Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 29.4s

Alternatives: 35

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = 8.0954869499425e+129
  2. Ec = 2.568152156190132e-243
  3. Vef = -1.365484493674379e+183
  4. EDonor = 5.823017527612347e-33
  5. mu = -3.9024772122074837e-165
  6. KbT = 4.4628086858779236e-91
  7. NaChar = 2.3179714010925482e+129
  8. Ev = -1.4266855345228011e-257
  9. EAccept = -1.9716159403906785e-39

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

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

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 (- mu EAccept))) 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 - (mu - EAccept))) / 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 - (mu - eaccept))) / 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 - (mu - EAccept))) / 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 - (mu - EAccept))) / 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(mu - EAccept))) / 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 - (mu - EAccept))) / 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[(mu - EAccept), $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%

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

Alternative 2: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -4.8 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -1.7 \cdot 10^{-258}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2 + mu \cdot \left(\frac{1}{KbT} + \frac{EDonor}{mu \cdot KbT}\right)}\\ \mathbf{elif}\;mu \leq -2.7 \cdot 10^{-297}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;mu \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;mu \leq 3.4 \cdot 10^{+107}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_2 (+ t_1 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))))
   (if (<= mu -4.8e-38)
     t_2
     (if (<= mu -1.7e-258)
       (+ t_1 (/ NdChar (+ 2.0 (* mu (+ (/ 1.0 KbT) (/ EDonor (* mu KbT)))))))
       (if (<= mu -2.7e-297)
         (+
          t_0
          (/
           NaChar
           (-
            1.0
            (+
             (/ mu KbT)
             (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))))))
         (if (<= mu 8.5e-125)
           (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
           (if (<= mu 3.4e+107)
             (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
             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 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + exp((mu / KbT))));
	double tmp;
	if (mu <= -4.8e-38) {
		tmp = t_2;
	} else if (mu <= -1.7e-258) {
		tmp = t_1 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))));
	} else if (mu <= -2.7e-297) {
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (mu <= 8.5e-125) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (mu <= 3.4e+107) {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	} 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 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    t_2 = t_1 + (ndchar / (1.0d0 + exp((mu / kbt))))
    if (mu <= (-4.8d-38)) then
        tmp = t_2
    else if (mu <= (-1.7d-258)) then
        tmp = t_1 + (ndchar / (2.0d0 + (mu * ((1.0d0 / kbt) + (edonor / (mu * kbt))))))
    else if (mu <= (-2.7d-297)) then
        tmp = t_0 + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))))))
    else if (mu <= 8.5d-125) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (mu <= 3.4d+107) then
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    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 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double tmp;
	if (mu <= -4.8e-38) {
		tmp = t_2;
	} else if (mu <= -1.7e-258) {
		tmp = t_1 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))));
	} else if (mu <= -2.7e-297) {
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (mu <= 8.5e-125) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (mu <= 3.4e+107) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	t_2 = t_1 + (NdChar / (1.0 + math.exp((mu / KbT))))
	tmp = 0
	if mu <= -4.8e-38:
		tmp = t_2
	elif mu <= -1.7e-258:
		tmp = t_1 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))))
	elif mu <= -2.7e-297:
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))))
	elif mu <= 8.5e-125:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif mu <= 3.4e+107:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	tmp = 0.0
	if (mu <= -4.8e-38)
		tmp = t_2;
	elseif (mu <= -1.7e-258)
		tmp = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(mu * Float64(Float64(1.0 / KbT) + Float64(EDonor / Float64(mu * KbT)))))));
	elseif (mu <= -2.7e-297)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 - Float64(Float64(mu / KbT) + Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))))))));
	elseif (mu <= 8.5e-125)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (mu <= 3.4e+107)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	t_2 = t_1 + (NdChar / (1.0 + exp((mu / KbT))));
	tmp = 0.0;
	if (mu <= -4.8e-38)
		tmp = t_2;
	elseif (mu <= -1.7e-258)
		tmp = t_1 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))));
	elseif (mu <= -2.7e-297)
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	elseif (mu <= 8.5e-125)
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (mu <= 3.4e+107)
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	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[(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$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -4.8e-38], t$95$2, If[LessEqual[mu, -1.7e-258], N[(t$95$1 + N[(NdChar / N[(2.0 + N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(EDonor / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -2.7e-297], N[(t$95$0 + N[(NaChar / N[(1.0 - N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 8.5e-125], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 3.4e+107], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if mu < -4.80000000000000044e-38 or 3.3999999999999997e107 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 89.3%

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

   if -4.80000000000000044e-38 < mu < -1.6999999999999999e-258

   1. Initial program 100.0%

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

   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 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate--l+ 68.4%

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

      3. associate--l+ 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in EDonor around -inf 70.5%

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

   9. Taylor expanded in mu around inf 72.4%

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

       1. *-commutative 72.4%

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

   11. Simplified 72.4%

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

   12. Taylor expanded in mu around inf 75.5%

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

       1. associate-*r/ 75.5%

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

       2. mul-1-neg 75.5%

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

       3. *-commutative 75.5%

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

   14. Simplified 75.5%

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

   if -1.6999999999999999e-258 < mu < -2.7000000000000001e-297

   1. Initial program 100.0%

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

   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%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -2.7000000000000001e-297 < mu < 8.5000000000000002e-125

   1. Initial program 100.0%

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

   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 79.1%

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

   if 8.5000000000000002e-125 < mu < 3.3999999999999997e107

   1. Initial program 100.0%

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

   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 84.1%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -4.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.7 \cdot 10^{-258}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + mu \cdot \left(\frac{1}{KbT} + \frac{EDonor}{mu \cdot KbT}\right)}\\ \mathbf{elif}\;mu \leq -2.7 \cdot 10^{-297}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;mu \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;mu \leq 3.4 \cdot 10^{+107}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -3.5 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -4.8 \cdot 10^{-260}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2 + mu \cdot \left(\frac{1}{KbT} + \frac{EDonor}{mu \cdot KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.26 \cdot 10^{-126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;mu \leq 1.6 \cdot 10^{-29}:\\ \;\;\;\;t\_0 - \frac{NdChar}{EDonor \cdot \left(\frac{-1}{KbT} + Vef \cdot \frac{\frac{-1}{KbT} + \frac{Ec - mu}{Vef \cdot KbT}}{EDonor}\right) - 2}\\ \mathbf{elif}\;mu \leq 5.6 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))))
   (if (<= mu -3.5e-38)
     t_1
     (if (<= mu -4.8e-260)
       (+ t_0 (/ NdChar (+ 2.0 (* mu (+ (/ 1.0 KbT) (/ EDonor (* mu KbT)))))))
       (if (<= mu 1.26e-126)
         (+
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
          (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))))
         (if (<= mu 1.6e-29)
           (-
            t_0
            (/
             NdChar
             (-
              (*
               EDonor
               (+
                (/ -1.0 KbT)
                (* Vef (/ (+ (/ -1.0 KbT) (/ (- Ec mu) (* Vef KbT))) EDonor))))
              2.0)))
           (if (<= mu 5.6e+44)
             (+
              (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
              (/ NdChar (+ 1.0 (exp (/ (+ EDonor Vef) 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 - (mu - EAccept))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	double tmp;
	if (mu <= -3.5e-38) {
		tmp = t_1;
	} else if (mu <= -4.8e-260) {
		tmp = t_0 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))));
	} else if (mu <= 1.26e-126) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((Ec / -KbT))));
	} else if (mu <= 1.6e-29) {
		tmp = t_0 - (NdChar / ((EDonor * ((-1.0 / KbT) + (Vef * (((-1.0 / KbT) + ((Ec - mu) / (Vef * KbT))) / EDonor)))) - 2.0));
	} else if (mu <= 5.6e+44) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((EDonor + Vef) / 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 - (mu - eaccept))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    if (mu <= (-3.5d-38)) then
        tmp = t_1
    else if (mu <= (-4.8d-260)) then
        tmp = t_0 + (ndchar / (2.0d0 + (mu * ((1.0d0 / kbt) + (edonor / (mu * kbt))))))
    else if (mu <= 1.26d-126) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((ec / -kbt))))
    else if (mu <= 1.6d-29) then
        tmp = t_0 - (ndchar / ((edonor * (((-1.0d0) / kbt) + (vef * ((((-1.0d0) / kbt) + ((ec - mu) / (vef * kbt))) / edonor)))) - 2.0d0))
    else if (mu <= 5.6d+44) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp(((edonor + vef) / 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 - (mu - EAccept))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double tmp;
	if (mu <= -3.5e-38) {
		tmp = t_1;
	} else if (mu <= -4.8e-260) {
		tmp = t_0 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))));
	} else if (mu <= 1.26e-126) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((Ec / -KbT))));
	} else if (mu <= 1.6e-29) {
		tmp = t_0 - (NdChar / ((EDonor * ((-1.0 / KbT) + (Vef * (((-1.0 / KbT) + ((Ec - mu) / (Vef * KbT))) / EDonor)))) - 2.0));
	} else if (mu <= 5.6e+44) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp(((EDonor + Vef) / 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 - (mu - EAccept))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	tmp = 0
	if mu <= -3.5e-38:
		tmp = t_1
	elif mu <= -4.8e-260:
		tmp = t_0 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))))
	elif mu <= 1.26e-126:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((Ec / -KbT))))
	elif mu <= 1.6e-29:
		tmp = t_0 - (NdChar / ((EDonor * ((-1.0 / KbT) + (Vef * (((-1.0 / KbT) + ((Ec - mu) / (Vef * KbT))) / EDonor)))) - 2.0))
	elif mu <= 5.6e+44:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp(((EDonor + Vef) / 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(mu - EAccept))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	tmp = 0.0
	if (mu <= -3.5e-38)
		tmp = t_1;
	elseif (mu <= -4.8e-260)
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 + Float64(mu * Float64(Float64(1.0 / KbT) + Float64(EDonor / Float64(mu * KbT)))))));
	elseif (mu <= 1.26e-126)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))));
	elseif (mu <= 1.6e-29)
		tmp = Float64(t_0 - Float64(NdChar / Float64(Float64(EDonor * Float64(Float64(-1.0 / KbT) + Float64(Vef * Float64(Float64(Float64(-1.0 / KbT) + Float64(Float64(Ec - mu) / Float64(Vef * KbT))) / EDonor)))) - 2.0)));
	elseif (mu <= 5.6e+44)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Vef) / 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 - (mu - EAccept))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	tmp = 0.0;
	if (mu <= -3.5e-38)
		tmp = t_1;
	elseif (mu <= -4.8e-260)
		tmp = t_0 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))));
	elseif (mu <= 1.26e-126)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((Ec / -KbT))));
	elseif (mu <= 1.6e-29)
		tmp = t_0 - (NdChar / ((EDonor * ((-1.0 / KbT) + (Vef * (((-1.0 / KbT) + ((Ec - mu) / (Vef * KbT))) / EDonor)))) - 2.0));
	elseif (mu <= 5.6e+44)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((EDonor + Vef) / 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[(mu - EAccept), $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]}, If[LessEqual[mu, -3.5e-38], t$95$1, If[LessEqual[mu, -4.8e-260], N[(t$95$0 + N[(NdChar / N[(2.0 + N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(EDonor / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.26e-126], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.6e-29], N[(t$95$0 - N[(NdChar / N[(N[(EDonor * N[(N[(-1.0 / KbT), $MachinePrecision] + N[(Vef * N[(N[(N[(-1.0 / KbT), $MachinePrecision] + N[(N[(Ec - mu), $MachinePrecision] / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 5.6e+44], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + Vef), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if mu < -3.5000000000000001e-38 or 5.6000000000000002e44 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 87.8%

