.8e-150)
           t_0
           (if (<= KbT 2.1e+103)
             t_2
             (+
              (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
              (/ NdChar (- 2.0 (/ Ec KbT)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = NdChar + t_1;
	double tmp;
	if (KbT <= -1e+124) {
		tmp = t_1 + (NdChar / 2.0);
	} else if (KbT <= -0.065) {
		tmp = t_0;
	} else if (KbT <= 5.6e-231) {
		tmp = t_2;
	} else if (KbT <= 3.8e-150) {
		tmp = t_0;
	} else if (KbT <= 2.1e+103) {
		tmp = t_2;
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_2 = ndchar + t_1
    if (kbt <= (-1d+124)) then
        tmp = t_1 + (ndchar / 2.0d0)
    else if (kbt <= (-0.065d0)) then
        tmp = t_0
    else if (kbt <= 5.6d-231) then
        tmp = t_2
    else if (kbt <= 3.8d-150) then
        tmp = t_0
    else if (kbt <= 2.1d+103) then
        tmp = t_2
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (2.0d0 - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = NdChar + t_1;
	double tmp;
	if (KbT <= -1e+124) {
		tmp = t_1 + (NdChar / 2.0);
	} else if (KbT <= -0.065) {
		tmp = t_0;
	} else if (KbT <= 5.6e-231) {
		tmp = t_2;
	} else if (KbT <= 3.8e-150) {
		tmp = t_0;
	} else if (KbT <= 2.1e+103) {
		tmp = t_2;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_2 = NdChar + t_1
	tmp = 0
	if KbT <= -1e+124:
		tmp = t_1 + (NdChar / 2.0)
	elif KbT <= -0.065:
		tmp = t_0
	elif KbT <= 5.6e-231:
		tmp = t_2
	elif KbT <= 3.8e-150:
		tmp = t_0
	elif KbT <= 2.1e+103:
		tmp = t_2
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (2.0 - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_2 = Float64(NdChar + t_1)
	tmp = 0.0
	if (KbT <= -1e+124)
		tmp = Float64(t_1 + Float64(NdChar / 2.0));
	elseif (KbT <= -0.065)
		tmp = t_0;
	elseif (KbT <= 5.6e-231)
		tmp = t_2;
	elseif (KbT <= 3.8e-150)
		tmp = t_0;
	elseif (KbT <= 2.1e+103)
		tmp = t_2;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_2 = NdChar + t_1;
	tmp = 0.0;
	if (KbT <= -1e+124)
		tmp = t_1 + (NdChar / 2.0);
	elseif (KbT <= -0.065)
		tmp = t_0;
	elseif (KbT <= 5.6e-231)
		tmp = t_2;
	elseif (KbT <= 3.8e-150)
		tmp = t_0;
	elseif (KbT <= 2.1e+103)
		tmp = t_2;
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar + t$95$1), $MachinePrecision]}, If[LessEqual[KbT, -1e+124], N[(t$95$1 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -0.065], t$95$0, If[LessEqual[KbT, 5.6e-231], t$95$2, If[LessEqual[KbT, 3.8e-150], t$95$0, If[LessEqual[KbT, 2.1e+103], t$95$2, N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -9.99999999999999948e123

   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 81.5%

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

   if -9.99999999999999948e123 < KbT < -0.065000000000000002 or 5.5999999999999997e-231 < KbT < 3.7999999999999998e-150

   1. Initial program 100.0%

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

   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 54.4%

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

   6. Taylor expanded in Ec around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. associate-/l* 40.3%

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

      3. distribute-lft-neg-in 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in KbT around 0 79.4%

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

   if -0.065000000000000002 < KbT < 5.5999999999999997e-231 or 3.7999999999999998e-150 < KbT < 2.1000000000000002e103

   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 41.4%

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

   6. Taylor expanded in Ec around -inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

      3. +-commutative 42.3%

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

      4. mul-1-neg 42.3%

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

      5. unsub-neg 42.3%

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

      6. associate-+r+ 42.3%

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

      7. +-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in mu around inf 47.3%

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

       1. associate-/r* 46.7%

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

   11. Simplified 46.7%

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

   12. Taylor expanded in KbT around inf 78.9%

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

   if 2.1000000000000002e103 < 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 Ec around inf 84.1%

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

      1. associate-*r/ 84.1%

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

      2. mul-1-neg 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in Ec around 0 76.2%

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

      1. neg-mul-1 63.0%

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

      2. unsub-neg 63.0%

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

   10. Simplified 76.2%

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

   11. Taylor expanded in Ev around inf 69.6%

       \[\leadsto \frac{NdChar}{2 - \frac{Ec}{KbT}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1 \cdot 10^{+124}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -0.065:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 5.6 \cdot 10^{-231}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;KbT \leq 3.8 \cdot 10^{-150}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 62.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -8.4 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 4.7 \cdot 10^{+213}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -8.4e+126)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (if (<= KbT 4.7e+213)
     (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
     (+ (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))) (* NaChar 0.5)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -8.4e+126) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 4.7e+213) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-8.4d+126)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 4.7d+213) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp((-ec / kbt)))) + (nachar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -8.4e+126) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 4.7e+213) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((-Ec / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -8.4e+126:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= 4.7e+213:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp((-Ec / KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -8.4e+126)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 4.7e+213)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -8.4e+126)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 4.7e+213)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	else
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -8.4e+126], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4.7e+213], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -8.3999999999999997e126