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

   if -3.5000000000000001e-38 < mu < -4.8000000000000001e-260

   1. Initial program 100.0%

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

   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 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate--l+ 68.4%

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

      3. associate--l+ 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in EDonor around -inf 70.5%

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

   9. Taylor expanded in mu around inf 72.4%

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

       1. *-commutative 72.4%

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

   11. Simplified 72.4%

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

   12. Taylor expanded in mu around inf 75.5%

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

       1. associate-*r/ 75.5%

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

       2. mul-1-neg 75.5%

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

       3. *-commutative 75.5%

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

   14. Simplified 75.5%

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

   if -4.8000000000000001e-260 < mu < 1.26e-126

   1. Initial program 100.0%

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

   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 78.7%

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

   6. Taylor expanded in Ec around inf 71.0%

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

      1. mul-1-neg 71.0%

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

   8. Simplified 71.0%

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

   if 1.26e-126 < mu < 1.6e-29

   1. Initial program 100.0%

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

   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 79.2%

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

      1. associate--l+ 79.2%

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

      2. associate--l+ 79.2%

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

      3. associate--l+ 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in Vef around inf 70.5%

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

      1. associate--l+ 70.5%

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

      2. associate-/r* 74.9%

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

      3. associate-/r* 74.9%

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

      4. div-sub 79.2%

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

      5. div-sub 79.2%

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

   10. Simplified 79.2%

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

   11. Taylor expanded in EDonor around inf 70.5%

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

       1. associate-/l* 78.8%

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

       2. associate--l+ 78.8%

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

       3. div-sub 87.5%

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

   13. Simplified 87.5%

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

   if 1.6e-29 < mu < 5.6000000000000002e44

   1. Initial program 100.0%

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

   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 93.1%

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

   6. Taylor expanded in Vef around inf 87.3%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -3.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -4.8 \cdot 10^{-260}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + mu \cdot \left(\frac{1}{KbT} + \frac{EDonor}{mu \cdot KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.26 \cdot 10^{-126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;mu \leq 1.6 \cdot 10^{-29}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} - \frac{NdChar}{EDonor \cdot \left(\frac{-1}{KbT} + Vef \cdot \frac{\frac{-1}{KbT} + \frac{Ec - mu}{Vef \cdot KbT}}{EDonor}\right) - 2}\\ \mathbf{elif}\;mu \leq 5.6 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -4.5 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -6.2 \cdot 10^{-260}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2 + mu \cdot \left(\frac{1}{KbT} + \frac{EDonor}{mu \cdot KbT}\right)}\\ \mathbf{elif}\;mu \leq 4.8 \cdot 10^{-128}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;mu \leq 3.9 \cdot 10^{+107}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))))
   (if (<= mu -4.5e-38)
     t_1
     (if (<= mu -6.2e-260)
       (+ t_0 (/ NdChar (+ 2.0 (* mu (+ (/ 1.0 KbT) (/ EDonor (* mu KbT)))))))
       (if (<= mu 4.8e-128)
         (+
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
          (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))))
         (if (<= mu 3.9e+107)
           (+
            (/ 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 - (mu - EAccept))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	double tmp;
	if (mu <= -4.5e-38) {
		tmp = t_1;
	} else if (mu <= -6.2e-260) {
		tmp = t_0 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))));
	} else if (mu <= 4.8e-128) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((Ec / -KbT))));
	} else if (mu <= 3.9e+107) {
		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 - (mu - eaccept))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    if (mu <= (-4.5d-38)) then
        tmp = t_1
    else if (mu <= (-6.2d-260)) then
        tmp = t_0 + (ndchar / (2.0d0 + (mu * ((1.0d0 / kbt) + (edonor / (mu * kbt))))))
    else if (mu <= 4.8d-128) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((ec / -kbt))))
    else if (mu <= 3.9d+107) 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 - (mu - EAccept))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double tmp;
	if (mu <= -4.5e-38) {
		tmp = t_1;
	} else if (mu <= -6.2e-260) {
		tmp = t_0 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))));
	} else if (mu <= 4.8e-128) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((Ec / -KbT))));
	} else if (mu <= 3.9e+107) {
		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 - (mu - EAccept))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	tmp = 0
	if mu <= -4.5e-38:
		tmp = t_1
	elif mu <= -6.2e-260:
		tmp = t_0 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))))
	elif mu <= 4.8e-128:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((Ec / -KbT))))
	elif mu <= 3.9e+107:
		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(mu - EAccept))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	tmp = 0.0
	if (mu <= -4.5e-38)
		tmp = t_1;
	elseif (mu <= -6.2e-260)
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 + Float64(mu * Float64(Float64(1.0 / KbT) + Float64(EDonor / Float64(mu * KbT)))))));
	elseif (mu <= 4.8e-128)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))));
	elseif (mu <= 3.9e+107)
		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 - (mu - EAccept))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	tmp = 0.0;
	if (mu <= -4.5e-38)
		tmp = t_1;
	elseif (mu <= -6.2e-260)
		tmp = t_0 + (NdChar / (2.0 + (mu * ((1.0 / KbT) + (EDonor / (mu * KbT))))));
	elseif (mu <= 4.8e-128)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((Ec / -KbT))));
	elseif (mu <= 3.9e+107)
		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[(mu - EAccept), $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]}, If[LessEqual[mu, -4.5e-38], t$95$1, If[LessEqual[mu, -6.2e-260], N[(t$95$0 + N[(NdChar / N[(2.0 + N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(EDonor / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 4.8e-128], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 3.9e+107], 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 4 regimes

2. if mu < -4.50000000000000009e-38 or 3.8999999999999998e107 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 89.3%

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

   if -4.50000000000000009e-38 < mu < -6.19999999999999965e-260

   1. Initial program 100.0%

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

   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 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate--l+ 68.4%

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

      3. associate--l+ 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in EDonor around -inf 70.5%

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

   9. Taylor expanded in mu around inf 72.4%

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

       1. *-commutative 72.4%

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

   11. Simplified 72.4%

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

   12. Taylor expanded in mu around inf 75.5%

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

       1. associate-*r/ 75.5%

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

       2. mul-1-neg 75.5%

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

       3. *-commutative 75.5%

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

   14. Simplified 75.5%

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

   if -6.19999999999999965e-260 < mu < 4.7999999999999996e-128

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 78.7%

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

   6. Taylor expanded in Ec around inf 71.0%

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

      1. mul-1-neg 71.0%

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

   8. Simplified 71.0%

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

   if 4.7999999999999996e-128 < mu < 3.8999999999999998e107

   1. Initial program 100.0%

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

   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 84.1%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -4.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -6.2 \cdot 10^{-260}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + mu \cdot \left(\frac{1}{KbT} + \frac{EDonor}{mu \cdot KbT}\right)}\\ \mathbf{elif}\;mu \leq 4.8 \cdot 10^{-128}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;mu \leq 3.9 \cdot 10^{+107}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -4 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq 1.65 \cdot 10^{-305}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -4e+82)
     t_1
     (if (<= Vef 1.65e-305)
       (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
       (if (<= Vef 1.45e+41)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
          (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -4e+82) {
		tmp = t_1;
	} else if (Vef <= 1.65e-305) {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (Vef <= 1.45e+41) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = t_0 + (nachar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-4d+82)) then
        tmp = t_1
    else if (vef <= 1.65d-305) then
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (vef <= 1.45d+41) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -4e+82) {
		tmp = t_1;
	} else if (Vef <= 1.65e-305) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (Vef <= 1.45e+41) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = t_0 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -4e+82:
		tmp = t_1
	elif Vef <= 1.65e-305:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif Vef <= 1.45e+41:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -4e+82)
		tmp = t_1;
	elseif (Vef <= 1.65e-305)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (Vef <= 1.45e+41)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -4e+82)
		tmp = t_1;
	elseif (Vef <= 1.65e-305)
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (Vef <= 1.45e+41)
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(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$1 = N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -4e+82], t$95$1, If[LessEqual[Vef, 1.65e-305], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.45e+41], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -3.9999999999999999e82 or 1.44999999999999994e41 < 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 83.7%

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

   if -3.9999999999999999e82 < Vef < 1.64999999999999991e-305

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 76.6%

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

   if 1.64999999999999991e-305 < Vef < 1.44999999999999994e41

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 85.4%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4 \cdot 10^{+82}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.65 \cdot 10^{-305}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{2 + \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{if}\;NaChar \leq -2.25 \cdot 10^{-184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 1.32 \cdot 10^{-182}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 4.2 \cdot 10^{-96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 9.2 \cdot 10^{-54}:\\ \;\;\;\;t\_0 + NaChar \cdot \frac{1}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2 + \left(\frac{EDonor}{KbT} - mu \cdot \left(\frac{-1}{KbT} + \frac{\frac{Ec}{KbT} - \frac{Vef}{KbT}}{mu}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_2
         (+
          t_1
          (/
           NdChar
           (+ 2.0 (/ (* EDonor (+ 1.0 (/ (- (+ mu Vef) Ec) EDonor))) KbT))))))
   (if (<= NaChar -2.25e-184)
     t_2
     (if (<= NaChar 1.32e-182)
       (+
        t_0
        (/
         NaChar
         (-
          1.0
          (+
           (/ mu KbT)
           (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))))))
       (if (<= NaChar 4.2e-96)
         t_2
         (if (<= NaChar 9.2e-54)
           (+ t_0 (* NaChar (/ 1.0 (+ (/ EAccept KbT) 2.0))))
           (+
            t_1
            (/
             NdChar
             (+
              2.0
              (-
               (/ EDonor KbT)
               (*
                mu
                (+ (/ -1.0 KbT) (/ (- (/ Ec KbT) (/ Vef KbT)) mu)))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = t_1 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	double tmp;
	if (NaChar <= -2.25e-184) {
		tmp = t_2;
	} else if (NaChar <= 1.32e-182) {
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (NaChar <= 4.2e-96) {
		tmp = t_2;
	} else if (NaChar <= 9.2e-54) {
		tmp = t_0 + (NaChar * (1.0 / ((EAccept / KbT) + 2.0)));
	} else {
		tmp = t_1 + (NdChar / (2.0 + ((EDonor / KbT) - (mu * ((-1.0 / KbT) + (((Ec / KbT) - (Vef / KbT)) / mu))))));
	}
	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 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    t_2 = t_1 + (ndchar / (2.0d0 + ((edonor * (1.0d0 + (((mu + vef) - ec) / edonor))) / kbt)))
    if (nachar <= (-2.25d-184)) then
        tmp = t_2
    else if (nachar <= 1.32d-182) then
        tmp = t_0 + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))))))
    else if (nachar <= 4.2d-96) then
        tmp = t_2
    else if (nachar <= 9.2d-54) then
        tmp = t_0 + (nachar * (1.0d0 / ((eaccept / kbt) + 2.0d0)))
    else
        tmp = t_1 + (ndchar / (2.0d0 + ((edonor / kbt) - (mu * (((-1.0d0) / kbt) + (((ec / kbt) - (vef / kbt)) / mu))))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = t_1 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	double tmp;
	if (NaChar <= -2.25e-184) {
		tmp = t_2;
	} else if (NaChar <= 1.32e-182) {
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (NaChar <= 4.2e-96) {
		tmp = t_2;
	} else if (NaChar <= 9.2e-54) {
		tmp = t_0 + (NaChar * (1.0 / ((EAccept / KbT) + 2.0)));
	} else {
		tmp = t_1 + (NdChar / (2.0 + ((EDonor / KbT) - (mu * ((-1.0 / KbT) + (((Ec / KbT) - (Vef / KbT)) / mu))))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	t_2 = t_1 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)))
	tmp = 0
	if NaChar <= -2.25e-184:
		tmp = t_2
	elif NaChar <= 1.32e-182:
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))))
	elif NaChar <= 4.2e-96:
		tmp = t_2
	elif NaChar <= 9.2e-54:
		tmp = t_0 + (NaChar * (1.0 / ((EAccept / KbT) + 2.0)))
	else:
		tmp = t_1 + (NdChar / (2.0 + ((EDonor / KbT) - (mu * ((-1.0 / KbT) + (((Ec / KbT) - (Vef / KbT)) / mu))))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(EDonor * Float64(1.0 + Float64(Float64(Float64(mu + Vef) - Ec) / EDonor))) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.25e-184)
		tmp = t_2;
	elseif (NaChar <= 1.32e-182)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 - Float64(Float64(mu / KbT) + Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))))))));
	elseif (NaChar <= 4.2e-96)
		tmp = t_2;
	elseif (NaChar <= 9.2e-54)
		tmp = Float64(t_0 + Float64(NaChar * Float64(1.0 / Float64(Float64(EAccept / KbT) + 2.0))));
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(EDonor / KbT) - Float64(mu * Float64(Float64(-1.0 / KbT) + Float64(Float64(Float64(Ec / KbT) - Float64(Vef / KbT)) / mu)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	t_2 = t_1 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.25e-184)
		tmp = t_2;
	elseif (NaChar <= 1.32e-182)
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	elseif (NaChar <= 4.2e-96)
		tmp = t_2;
	elseif (NaChar <= 9.2e-54)
		tmp = t_0 + (NaChar * (1.0 / ((EAccept / KbT) + 2.0)));
	else
		tmp = t_1 + (NdChar / (2.0 + ((EDonor / KbT) - (mu * ((-1.0 / KbT) + (((Ec / KbT) - (Vef / KbT)) / mu))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(EDonor * N[(1.0 + N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.25e-184], t$95$2, If[LessEqual[NaChar, 1.32e-182], N[(t$95$0 + N[(NaChar / N[(1.0 - N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.2e-96], t$95$2, If[LessEqual[NaChar, 9.2e-54], N[(t$95$0 + N[(NaChar * N[(1.0 / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] - N[(mu * N[(N[(-1.0 / KbT), $MachinePrecision] + N[(N[(N[(Ec / KbT), $MachinePrecision] - N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.2500000000000001e-184 or 1.32e-182 < NaChar < 4.20000000000000002e-96

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.1%

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

      1. associate--l+ 63.1%

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

      2. associate--l+ 63.1%

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

      3. associate--l+ 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in EDonor around -inf 71.3%

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

   9. Taylor expanded in KbT around 0 74.5%

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

   if -2.2500000000000001e-184 < NaChar < 1.32e-182

   1. Initial program 100.0%

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

   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 77.9%

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

      1. +-commutative 77.9%

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

   7. Simplified 77.9%

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

   if 4.20000000000000002e-96 < NaChar < 9.1999999999999996e-54

   1. Initial program 100.0%

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

   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 86.5%

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

   6. Taylor expanded in EAccept around 0 86.2%

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

      1. div-inv 86.2%

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

   8. Applied egg-rr 86.2%

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

   if 9.1999999999999996e-54 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.7%

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

      1. associate--l+ 73.7%

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

      2. associate--l+ 73.7%

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

      3. associate--l+ 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in mu around inf 66.1%

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

      1. associate--l+ 66.1%

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

      2. associate-/r* 68.5%

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

      3. associate-/r* 72.1%

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

      4. div-sub 74.7%

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

   10. Simplified 74.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.25 \cdot 10^{-184}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.32 \cdot 10^{-182}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 4.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 9.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot \frac{1}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \left(\frac{EDonor}{KbT} - mu \cdot \left(\frac{-1}{KbT} + \frac{\frac{Ec}{KbT} - \frac{Vef}{KbT}}{mu}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{2 + \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{if}\;NaChar \leq -6.1 \cdot 10^{-183}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 2.1 \cdot 10^{-181}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 4.2 \cdot 10^{-94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 1.05 \cdot 10^{-54}:\\ \;\;\;\;t\_0 + NaChar \cdot \frac{1}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{mu}{EDonor \cdot KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_2
         (+
          t_1
          (/
           NdChar
           (+ 2.0 (/ (* EDonor (+ 1.0 (/ (- (+ mu Vef) Ec) EDonor))) KbT))))))
   (if (<= NaChar -6.1e-183)
     t_2
     (if (<= NaChar 2.1e-181)
       (+
        t_0
        (/
         NaChar
         (-
          1.0
          (+
           (/ mu KbT)
           (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))))))
       (if (<= NaChar 4.2e-94)
         t_2
         (if (<= NaChar 1.05e-54)
           (+ t_0 (* NaChar (/ 1.0 (+ (/ EAccept KbT) 2.0))))
           (+
            t_1
            (/
             NdChar
             (+ 2.0 (* EDonor (+ (/ 1.0 KbT) (/ mu (* 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 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = t_1 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	double tmp;
	if (NaChar <= -6.1e-183) {
		tmp = t_2;
	} else if (NaChar <= 2.1e-181) {
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (NaChar <= 4.2e-94) {
		tmp = t_2;
	} else if (NaChar <= 1.05e-54) {
		tmp = t_0 + (NaChar * (1.0 / ((EAccept / KbT) + 2.0)));
	} else {
		tmp = t_1 + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    t_2 = t_1 + (ndchar / (2.0d0 + ((edonor * (1.0d0 + (((mu + vef) - ec) / edonor))) / kbt)))
    if (nachar <= (-6.1d-183)) then
        tmp = t_2
    else if (nachar <= 2.1d-181) then
        tmp = t_0 + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))))))
    else if (nachar <= 4.2d-94) then
        tmp = t_2
    else if (nachar <= 1.05d-54) then
        tmp = t_0 + (nachar * (1.0d0 / ((eaccept / kbt) + 2.0d0)))
    else
        tmp = t_1 + (ndchar / (2.0d0 + (edonor * ((1.0d0 / kbt) + (mu / (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 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = t_1 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	double tmp;
	if (NaChar <= -6.1e-183) {
		tmp = t_2;
	} else if (NaChar <= 2.1e-181) {
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (NaChar <= 4.2e-94) {
		tmp = t_2;
	} else if (NaChar <= 1.05e-54) {
		tmp = t_0 + (NaChar * (1.0 / ((EAccept / KbT) + 2.0)));
	} else {
		tmp = t_1 + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	t_2 = t_1 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)))
	tmp = 0
	if NaChar <= -6.1e-183:
		tmp = t_2
	elif NaChar <= 2.1e-181:
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))))
	elif NaChar <= 4.2e-94:
		tmp = t_2
	elif NaChar <= 1.05e-54:
		tmp = t_0 + (NaChar * (1.0 / ((EAccept / KbT) + 2.0)))
	else:
		tmp = t_1 + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(EDonor * Float64(1.0 + Float64(Float64(Float64(mu + Vef) - Ec) / EDonor))) / KbT))))
	tmp = 0.0
	if (NaChar <= -6.1e-183)
		tmp = t_2;
	elseif (NaChar <= 2.1e-181)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 - Float64(Float64(mu / KbT) + Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))))))));
	elseif (NaChar <= 4.2e-94)
		tmp = t_2;
	elseif (NaChar <= 1.05e-54)
		tmp = Float64(t_0 + Float64(NaChar * Float64(1.0 / Float64(Float64(EAccept / KbT) + 2.0))));
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(mu / Float64(EDonor * 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(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	t_2 = t_1 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -6.1e-183)
		tmp = t_2;
	elseif (NaChar <= 2.1e-181)
		tmp = t_0 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	elseif (NaChar <= 4.2e-94)
		tmp = t_2;
	elseif (NaChar <= 1.05e-54)
		tmp = t_0 + (NaChar * (1.0 / ((EAccept / KbT) + 2.0)));
	else
		tmp = t_1 + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(EDonor * N[(1.0 + N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.1e-183], t$95$2, If[LessEqual[NaChar, 2.1e-181], N[(t$95$0 + N[(NaChar / N[(1.0 - N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.2e-94], t$95$2, If[LessEqual[NaChar, 1.05e-54], N[(t$95$0 + N[(NaChar * N[(1.0 / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NdChar / N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -6.1000000000000002e-183 or 2.10000000000000003e-181 < NaChar < 4.2000000000000002e-94

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.1%

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

      1. associate--l+ 63.1%

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

      2. associate--l+ 63.1%

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

      3. associate--l+ 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in EDonor around -inf 71.3%

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

   9. Taylor expanded in KbT around 0 74.5%

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

   if -6.1000000000000002e-183 < NaChar < 2.10000000000000003e-181

   1. Initial program 100.0%

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

   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 77.9%

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

      1. +-commutative 77.9%

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

   7. Simplified 77.9%

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

   if 4.2000000000000002e-94 < NaChar < 1.05e-54

   1. Initial program 100.0%

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

   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 86.5%

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

   6. Taylor expanded in EAccept around 0 86.2%

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

      1. div-inv 86.2%

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

   8. Applied egg-rr 86.2%

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

   if 1.05e-54 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.7%

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

      1. associate--l+ 73.7%

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

      2. associate--l+ 73.7%

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

      3. associate--l+ 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in EDonor around -inf 74.9%