   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 81.5%

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

   6. Taylor expanded in EAccept around inf 77.4%

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

   if -8.3999999999999997e126 < KbT < 4.6999999999999998e213

   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 47.2%

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

   6. Taylor expanded in Ec around inf 34.9%

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

      1. mul-1-neg 34.9%

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

      2. associate-/l* 34.7%

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

      3. distribute-lft-neg-in 34.7%

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

   8. Simplified 34.7%

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

   9. Taylor expanded in KbT around 0 59.1%

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

   if 4.6999999999999998e213 < 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 Ec around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in KbT around inf 94.6%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -8.4 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 4.7 \cdot 10^{+213}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -3.25 \cdot 10^{-78}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.05 \cdot 10^{-140}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -3.25e-78)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (if (<= KbT 1.05e-140)
     (+ (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))) (* NaChar 0.5))
     (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ 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 <= -3.25e-78) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.05e-140) {
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (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 <= (-3.25d-78)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 1.05d-140) then
        tmp = (ndchar / (1.0d0 + exp((-ec / kbt)))) + (nachar * 0.5d0)
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (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 <= -3.25e-78) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.05e-140) {
		tmp = (NdChar / (1.0 + Math.exp((-Ec / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -3.25e-78:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= 1.05e-140:
		tmp = (NdChar / (1.0 + math.exp((-Ec / KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -3.25e-78)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 1.05e-140)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + 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 <= -3.25e-78)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 1.05e-140)
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar * 0.5);
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -3.25e-78], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.05e-140], N[(N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -3.2500000000000001e-78

   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 inf 51.9%

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

   if -3.2500000000000001e-78 < KbT < 1.05000000000000009e-140

   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 66.6%

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

      1. associate-*r/ 66.6%

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

      2. mul-1-neg 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in KbT around inf 30.8%

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

   if 1.05000000000000009e-140 < 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 61.1%

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

   6. Taylor expanded in Ev around inf 45.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.25 \cdot 10^{-78}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.05 \cdot 10^{-140}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 35.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -3.25 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.45 \cdot 10^{-230}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -3.25e-91)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (if (<= KbT 1.45e-230)
     (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (* NaChar 0.5))
     (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ 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 <= -3.25e-91) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.45e-230) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (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 <= (-3.25d-91)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 1.45d-230) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar * 0.5d0)
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (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 <= -3.25e-91) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.45e-230) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -3.25e-91:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= 1.45e-230:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -3.25e-91)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 1.45e-230)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + 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 <= -3.25e-91)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 1.45e-230)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar * 0.5);
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -3.25e-91], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.45e-230], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -3.25e-91

   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 61.6%

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

   6. Taylor expanded in EAccept around inf 52.1%

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

   if -3.25e-91 < KbT < 1.45000000000000003e-230

   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 61.9%

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

   6. Taylor expanded in KbT around inf 29.4%

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

   if 1.45000000000000003e-230 < 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 55.6%

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

   6. Taylor expanded in Ev around inf 42.1%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.25 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.45 \cdot 10^{-230}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq 8.5 \cdot 10^{-286}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT 8.5e-286)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ 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 <= 8.5e-286) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (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 <= 8.5d-286) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (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 <= 8.5e-286) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= 8.5e-286:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= 8.5e-286)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + 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 <= 8.5e-286)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, 8.5e-286], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < 8.4999999999999998e-286

   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 50.3%

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

   6. Taylor expanded in EAccept around inf 41.4%

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

   if 8.4999999999999998e-286 < 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 53.1%

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

   6. Taylor expanded in Ev around inf 38.8%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 8.5 \cdot 10^{-286}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 35.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ 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 / (1.0 + exp((EAccept / KbT)))) + (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 / (1.0d0 + exp((eaccept / kbt)))) + (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 / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $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 51.6%

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

6. Taylor expanded in EAccept around inf 41.3%

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

7. Final simplification 41.3%

   \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2} \]
8. Add Preprocessing

Alternative 24: 27.6% accurate, 45.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in Ec around inf 74.8%

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

   1. associate-*r/ 74.8%

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

   2. mul-1-neg 74.8%

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

7. Simplified 74.8%

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

8. Taylor expanded in KbT around inf 39.9%

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

9. Taylor expanded in Ec around 0 28.6%

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

    1. neg-mul-1 28.6%

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

    2. unsub-neg 28.6%

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

11. Simplified 28.6%

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

12. Taylor expanded in Ec around 0 30.2%

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

    1. distribute-lft-out 30.2%

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

14. Simplified 30.2%

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

15. Final simplification 30.2%

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

Alternative 25: 18.6% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 74.8%

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

   1. associate-*r/ 74.8%

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

   2. mul-1-neg 74.8%

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

7. Simplified 74.8%

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

8. Taylor expanded in KbT around inf 39.9%

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

9. Taylor expanded in Ec around 0 28.6%

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

    1. neg-mul-1 28.6%

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

    2. unsub-neg 28.6%

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

11. Simplified 28.6%

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

12. Taylor expanded in NdChar around 0 18.2%

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

13. Final simplification 18.2%

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

Reproduce

herbie shell --seed 2024075 
(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))))))