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

   9. Taylor expanded in mu around inf 74.2%

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

       1. *-commutative 74.2%

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

   11. Simplified 74.2%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.1 \cdot 10^{-183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.1 \cdot 10^{-181}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 4.2 \cdot 10^{-94}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.05 \cdot 10^{-54}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot \frac{1}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{mu}{EDonor \cdot KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}\\ t_1 := e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}\\ t_2 := \frac{NaChar}{-1 - t\_1}\\ \mathbf{if}\;NaChar \leq -1.22 \cdot 10^{-185}:\\ \;\;\;\;\frac{NdChar}{2 - EDonor \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{EDonor}}{KbT}\right)} - t\_2\\ \mathbf{elif}\;NaChar \leq 7.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{-133}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor - Vef \cdot \left(-1 + \frac{Ec - mu}{Vef}\right)} - t\_2\\ \mathbf{elif}\;NaChar \leq 1.15 \cdot 10^{-54}:\\ \;\;\;\;\frac{KbT \cdot NaChar}{EAccept} - \frac{NdChar}{-1 - t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + t\_1} + \frac{NdChar}{\left(\frac{Vef}{KbT} + \left(2 + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))
        (t_1 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))
        (t_2 (/ NaChar (- -1.0 t_1))))
   (if (<= NaChar -1.22e-185)
     (-
      (/ NdChar (- 2.0 (* EDonor (- (/ 1.0 KbT) (/ (/ mu EDonor) KbT)))))
      t_2)
     (if (<= NaChar 7.5e-169)
       (+ (/ NdChar (+ 1.0 t_0)) (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT)))))
       (if (<= NaChar 1.1e-133)
         (-
          (* KbT (/ NdChar (- EDonor (* Vef (+ -1.0 (/ (- Ec mu) Vef))))))
          t_2)
         (if (<= NaChar 1.15e-54)
           (- (/ (* KbT NaChar) EAccept) (/ NdChar (- -1.0 t_0)))
           (+
            (/ NaChar (+ 1.0 t_1))
            (/
             NdChar
             (- (+ (/ Vef KbT) (+ 2.0 (/ EDonor KbT))) (/ 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 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double t_2 = NaChar / (-1.0 - t_1);
	double tmp;
	if (NaChar <= -1.22e-185) {
		tmp = (NdChar / (2.0 - (EDonor * ((1.0 / KbT) - ((mu / EDonor) / KbT))))) - t_2;
	} else if (NaChar <= 7.5e-169) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	} else if (NaChar <= 1.1e-133) {
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - t_2;
	} else if (NaChar <= 1.15e-54) {
		tmp = ((KbT * NaChar) / EAccept) - (NdChar / (-1.0 - t_0));
	} else {
		tmp = (NaChar / (1.0 + t_1)) + (NdChar / (((Vef / KbT) + (2.0 + (EDonor / KbT))) - (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 = exp(((edonor + (mu + (vef - ec))) / kbt))
    t_1 = exp(((vef + (ev - (mu - eaccept))) / kbt))
    t_2 = nachar / ((-1.0d0) - t_1)
    if (nachar <= (-1.22d-185)) then
        tmp = (ndchar / (2.0d0 - (edonor * ((1.0d0 / kbt) - ((mu / edonor) / kbt))))) - t_2
    else if (nachar <= 7.5d-169) then
        tmp = (ndchar / (1.0d0 + t_0)) + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    else if (nachar <= 1.1d-133) then
        tmp = (kbt * (ndchar / (edonor - (vef * ((-1.0d0) + ((ec - mu) / vef)))))) - t_2
    else if (nachar <= 1.15d-54) then
        tmp = ((kbt * nachar) / eaccept) - (ndchar / ((-1.0d0) - t_0))
    else
        tmp = (nachar / (1.0d0 + t_1)) + (ndchar / (((vef / kbt) + (2.0d0 + (edonor / kbt))) - (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 = Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double t_2 = NaChar / (-1.0 - t_1);
	double tmp;
	if (NaChar <= -1.22e-185) {
		tmp = (NdChar / (2.0 - (EDonor * ((1.0 / KbT) - ((mu / EDonor) / KbT))))) - t_2;
	} else if (NaChar <= 7.5e-169) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	} else if (NaChar <= 1.1e-133) {
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - t_2;
	} else if (NaChar <= 1.15e-54) {
		tmp = ((KbT * NaChar) / EAccept) - (NdChar / (-1.0 - t_0));
	} else {
		tmp = (NaChar / (1.0 + t_1)) + (NdChar / (((Vef / KbT) + (2.0 + (EDonor / KbT))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))
	t_1 = math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))
	t_2 = NaChar / (-1.0 - t_1)
	tmp = 0
	if NaChar <= -1.22e-185:
		tmp = (NdChar / (2.0 - (EDonor * ((1.0 / KbT) - ((mu / EDonor) / KbT))))) - t_2
	elif NaChar <= 7.5e-169:
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	elif NaChar <= 1.1e-133:
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - t_2
	elif NaChar <= 1.15e-54:
		tmp = ((KbT * NaChar) / EAccept) - (NdChar / (-1.0 - t_0))
	else:
		tmp = (NaChar / (1.0 + t_1)) + (NdChar / (((Vef / KbT) + (2.0 + (EDonor / KbT))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))
	t_1 = exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))
	t_2 = Float64(NaChar / Float64(-1.0 - t_1))
	tmp = 0.0
	if (NaChar <= -1.22e-185)
		tmp = Float64(Float64(NdChar / Float64(2.0 - Float64(EDonor * Float64(Float64(1.0 / KbT) - Float64(Float64(mu / EDonor) / KbT))))) - t_2);
	elseif (NaChar <= 7.5e-169)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / KbT)))));
	elseif (NaChar <= 1.1e-133)
		tmp = Float64(Float64(KbT * Float64(NdChar / Float64(EDonor - Float64(Vef * Float64(-1.0 + Float64(Float64(Ec - mu) / Vef)))))) - t_2);
	elseif (NaChar <= 1.15e-54)
		tmp = Float64(Float64(Float64(KbT * NaChar) / EAccept) - Float64(NdChar / Float64(-1.0 - t_0)));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + t_1)) + Float64(NdChar / Float64(Float64(Float64(Vef / KbT) + Float64(2.0 + Float64(EDonor / KbT))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	t_1 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	t_2 = NaChar / (-1.0 - t_1);
	tmp = 0.0;
	if (NaChar <= -1.22e-185)
		tmp = (NdChar / (2.0 - (EDonor * ((1.0 / KbT) - ((mu / EDonor) / KbT))))) - t_2;
	elseif (NaChar <= 7.5e-169)
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	elseif (NaChar <= 1.1e-133)
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - t_2;
	elseif (NaChar <= 1.15e-54)
		tmp = ((KbT * NaChar) / EAccept) - (NdChar / (-1.0 - t_0));
	else
		tmp = (NaChar / (1.0 + t_1)) + (NdChar / (((Vef / KbT) + (2.0 + (EDonor / KbT))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.22e-185], N[(N[(NdChar / N[(2.0 - N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(mu / EDonor), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[NaChar, 7.5e-169], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.1e-133], N[(N[(KbT * N[(NdChar / N[(EDonor - N[(Vef * N[(-1.0 + N[(N[(Ec - mu), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[NaChar, 1.15e-54], N[(N[(N[(KbT * NaChar), $MachinePrecision] / EAccept), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -1.21999999999999996e-185

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.0%

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

      1. associate--l+ 65.0%

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

      2. associate--l+ 65.0%

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

      3. associate--l+ 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in EDonor around -inf 71.7%

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

   9. Taylor expanded in mu around inf 73.6%

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

       1. *-commutative 73.6%

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

   11. Simplified 73.6%

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

       1. *-un-lft-identity 73.6%

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

       2. add-sqr-sqrt 42.3%

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

       3. sqrt-unprod 74.7%

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

       4. mul-1-neg 74.7%

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

       5. mul-1-neg 74.7%

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

       6. sqr-neg 74.7%

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

       7. sqrt-unprod 33.5%

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

       8. add-sqr-sqrt 73.8%

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

   13. Applied egg-rr 72.7%

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

       1. *-lft-identity 72.7%

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

       2. associate-/l/ 73.6%

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

       3. associate-/r* 73.5%

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

   15. Simplified 73.5%

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

   if -1.21999999999999996e-185 < NaChar < 7.49999999999999978e-169

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 82.2%

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

   6. Taylor expanded in Ev around 0 75.2%

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

   if 7.49999999999999978e-169 < NaChar < 1.1e-133

   1. Initial program 100.0%

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

   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 84.3%

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

      1. associate--l+ 84.3%

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

      2. associate--l+ 84.3%

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

      3. associate--l+ 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in Vef around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-/r* 100.0%

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

      3. associate-/r* 100.0%

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

      4. div-sub 100.0%

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

      5. div-sub 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in KbT around 0 100.0%

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

       1. associate-/l* 100.0%

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

       2. associate--l+ 100.0%

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

       3. div-sub 100.0%

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

   13. Simplified 100.0%

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

   if 1.1e-133 < NaChar < 1.1499999999999999e-54

   1. Initial program 100.0%

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

   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 59.9%

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

   6. Taylor expanded in EAccept around 0 53.5%

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

   7. Taylor expanded in EAccept around inf 52.0%

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

   if 1.1499999999999999e-54 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.7%

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

      1. associate--l+ 73.7%

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

      2. associate--l+ 73.7%

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

      3. associate--l+ 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in mu around 0 72.2%

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

      1. associate-+r+ 72.2%

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

   10. Simplified 72.2%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.22 \cdot 10^{-185}:\\ \;\;\;\;\frac{NdChar}{2 - EDonor \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{EDonor}}{KbT}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 7.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{-133}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor - Vef \cdot \left(-1 + \frac{Ec - mu}{Vef}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.15 \cdot 10^{-54}:\\ \;\;\;\;\frac{KbT \cdot NaChar}{EAccept} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(\frac{Vef}{KbT} + \left(2 + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_1 := e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}\\ t_2 := \frac{NdChar}{2 - EDonor \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{EDonor}}{KbT}\right)} - t\_0\\ \mathbf{if}\;NaChar \leq -7.6 \cdot 10^{-182}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{NdChar}{1 + t\_1} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{-133}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor - Vef \cdot \left(-1 + \frac{Ec - mu}{Vef}\right)} - t\_0\\ \mathbf{elif}\;NaChar \leq 9.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{KbT \cdot NaChar}{EAccept} - \frac{NdChar}{-1 - t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_1 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))
        (t_2
         (-
          (/ NdChar (- 2.0 (* EDonor (- (/ 1.0 KbT) (/ (/ mu EDonor) KbT)))))
          t_0)))
   (if (<= NaChar -7.6e-182)
     t_2
     (if (<= NaChar 8.5e-169)
       (+ (/ NdChar (+ 1.0 t_1)) (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT)))))
       (if (<= NaChar 4.1e-133)
         (-
          (* KbT (/ NdChar (- EDonor (* Vef (+ -1.0 (/ (- Ec mu) Vef))))))
          t_0)
         (if (<= NaChar 9.5e-55)
           (- (/ (* KbT NaChar) EAccept) (/ NdChar (- -1.0 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 - (mu - EAccept))) / KbT)));
	double t_1 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_2 = (NdChar / (2.0 - (EDonor * ((1.0 / KbT) - ((mu / EDonor) / KbT))))) - t_0;
	double tmp;
	if (NaChar <= -7.6e-182) {
		tmp = t_2;
	} else if (NaChar <= 8.5e-169) {
		tmp = (NdChar / (1.0 + t_1)) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	} else if (NaChar <= 4.1e-133) {
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - t_0;
	} else if (NaChar <= 9.5e-55) {
		tmp = ((KbT * NaChar) / EAccept) - (NdChar / (-1.0 - 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 - (mu - eaccept))) / kbt)))
    t_1 = exp(((edonor + (mu + (vef - ec))) / kbt))
    t_2 = (ndchar / (2.0d0 - (edonor * ((1.0d0 / kbt) - ((mu / edonor) / kbt))))) - t_0
    if (nachar <= (-7.6d-182)) then
        tmp = t_2
    else if (nachar <= 8.5d-169) then
        tmp = (ndchar / (1.0d0 + t_1)) + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    else if (nachar <= 4.1d-133) then
        tmp = (kbt * (ndchar / (edonor - (vef * ((-1.0d0) + ((ec - mu) / vef)))))) - t_0
    else if (nachar <= 9.5d-55) then
        tmp = ((kbt * nachar) / eaccept) - (ndchar / ((-1.0d0) - 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 - (mu - EAccept))) / KbT)));
	double t_1 = Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_2 = (NdChar / (2.0 - (EDonor * ((1.0 / KbT) - ((mu / EDonor) / KbT))))) - t_0;
	double tmp;
	if (NaChar <= -7.6e-182) {
		tmp = t_2;
	} else if (NaChar <= 8.5e-169) {
		tmp = (NdChar / (1.0 + t_1)) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	} else if (NaChar <= 4.1e-133) {
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - t_0;
	} else if (NaChar <= 9.5e-55) {
		tmp = ((KbT * NaChar) / EAccept) - (NdChar / (-1.0 - 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 - (mu - EAccept))) / KbT)))
	t_1 = math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))
	t_2 = (NdChar / (2.0 - (EDonor * ((1.0 / KbT) - ((mu / EDonor) / KbT))))) - t_0
	tmp = 0
	if NaChar <= -7.6e-182:
		tmp = t_2
	elif NaChar <= 8.5e-169:
		tmp = (NdChar / (1.0 + t_1)) + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	elif NaChar <= 4.1e-133:
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - t_0
	elif NaChar <= 9.5e-55:
		tmp = ((KbT * NaChar) / EAccept) - (NdChar / (-1.0 - 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(mu - EAccept))) / KbT))))
	t_1 = exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))
	t_2 = Float64(Float64(NdChar / Float64(2.0 - Float64(EDonor * Float64(Float64(1.0 / KbT) - Float64(Float64(mu / EDonor) / KbT))))) - t_0)
	tmp = 0.0
	if (NaChar <= -7.6e-182)
		tmp = t_2;
	elseif (NaChar <= 8.5e-169)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_1)) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / KbT)))));
	elseif (NaChar <= 4.1e-133)
		tmp = Float64(Float64(KbT * Float64(NdChar / Float64(EDonor - Float64(Vef * Float64(-1.0 + Float64(Float64(Ec - mu) / Vef)))))) - t_0);
	elseif (NaChar <= 9.5e-55)
		tmp = Float64(Float64(Float64(KbT * NaChar) / EAccept) - Float64(NdChar / Float64(-1.0 - 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 - (mu - EAccept))) / KbT)));
	t_1 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	t_2 = (NdChar / (2.0 - (EDonor * ((1.0 / KbT) - ((mu / EDonor) / KbT))))) - t_0;
	tmp = 0.0;
	if (NaChar <= -7.6e-182)
		tmp = t_2;
	elseif (NaChar <= 8.5e-169)
		tmp = (NdChar / (1.0 + t_1)) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	elseif (NaChar <= 4.1e-133)
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - t_0;
	elseif (NaChar <= 9.5e-55)
		tmp = ((KbT * NaChar) / EAccept) - (NdChar / (-1.0 - 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[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(2.0 - N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(mu / EDonor), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[NaChar, -7.6e-182], t$95$2, If[LessEqual[NaChar, 8.5e-169], N[(N[(NdChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.1e-133], N[(N[(KbT * N[(NdChar / N[(EDonor - N[(Vef * N[(-1.0 + N[(N[(Ec - mu), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, 9.5e-55], N[(N[(N[(KbT * NaChar), $MachinePrecision] / EAccept), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -7.6000000000000006e-182 or 9.5000000000000006e-55 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. associate--l+ 68.9%

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

      3. associate--l+ 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in EDonor around -inf 73.1%

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

   9. Taylor expanded in mu around inf 73.9%

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

       1. *-commutative 73.9%

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

   11. Simplified 73.9%

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

       1. *-un-lft-identity 73.9%

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

       2. add-sqr-sqrt 47.2%

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

       3. sqrt-unprod 74.9%

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

       4. mul-1-neg 74.9%

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

       5. mul-1-neg 74.9%

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

       6. sqr-neg 74.9%

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

       7. sqrt-unprod 31.5%

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

       8. add-sqr-sqrt 73.8%

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

   13. Applied egg-rr 72.4%

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

       1. *-lft-identity 72.4%

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

       2. associate-/l/ 73.9%

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

       3. associate-/r* 72.8%

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

   15. Simplified 72.8%

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

   if -7.6000000000000006e-182 < NaChar < 8.50000000000000054e-169

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 82.2%

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

   6. Taylor expanded in Ev around 0 75.2%

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

   if 8.50000000000000054e-169 < NaChar < 4.10000000000000022e-133

   1. Initial program 100.0%

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

   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 84.3%

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

      1. associate--l+ 84.3%

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

      2. associate--l+ 84.3%

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

      3. associate--l+ 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in Vef around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-/r* 100.0%

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

      3. associate-/r* 100.0%

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

      4. div-sub 100.0%

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

      5. div-sub 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in KbT around 0 100.0%

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

       1. associate-/l* 100.0%

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

       2. associate--l+ 100.0%

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

       3. div-sub 100.0%

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

   13. Simplified 100.0%

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

   if 4.10000000000000022e-133 < NaChar < 9.5000000000000006e-55

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 59.9%

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

   6. Taylor expanded in EAccept around 0 53.5%

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

   7. Taylor expanded in EAccept around inf 52.0%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7.6 \cdot 10^{-182}:\\ \;\;\;\;\frac{NdChar}{2 - EDonor \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{EDonor}}{KbT}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{-133}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor - Vef \cdot \left(-1 + \frac{Ec - mu}{Vef}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 9.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{KbT \cdot NaChar}{EAccept} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 - EDonor \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{EDonor}}{KbT}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.22 \cdot 10^{-182}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2 + \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 5.3 \cdot 10^{-189}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2 + Ec \cdot \left(\frac{\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
   (if (<= NaChar -1.22e-182)
     (+
      t_0
      (/
       NdChar
       (+ 2.0 (/ (* EDonor (+ 1.0 (/ (- (+ mu Vef) Ec) EDonor))) KbT))))
     (if (<= NaChar 5.3e-189)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
        (/
         NaChar
         (-
          1.0
          (+
           (/ mu KbT)
           (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))))))
       (+
        t_0
        (/
         NdChar
         (+
          2.0
          (*
           Ec
           (+
            (/ (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))) Ec)
            (/ -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(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.22e-182) {
		tmp = t_0 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	} else if (NaChar <= 5.3e-189) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else {
		tmp = t_0 + (NdChar / (2.0 + (Ec * ((((EDonor / KbT) + ((Vef / KbT) + (mu / KbT))) / Ec) + (-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) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    if (nachar <= (-1.22d-182)) then
        tmp = t_0 + (ndchar / (2.0d0 + ((edonor * (1.0d0 + (((mu + vef) - ec) / edonor))) / kbt)))
    else if (nachar <= 5.3d-189) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))))))
    else
        tmp = t_0 + (ndchar / (2.0d0 + (ec * ((((edonor / kbt) + ((vef / kbt) + (mu / kbt))) / ec) + ((-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(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.22e-182) {
		tmp = t_0 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	} else if (NaChar <= 5.3e-189) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else {
		tmp = t_0 + (NdChar / (2.0 + (Ec * ((((EDonor / KbT) + ((Vef / KbT) + (mu / KbT))) / Ec) + (-1.0 / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	tmp = 0
	if NaChar <= -1.22e-182:
		tmp = t_0 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)))
	elif NaChar <= 5.3e-189:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))))
	else:
		tmp = t_0 + (NdChar / (2.0 + (Ec * ((((EDonor / KbT) + ((Vef / KbT) + (mu / KbT))) / Ec) + (-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(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.22e-182)
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 + Float64(Float64(EDonor * Float64(1.0 + Float64(Float64(Float64(mu + Vef) - Ec) / EDonor))) / KbT))));
	elseif (NaChar <= 5.3e-189)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 - Float64(Float64(mu / KbT) + Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))))))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 + Float64(Ec * Float64(Float64(Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) / Ec) + 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(((Vef + (Ev - (mu - EAccept))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.22e-182)
		tmp = t_0 + (NdChar / (2.0 + ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	elseif (NaChar <= 5.3e-189)
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	else
		tmp = t_0 + (NdChar / (2.0 + (Ec * ((((EDonor / KbT) + ((Vef / KbT) + (mu / KbT))) / Ec) + (-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[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.22e-182], N[(t$95$0 + N[(NdChar / N[(2.0 + N[(N[(EDonor * N[(1.0 + N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 5.3e-189], 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[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(2.0 + N[(Ec * N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.22e-182

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.0%

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

      1. associate--l+ 65.0%

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

      2. associate--l+ 65.0%

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

      3. associate--l+ 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in EDonor around -inf 71.7%

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

   9. Taylor expanded in KbT around 0 75.5%

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

   if -1.22e-182 < NaChar < 5.2999999999999998e-189

   1. Initial program 100.0%

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

   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 77.9%

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

      1. +-commutative 77.9%

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

   7. Simplified 77.9%

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

   if 5.2999999999999998e-189 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate--l+ 68.2%

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

      3. associate--l+ 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in Ec around -inf 72.8%

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

      1. associate-*r* 72.8%

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

      2. mul-1-neg 72.8%

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

      3. +-commutative 72.8%

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

      4. mul-1-neg 72.8%

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

      5. unsub-neg 72.8%

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

      6. +-commutative 72.8%

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

   10. Simplified 72.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.22 \cdot 10^{-182}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 5.3 \cdot 10^{-189}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + Ec \cdot \left(\frac{\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5.4 \cdot 10^{-182} \lor \neg \left(NaChar \leq 1.75 \cdot 10^{-181}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{mu}{EDonor \cdot KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -5.4e-182) (not (<= NaChar 1.75e-181)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
    (/ NdChar (+ 2.0 (* EDonor (+ (/ 1.0 KbT) (/ mu (* EDonor KbT)))))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/
     NaChar
     (-
      1.0
      (+
       (/ mu KbT)
       (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -5.4e-182) || !(NaChar <= 1.75e-181)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))));
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-5.4d-182)) .or. (.not. (nachar <= 1.75d-181))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (2.0d0 + (edonor * ((1.0d0 / kbt) + (mu / (edonor * kbt))))))
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -5.4e-182) || !(NaChar <= 1.75e-181)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -5.4e-182) or not (NaChar <= 1.75e-181):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))))
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -5.4e-182) || !(NaChar <= 1.75e-181))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(mu / Float64(EDonor * KbT)))))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 - Float64(Float64(mu / KbT) + Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -5.4e-182) || ~((NaChar <= 1.75e-181)))
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))));
	else
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -5.4e-182], N[Not[LessEqual[NaChar, 1.75e-181]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -5.39999999999999999e-182 or 1.74999999999999998e-181 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.7%

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

      1. associate--l+ 66.7%

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

      2. associate--l+ 66.7%

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

      3. associate--l+ 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in EDonor around -inf 71.8%

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

   9. Taylor expanded in mu around inf 72.0%

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

       1. *-commutative 72.0%

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

   11. Simplified 72.0%

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

   if -5.39999999999999999e-182 < NaChar < 1.74999999999999998e-181

   1. Initial program 100.0%

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

   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 77.9%

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

      1. +-commutative 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.4 \cdot 10^{-182} \lor \neg \left(NaChar \leq 1.75 \cdot 10^{-181}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{mu}{EDonor \cdot KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -1 \cdot 10^{-17}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{NdChar}{2 + Vef \cdot \left(\frac{1}{KbT} - \frac{Ec - mu}{Vef \cdot KbT}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NdChar -1e-17)
     (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))
     (if (<= NdChar 1.4e+59)
       (-
        (/ NdChar (+ 2.0 (* Vef (- (/ 1.0 KbT) (/ (- Ec mu) (* Vef KbT))))))
        (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
       (+ t_0 (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -1e-17) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 1.4e+59) {
		tmp = (NdChar / (2.0 + (Vef * ((1.0 / KbT) - ((Ec - mu) / (Vef * KbT)))))) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (ndchar <= (-1d-17)) then
        tmp = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= 1.4d+59) then
        tmp = (ndchar / (2.0d0 + (vef * ((1.0d0 / kbt) - ((ec - mu) / (vef * kbt)))))) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -1e-17) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 1.4e+59) {
		tmp = (NdChar / (2.0 + (Vef * ((1.0 / KbT) - ((Ec - mu) / (Vef * KbT)))))) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -1e-17:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= 1.4e+59:
		tmp = (NdChar / (2.0 + (Vef * ((1.0 / KbT) - ((Ec - mu) / (Vef * KbT)))))) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -1e-17)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= 1.4e+59)
		tmp = Float64(Float64(NdChar / Float64(2.0 + Float64(Vef * Float64(Float64(1.0 / KbT) - Float64(Float64(Ec - mu) / Float64(Vef * KbT)))))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / 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(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -1e-17)
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= 1.4e+59)
		tmp = (NdChar / (2.0 + (Vef * ((1.0 / KbT) - ((Ec - mu) / (Vef * KbT)))))) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1e-17], N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.4e+59], N[(N[(NdChar / N[(2.0 + N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(Ec - mu), $MachinePrecision] / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -1.00000000000000007e-17

   1. Initial program 100.0%

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

   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 74.5%

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

   6. Taylor expanded in EAccept around 0 63.3%

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

   if -1.00000000000000007e-17 < NdChar < 1.3999999999999999e59

   1. Initial program 100.0%

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

   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 70.4%

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

      1. associate--l+ 70.4%

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

      2. associate--l+ 70.4%

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

      3. associate--l+ 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in Vef around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. associate-/r* 70.9%

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

      3. associate-/r* 71.6%

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

      4. div-sub 72.3%

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

      5. div-sub 72.9%

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

   10. Simplified 72.9%

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

   11. Taylor expanded in EDonor around 0 70.1%

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

       1. associate--l+ 70.1%

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

       2. div-sub 73.6%

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

   13. Simplified 73.6%

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

   if 1.3999999999999999e59 < 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 78.8%

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

   6. Taylor expanded in Ev around 0 76.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1 \cdot 10^{-17}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{NdChar}{2 + Vef \cdot \left(\frac{1}{KbT} - \frac{Ec - mu}{Vef \cdot KbT}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}\\ \mathbf{if}\;NdChar \leq -3 \cdot 10^{-21}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -2.3 \cdot 10^{-226}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor - Vef \cdot \left(-1 + \frac{Ec - mu}{Vef}\right)} - \frac{NaChar}{-1 - t\_1}\\ \mathbf{elif}\;NdChar \leq 2.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{NaChar}{1 + t\_1} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
   (if (<= NdChar -3e-21)
     (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))
     (if (<= NdChar -2.3e-226)
       (-
        (* KbT (/ NdChar (- EDonor (* Vef (+ -1.0 (/ (- Ec mu) Vef))))))
        (/ NaChar (- -1.0 t_1)))
       (if (<= NdChar 2.6e+43)
         (+
          (/ NaChar (+ 1.0 t_1))
          (/ NdChar (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT)))))
         (+ t_0 (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double tmp;
	if (NdChar <= -3e-21) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -2.3e-226) {
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - (NaChar / (-1.0 - t_1));
	} else if (NdChar <= 2.6e+43) {
		tmp = (NaChar / (1.0 + t_1)) + (NdChar / (2.0 + ((Vef / KbT) + (EDonor / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = exp(((vef + (ev - (mu - eaccept))) / kbt))
    if (ndchar <= (-3d-21)) then
        tmp = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= (-2.3d-226)) then
        tmp = (kbt * (ndchar / (edonor - (vef * ((-1.0d0) + ((ec - mu) / vef)))))) - (nachar / ((-1.0d0) - t_1))
    else if (ndchar <= 2.6d+43) then
        tmp = (nachar / (1.0d0 + t_1)) + (ndchar / (2.0d0 + ((vef / kbt) + (edonor / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double tmp;
	if (NdChar <= -3e-21) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -2.3e-226) {
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - (NaChar / (-1.0 - t_1));
	} else if (NdChar <= 2.6e+43) {
		tmp = (NaChar / (1.0 + t_1)) + (NdChar / (2.0 + ((Vef / KbT) + (EDonor / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))
	tmp = 0
	if NdChar <= -3e-21:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= -2.3e-226:
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - (NaChar / (-1.0 - t_1))
	elif NdChar <= 2.6e+43:
		tmp = (NaChar / (1.0 + t_1)) + (NdChar / (2.0 + ((Vef / KbT) + (EDonor / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))
	tmp = 0.0
	if (NdChar <= -3e-21)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= -2.3e-226)
		tmp = Float64(Float64(KbT * Float64(NdChar / Float64(EDonor - Float64(Vef * Float64(-1.0 + Float64(Float64(Ec - mu) / Vef)))))) - Float64(NaChar / Float64(-1.0 - t_1)));
	elseif (NdChar <= 2.6e+43)
		tmp = Float64(Float64(NaChar / Float64(1.0 + t_1)) + Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / 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(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	tmp = 0.0;
	if (NdChar <= -3e-21)
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= -2.3e-226)
		tmp = (KbT * (NdChar / (EDonor - (Vef * (-1.0 + ((Ec - mu) / Vef)))))) - (NaChar / (-1.0 - t_1));
	elseif (NdChar <= 2.6e+43)
		tmp = (NaChar / (1.0 + t_1)) + (NdChar / (2.0 + ((Vef / KbT) + (EDonor / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[NdChar, -3e-21], N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -2.3e-226], N[(N[(KbT * N[(NdChar / N[(EDonor - N[(Vef * N[(-1.0 + N[(N[(Ec - mu), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.6e+43], N[(N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -2.99999999999999991e-21

   1. Initial program 100.0%

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

   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 74.5%

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

   6. Taylor expanded in EAccept around 0 63.3%

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

   if -2.99999999999999991e-21 < NdChar < -2.3e-226

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. associate--l+ 66.6%

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

      3. associate--l+ 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in Vef around inf 62.5%

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

      1. associate--l+ 62.5%

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

      2. associate-/r* 66.4%

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

      3. associate-/r* 70.3%

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

      4. div-sub 70.3%

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

      5. div-sub 70.3%

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

   10. Simplified 70.3%

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

   11. Taylor expanded in KbT around 0 63.9%

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

       1. associate-/l* 67.6%

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

       2. associate--l+ 67.6%

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

       3. div-sub 67.6%

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

   13. Simplified 67.6%

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

   if -2.3e-226 < NdChar < 2.60000000000000021e43

   1. Initial program 100.0%

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

   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 72.6%

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

      1. associate--l+ 72.6%

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

      2. associate--l+ 72.6%

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

      3. associate--l+ 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in Vef around inf 72.5%

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

      1. associate--l+ 72.5%

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

      2. associate-/r* 72.5%

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

      3. associate-/r* 71.5%

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

      4. div-sub 72.6%

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

      5. div-sub 73.7%

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

   10. Simplified 73.7%

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

   11. Taylor expanded in Vef around inf 74.8%

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

   if 2.60000000000000021e43 < 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 75.5%

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

   6. Taylor expanded in Ev around 0 71.2%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3 \cdot 10^{-21}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -2.3 \cdot 10^{-226}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor - Vef \cdot \left(-1 + \frac{Ec - mu}{Vef}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 2.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.28 \cdot 10^{-182} \lor \neg \left(NaChar \leq 3.8 \cdot 10^{-169}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{mu}{EDonor \cdot KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.28e-182) (not (<= NaChar 3.8e-169)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
    (/ NdChar (+ 2.0 (* EDonor (+ (/ 1.0 KbT) (/ mu (* EDonor KbT)))))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.28e-182) || !(NaChar <= 3.8e-169)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))));
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-1.28d-182)) .or. (.not. (nachar <= 3.8d-169))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (2.0d0 + (edonor * ((1.0d0 / kbt) + (mu / (edonor * kbt))))))
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.28e-182) || !(NaChar <= 3.8e-169)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.28e-182) or not (NaChar <= 3.8e-169):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))))
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.28e-182) || !(NaChar <= 3.8e-169))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(mu / Float64(EDonor * KbT)))))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1.28e-182) || ~((NaChar <= 3.8e-169)))
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor * ((1.0 / KbT) + (mu / (EDonor * KbT))))));
	else
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.28e-182], N[Not[LessEqual[NaChar, 3.8e-169]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.2800000000000001e-182 or 3.8e-169 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.8%

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

      1. associate--l+ 66.8%

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

      2. associate--l+ 66.8%

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

      3. associate--l+ 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in EDonor around -inf 72.0%

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

   9. Taylor expanded in mu around inf 72.2%

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

       1. *-commutative 72.2%

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

   11. Simplified 72.2%

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

   if -1.2800000000000001e-182 < NaChar < 3.8e-169

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 82.2%

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

   6. Taylor expanded in Ev around 0 75.2%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.28 \cdot 10^{-182} \lor \neg \left(NaChar \leq 3.8 \cdot 10^{-169}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{mu}{EDonor \cdot KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{if}\;NdChar \leq -1.6 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;\frac{NaChar}{1 + t\_0} - \frac{NdChar \cdot KbT}{Ec}\\ \mathbf{elif}\;NdChar \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - t\_0}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
          (/ NaChar (+ (/ EAccept KbT) 2.0)))))
   (if (<= NdChar -1.6e-19)
     t_1
     (if (<= NdChar -1.8e-223)
       (- (/ NaChar (+ 1.0 t_0)) (/ (* NdChar KbT) Ec))
       (if (<= NdChar 1.85e+53)
         (- (/ NdChar 2.0) (/ NaChar (- -1.0 t_0)))
         t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double t_1 = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	double tmp;
	if (NdChar <= -1.6e-19) {
		tmp = t_1;
	} else if (NdChar <= -1.8e-223) {
		tmp = (NaChar / (1.0 + t_0)) - ((NdChar * KbT) / Ec);
	} else if (NdChar <= 1.85e+53) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - t_0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = exp(((vef + (ev - (mu - eaccept))) / kbt))
    t_1 = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    if (ndchar <= (-1.6d-19)) then
        tmp = t_1
    else if (ndchar <= (-1.8d-223)) then
        tmp = (nachar / (1.0d0 + t_0)) - ((ndchar * kbt) / ec)
    else if (ndchar <= 1.85d+53) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - t_0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double t_1 = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	double tmp;
	if (NdChar <= -1.6e-19) {
		tmp = t_1;
	} else if (NdChar <= -1.8e-223) {
		tmp = (NaChar / (1.0 + t_0)) - ((NdChar * KbT) / Ec);
	} else if (NdChar <= 1.85e+53) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - t_0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))
	t_1 = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	tmp = 0
	if NdChar <= -1.6e-19:
		tmp = t_1
	elif NdChar <= -1.8e-223:
		tmp = (NaChar / (1.0 + t_0)) - ((NdChar * KbT) / Ec)
	elif NdChar <= 1.85e+53:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - t_0))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)))
	tmp = 0.0
	if (NdChar <= -1.6e-19)
		tmp = t_1;
	elseif (NdChar <= -1.8e-223)
		tmp = Float64(Float64(NaChar / Float64(1.0 + t_0)) - Float64(Float64(NdChar * KbT) / Ec));
	elseif (NdChar <= 1.85e+53)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - t_0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	t_1 = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	tmp = 0.0;
	if (NdChar <= -1.6e-19)
		tmp = t_1;
	elseif (NdChar <= -1.8e-223)
		tmp = (NaChar / (1.0 + t_0)) - ((NdChar * KbT) / Ec);
	elseif (NdChar <= 1.85e+53)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - t_0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $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 / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.6e-19], t$95$1, If[LessEqual[NdChar, -1.8e-223], N[(N[(NaChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] - N[(N[(NdChar * KbT), $MachinePrecision] / Ec), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.85e+53], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -1.59999999999999991e-19 or 1.85e53 < 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 77.7%

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

   6. Taylor expanded in EAccept around 0 63.7%

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

   if -1.59999999999999991e-19 < NdChar < -1.8000000000000002e-223

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. associate--l+ 66.6%

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

      3. associate--l+ 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in Ec around inf 58.8%

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

      1. associate-*r/ 58.8%

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

      2. associate-*r* 58.8%

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

      3. neg-mul-1 58.8%

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

   10. Simplified 58.8%

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

   if -1.8000000000000002e-223 < NdChar < 1.85e53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.8 \cdot 10^{-223}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} - \frac{NdChar \cdot KbT}{Ec}\\ \mathbf{elif}\;NdChar \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -7.8 \cdot 10^{-19}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 3.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NdChar -7.8e-19)
     (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))
     (if (<= NdChar 3.8e+43)
       (+
        (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
        (/ NdChar (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT)))))
       (+ t_0 (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -7.8e-19) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 3.8e+43) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + ((Vef / KbT) + (EDonor / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (ndchar <= (-7.8d-19)) then
        tmp = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= 3.8d+43) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (2.0d0 + ((vef / kbt) + (edonor / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -7.8e-19) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 3.8e+43) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + ((Vef / KbT) + (EDonor / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -7.8e-19:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= 3.8e+43:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + ((Vef / KbT) + (EDonor / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -7.8e-19)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= 3.8e+43)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / 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(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -7.8e-19)
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= 3.8e+43)
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + ((Vef / KbT) + (EDonor / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -7.8e-19], N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.8e+43], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -7.7999999999999999e-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 EAccept around inf 74.5%

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

   6. Taylor expanded in EAccept around 0 63.3%

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

   if -7.7999999999999999e-19 < NdChar < 3.80000000000000008e43

   1. Initial program 100.0%

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

   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 70.5%

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

      1. associate--l+ 70.5%

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

      2. associate--l+ 70.5%

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

      3. associate--l+ 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in Vef around inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. associate-/r* 70.4%

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

      3. associate-/r* 71.1%

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

      4. div-sub 71.8%

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

      5. div-sub 72.5%

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

   10. Simplified 72.5%

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

   11. Taylor expanded in Vef around inf 69.1%

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

   if 3.80000000000000008e43 < 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 75.5%

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

   6. Taylor expanded in Ev around 0 71.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -7.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 3.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -6 \cdot 10^{-18}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 2000000000:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NdChar -6e-18)
     (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))
     (if (<= NdChar 2000000000.0)
       (-
        (/ NdChar (- 2.0 (/ Ec KbT)))
        (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
       (+ t_0 (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -6e-18) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 2000000000.0) {
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (ndchar <= (-6d-18)) then
        tmp = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= 2000000000.0d0) then
        tmp = (ndchar / (2.0d0 - (ec / kbt))) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -6e-18) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 2000000000.0) {
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -6e-18:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= 2000000000.0:
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -6e-18)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= 2000000000.0)
		tmp = Float64(Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / 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(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -6e-18)
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= 2000000000.0)
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -6e-18], N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2000000000.0], N[(N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -5.99999999999999966e-18

   1. Initial program 100.0%

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

   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 74.5%

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

   6. Taylor expanded in EAccept around 0 63.3%

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

   if -5.99999999999999966e-18 < NdChar < 2e9

   1. Initial program 100.0%

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

   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 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate--l+ 73.1%

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

      3. associate--l+ 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in Ec around inf 71.4%

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

      1. neg-mul-1 71.4%

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

      2. distribute-neg-frac2 71.4%

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

   10. Simplified 71.4%

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

   if 2e9 < 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 70.7%

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

   6. Taylor expanded in Ev around 0 63.7%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6 \cdot 10^{-18}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 2000000000:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{EAccept}{KbT} + 2\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -1.25 \cdot 10^{-21}:\\ \;\;\;\;t\_1 + \frac{NaChar}{t\_0}\\ \mathbf{elif}\;NdChar \leq 2.6 \cdot 10^{+54}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + NaChar \cdot \frac{1}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ EAccept KbT) 2.0))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NdChar -1.25e-21)
     (+ t_1 (/ NaChar t_0))
     (if (<= NdChar 2.6e+54)
       (-
        (/ NdChar (- 2.0 (/ Ec KbT)))
        (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
       (+ t_1 (* NaChar (/ 1.0 t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (EAccept / KbT) + 2.0;
	double t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -1.25e-21) {
		tmp = t_1 + (NaChar / t_0);
	} else if (NdChar <= 2.6e+54) {
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = t_1 + (NaChar * (1.0 / t_0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (eaccept / kbt) + 2.0d0
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (ndchar <= (-1.25d-21)) then
        tmp = t_1 + (nachar / t_0)
    else if (ndchar <= 2.6d+54) then
        tmp = (ndchar / (2.0d0 - (ec / kbt))) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else
        tmp = t_1 + (nachar * (1.0d0 / t_0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (EAccept / KbT) + 2.0;
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -1.25e-21) {
		tmp = t_1 + (NaChar / t_0);
	} else if (NdChar <= 2.6e+54) {
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = t_1 + (NaChar * (1.0 / t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (EAccept / KbT) + 2.0
	t_1 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -1.25e-21:
		tmp = t_1 + (NaChar / t_0)
	elif NdChar <= 2.6e+54:
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	else:
		tmp = t_1 + (NaChar * (1.0 / t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(EAccept / KbT) + 2.0)
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -1.25e-21)
		tmp = Float64(t_1 + Float64(NaChar / t_0));
	elseif (NdChar <= 2.6e+54)
		tmp = Float64(Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	else
		tmp = Float64(t_1 + Float64(NaChar * Float64(1.0 / t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (EAccept / KbT) + 2.0;
	t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -1.25e-21)
		tmp = t_1 + (NaChar / t_0);
	elseif (NdChar <= 2.6e+54)
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	else
		tmp = t_1 + (NaChar * (1.0 / t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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]}, If[LessEqual[NdChar, -1.25e-21], N[(t$95$1 + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.6e+54], N[(N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NaChar * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -1.24999999999999993e-21

   1. Initial program 100.0%

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

   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 74.5%

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

   6. Taylor expanded in EAccept around 0 63.3%

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

   if -1.24999999999999993e-21 < NdChar < 2.60000000000000007e54

   1. Initial program 100.0%

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

   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 69.8%

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

      1. associate--l+ 69.8%

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

      2. associate--l+ 69.8%

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

      3. associate--l+ 69.8%

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

   7. Simplified 69.8%

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

   8. Taylor expanded in Ec around inf 67.7%

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

      1. neg-mul-1 67.7%

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

      2. distribute-neg-frac2 67.7%

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

   10. Simplified 67.7%

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

   if 2.60000000000000007e54 < 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 82.3%

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

   6. Taylor expanded in EAccept around 0 65.8%

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

      1. div-inv 65.8%

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

   8. Applied egg-rr 65.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.25 \cdot 10^{-21}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 2.6 \cdot 10^{+54}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot \frac{1}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 54.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}\\ t_1 := e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}\\ \mathbf{if}\;NdChar \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq -1.5 \cdot 10^{-227}:\\ \;\;\;\;\frac{NaChar}{1 + t\_1} - \frac{NdChar \cdot KbT}{Ec}\\ \mathbf{elif}\;NdChar \leq 1.9 \cdot 10^{+53}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))
        (t_1 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
   (if (<= NdChar -2.4e-20)
     (+ (/ NdChar (+ 1.0 t_0)) (* NaChar 0.5))
     (if (<= NdChar -1.5e-227)
       (- (/ NaChar (+ 1.0 t_1)) (/ (* NdChar KbT) Ec))
       (if (<= NdChar 1.9e+53)
         (- (/ NdChar 2.0) (/ NaChar (- -1.0 t_1)))
         (- (/ NaChar 2.0) (/ NdChar (- -1.0 t_0))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double tmp;
	if (NdChar <= -2.4e-20) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar * 0.5);
	} else if (NdChar <= -1.5e-227) {
		tmp = (NaChar / (1.0 + t_1)) - ((NdChar * KbT) / Ec);
	} else if (NdChar <= 1.9e+53) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - t_1));
	} else {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - t_0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = exp(((edonor + (mu + (vef - ec))) / kbt))
    t_1 = exp(((vef + (ev - (mu - eaccept))) / kbt))
    if (ndchar <= (-2.4d-20)) then
        tmp = (ndchar / (1.0d0 + t_0)) + (nachar * 0.5d0)
    else if (ndchar <= (-1.5d-227)) then
        tmp = (nachar / (1.0d0 + t_1)) - ((ndchar * kbt) / ec)
    else if (ndchar <= 1.9d+53) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - t_1))
    else
        tmp = (nachar / 2.0d0) - (ndchar / ((-1.0d0) - t_0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double tmp;
	if (NdChar <= -2.4e-20) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar * 0.5);
	} else if (NdChar <= -1.5e-227) {
		tmp = (NaChar / (1.0 + t_1)) - ((NdChar * KbT) / Ec);
	} else if (NdChar <= 1.9e+53) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - t_1));
	} else {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))
	t_1 = math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))
	tmp = 0
	if NdChar <= -2.4e-20:
		tmp = (NdChar / (1.0 + t_0)) + (NaChar * 0.5)
	elif NdChar <= -1.5e-227:
		tmp = (NaChar / (1.0 + t_1)) - ((NdChar * KbT) / Ec)
	elif NdChar <= 1.9e+53:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - t_1))
	else:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))
	t_1 = exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))
	tmp = 0.0
	if (NdChar <= -2.4e-20)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) + Float64(NaChar * 0.5));
	elseif (NdChar <= -1.5e-227)
		tmp = Float64(Float64(NaChar / Float64(1.0 + t_1)) - Float64(Float64(NdChar * KbT) / Ec));
	elseif (NdChar <= 1.9e+53)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - t_1)));
	else
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 - t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	t_1 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	tmp = 0.0;
	if (NdChar <= -2.4e-20)
		tmp = (NdChar / (1.0 + t_0)) + (NaChar * 0.5);
	elseif (NdChar <= -1.5e-227)
		tmp = (NaChar / (1.0 + t_1)) - ((NdChar * KbT) / Ec);
	elseif (NdChar <= 1.9e+53)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - t_1));
	else
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[NdChar, -2.4e-20], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -1.5e-227], N[(N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(NdChar * KbT), $MachinePrecision] / Ec), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.9e+53], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -2.39999999999999993e-20

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 74.5%

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

   6. Taylor expanded in EAccept around 0 63.3%

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

   7. Taylor expanded in EAccept around 0 59.5%

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

   if -2.39999999999999993e-20 < NdChar < -1.5e-227

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. associate--l+ 66.6%

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

      3. associate--l+ 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in Ec around inf 58.8%

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

      1. associate-*r/ 58.8%

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

      2. associate-*r* 58.8%

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

      3. neg-mul-1 58.8%

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

   10. Simplified 58.8%

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

   if -1.5e-227 < NdChar < 1.89999999999999999e53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.1%

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

   if 1.89999999999999999e53 < 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 KbT around inf 55.1%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq -1.5 \cdot 10^{-227}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} - \frac{NdChar \cdot KbT}{Ec}\\ \mathbf{elif}\;NdChar \leq 1.9 \cdot 10^{+53}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 62.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -5 \cdot 10^{-18} \lor \neg \left(NdChar \leq 1.35 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -5e-18) (not (<= NdChar 1.35e+54)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ EAccept KbT) 2.0)))
   (-
    (/ NdChar (- 2.0 (/ Ec KbT)))
    (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -5e-18) || !(NdChar <= 1.35e+54)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-5d-18)) .or. (.not. (ndchar <= 1.35d+54))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else
        tmp = (ndchar / (2.0d0 - (ec / kbt))) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -5e-18) || !(NdChar <= 1.35e+54)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -5e-18) or not (NdChar <= 1.35e+54):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	else:
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -5e-18) || !(NdChar <= 1.35e+54))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -5e-18) || ~((NdChar <= 1.35e+54)))
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	else
		tmp = (NdChar / (2.0 - (Ec / KbT))) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -5e-18], N[Not[LessEqual[NdChar, 1.35e+54]], $MachinePrecision]], 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[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -5.00000000000000036e-18 or 1.35000000000000005e54 < 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 77.5%

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

   6. Taylor expanded in EAccept around 0 64.3%

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

   if -5.00000000000000036e-18 < NdChar < 1.35000000000000005e54

   1. Initial program 100.0%

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

   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 69.8%

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

      1. associate--l+ 69.8%

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

      2. associate--l+ 69.8%

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

      3. associate--l+ 69.8%

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

   7. Simplified 69.8%

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

   8. Taylor expanded in Ec around inf 67.7%

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

      1. neg-mul-1 67.7%

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

      2. distribute-neg-frac2 67.7%

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

   10. Simplified 67.7%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -5 \cdot 10^{-18} \lor \neg \left(NdChar \leq 1.35 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 62.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -4.8 \cdot 10^{-21} \lor \neg \left(NdChar \leq 1.8 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -4.8e-21) (not (<= NdChar 1.8e+57)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ EAccept KbT) 2.0)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
    (/ NdChar (+ (/ mu KbT) 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -4.8e-21) || !(NdChar <= 1.8e+57)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-4.8d-21)) .or. (.not. (ndchar <= 1.8d+57))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -4.8e-21) || !(NdChar <= 1.8e+57)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -4.8e-21) or not (NdChar <= 1.8e+57):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -4.8e-21) || !(NdChar <= 1.8e+57))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -4.8e-21) || ~((NdChar <= 1.8e+57)))
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -4.8e-21], N[Not[LessEqual[NdChar, 1.8e+57]], $MachinePrecision]], 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[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -4.7999999999999999e-21 or 1.8000000000000001e57 < 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 78.7%

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

   6. Taylor expanded in EAccept around 0 65.3%

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

   if -4.7999999999999999e-21 < NdChar < 1.8000000000000001e57

   1. Initial program 100.0%

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

   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 70.2%

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

      1. associate--l+ 70.2%

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

      2. associate--l+ 70.2%

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

      3. associate--l+ 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in mu around inf 65.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.8 \cdot 10^{-21} \lor \neg \left(NdChar \leq 1.8 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 62.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -1.05 \cdot 10^{-17} \lor \neg \left(NdChar \leq 1.8 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -1.05e-17) (not (<= NdChar 1.8e+57)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ EAccept KbT) 2.0)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
    (/ NdChar (+ 2.0 (/ 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 ((NdChar <= -1.05e-17) || !(NdChar <= 1.8e+57)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (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 ((ndchar <= (-1.05d-17)) .or. (.not. (ndchar <= 1.8d+57))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (2.0d0 + (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 ((NdChar <= -1.05e-17) || !(NdChar <= 1.8e+57)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -1.05e-17) or not (NdChar <= 1.8e+57):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -1.05e-17) || !(NdChar <= 1.8e+57))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(2.0 + 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 ((NdChar <= -1.05e-17) || ~((NdChar <= 1.8e+57)))
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -1.05e-17], N[Not[LessEqual[NdChar, 1.8e+57]], $MachinePrecision]], 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[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -1.04999999999999996e-17 or 1.8000000000000001e57 < 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 78.7%

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

   6. Taylor expanded in EAccept around 0 65.3%

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

   if -1.04999999999999996e-17 < NdChar < 1.8000000000000001e57

   1. Initial program 100.0%

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

   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 70.2%

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

      1. associate--l+ 70.2%

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

      2. associate--l+ 70.2%

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

      3. associate--l+ 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in EDonor around inf 64.1%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.05 \cdot 10^{-17} \lor \neg \left(NdChar \leq 1.8 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 57.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -1.7 \cdot 10^{-7} \lor \neg \left(NdChar \leq 2.35 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -1.7e-7) (not (<= NdChar 2.35e+53)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (* NaChar 0.5))
   (-
    (/ NdChar 2.0)
    (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -1.7e-7) || !(NdChar <= 2.35e+53)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-1.7d-7)) .or. (.not. (ndchar <= 2.35d+53))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar * 0.5d0)
    else
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -1.7e-7) || !(NdChar <= 2.35e+53)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -1.7e-7) or not (NdChar <= 2.35e+53):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -1.7e-7) || !(NdChar <= 2.35e+53))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -1.7e-7) || ~((NdChar <= 2.35e+53)))
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	else
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -1.7e-7], N[Not[LessEqual[NdChar, 2.35e+53]], $MachinePrecision]], 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 * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -1.69999999999999987e-7 or 2.34999999999999988e53 < 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 77.7%

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

   6. Taylor expanded in EAccept around 0 63.2%

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

   7. Taylor expanded in EAccept around 0 57.1%

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

   if -1.69999999999999987e-7 < NdChar < 2.34999999999999988e53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.2%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.7 \cdot 10^{-7} \lor \neg \left(NdChar \leq 2.35 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 50.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -6.5 \cdot 10^{+129} \lor \neg \left(NdChar \leq 7 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -6.5e+129) (not (<= NdChar 7e+53)))
   (+
    (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
    (/ NaChar (+ (/ EAccept KbT) 2.0)))
   (-
    (/ NdChar 2.0)
    (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -6.5e+129) || !(NdChar <= 7e+53)) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-6.5d+129)) .or. (.not. (ndchar <= 7d+53))) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -6.5e+129) || !(NdChar <= 7e+53)) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -6.5e+129) or not (NdChar <= 7e+53):
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	else:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -6.5e+129) || !(NdChar <= 7e+53))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -6.5e+129) || ~((NdChar <= 7e+53)))
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	else
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -6.5e+129], N[Not[LessEqual[NdChar, 7e+53]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -6.4999999999999995e129 or 7.00000000000000038e53 < 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 78.3%

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

   6. Taylor expanded in EAccept around 0 64.6%

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

   7. Taylor expanded in Ec around inf 51.9%

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

      1. mul-1-neg 60.0%

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

   9. Simplified 51.9%

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

   if -6.4999999999999995e129 < NdChar < 7.00000000000000038e53

   1. Initial program 100.0%

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

   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 57.9%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6.5 \cdot 10^{+129} \lor \neg \left(NdChar \leq 7 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 57.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}\\ \mathbf{if}\;NdChar \leq -3.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 3.1 \cdot 10^{+53}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
   (if (<= NdChar -3.2e-9)
     (+ (/ NdChar (+ 1.0 t_0)) (* NaChar 0.5))
     (if (<= NdChar 3.1e+53)
       (-
        (/ NdChar 2.0)
        (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
       (- (/ NaChar 2.0) (/ NdChar (- -1.0 t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double tmp;
	if (NdChar <= -3.2e-9) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar * 0.5);
	} else if (NdChar <= 3.1e+53) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - t_0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(((edonor + (mu + (vef - ec))) / kbt))
    if (ndchar <= (-3.2d-9)) then
        tmp = (ndchar / (1.0d0 + t_0)) + (nachar * 0.5d0)
    else if (ndchar <= 3.1d+53) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else
        tmp = (nachar / 2.0d0) - (ndchar / ((-1.0d0) - t_0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double tmp;
	if (NdChar <= -3.2e-9) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar * 0.5);
	} else if (NdChar <= 3.1e+53) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))
	tmp = 0
	if NdChar <= -3.2e-9:
		tmp = (NdChar / (1.0 + t_0)) + (NaChar * 0.5)
	elif NdChar <= 3.1e+53:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	else:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))
	tmp = 0.0
	if (NdChar <= -3.2e-9)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) + Float64(NaChar * 0.5));
	elseif (NdChar <= 3.1e+53)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 - t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	tmp = 0.0;
	if (NdChar <= -3.2e-9)
		tmp = (NdChar / (1.0 + t_0)) + (NaChar * 0.5);
	elseif (NdChar <= 3.1e+53)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	else
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[NdChar, -3.2e-9], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.1e+53], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -3.20000000000000012e-9

   1. Initial program 100.0%

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

   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 74.3%

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

   6. Taylor expanded in EAccept around 0 62.4%

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

   7. Taylor expanded in EAccept around 0 58.3%

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

   if -3.20000000000000012e-9 < NdChar < 3.10000000000000019e53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.2%

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

   if 3.10000000000000019e53 < 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 KbT around inf 55.1%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 3.1 \cdot 10^{+53}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{if}\;Ec \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ec \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (/ EAccept KbT) 2.0))))
   (if (<= Ec -1.9e-61)
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
     (if (<= Ec 2e+69)
       (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ EAccept KbT)))))
       (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / ((EAccept / KbT) + 2.0);
	double tmp;
	if (Ec <= -1.9e-61) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (Ec <= 2e+69) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	} else {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / ((eaccept / kbt) + 2.0d0)
    if (ec <= (-1.9d-61)) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (ec <= 2d+69) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    else
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / ((EAccept / KbT) + 2.0);
	double tmp;
	if (Ec <= -1.9e-61) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (Ec <= 2e+69) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / ((EAccept / KbT) + 2.0)
	tmp = 0
	if Ec <= -1.9e-61:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif Ec <= 2e+69:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	else:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0))
	tmp = 0.0
	if (Ec <= -1.9e-61)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (Ec <= 2e+69)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / ((EAccept / KbT) + 2.0);
	tmp = 0.0;
	if (Ec <= -1.9e-61)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (Ec <= 2e+69)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	else
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ec, -1.9e-61], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 2e+69], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if Ec < -1.8999999999999999e-61

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 73.4%

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

   6. Taylor expanded in EAccept around 0 52.4%

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

   7. Taylor expanded in EDonor around inf 44.0%

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

   if -1.8999999999999999e-61 < Ec < 2.0000000000000001e69

   1. Initial program 100.0%

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

   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 57.6%

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

   6. Taylor expanded in EAccept around inf 41.5%

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

   if 2.0000000000000001e69 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 70.2%

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

   6. Taylor expanded in EAccept around 0 60.4%

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

   7. Taylor expanded in Ec around inf 58.7%

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

      1. mul-1-neg 81.5%

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

   9. Simplified 58.7%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ec \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 37.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq -3.1 \cdot 10^{-246}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;EAccept \leq 1.06 \cdot 10^{+133}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept -3.1e-246)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (if (<= EAccept 1.06e+133)
     (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ mu (- KbT))))))
     (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ EAccept KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= -3.1e-246) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (EAccept <= 1.06e+133) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((mu / -KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= (-3.1d-246)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else if (eaccept <= 1.06d+133) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((mu / -kbt))))
    else
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= -3.1e-246) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (EAccept <= 1.06e+133) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((mu / -KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= -3.1e-246:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	elif EAccept <= 1.06e+133:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((mu / -KbT))))
	else:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= -3.1e-246)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	elseif (EAccept <= 1.06e+133)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(mu / Float64(-KbT))))));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= -3.1e-246)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	elseif (EAccept <= 1.06e+133)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((mu / -KbT))));
	else
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, -3.1e-246], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.06e+133], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < -3.1e-246

   1. Initial program 100.0%

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

   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 50.9%

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

   6. Taylor expanded in Ev around inf 35.0%

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

   if -3.1e-246 < EAccept < 1.06e133

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 49.4%

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

   6. Taylor expanded in mu around inf 37.5%

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

      1. associate-*r/ 37.5%

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

      2. mul-1-neg 37.5%

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

   8. Simplified 37.5%

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

   if 1.06e133 < 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 KbT around inf 59.0%

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

   6. Taylor expanded in EAccept around inf 54.3%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -3.1 \cdot 10^{-246}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;EAccept \leq 1.06 \cdot 10^{+133}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 37.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 8.5 \cdot 10^{-282}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;EAccept \leq 6.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 8.5e-282)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (if (<= EAccept 6.2e-20)
     (- (/ NaChar 2.0) (/ NdChar (- -1.0 (exp (/ mu KbT)))))
     (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ EAccept KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 8.5e-282) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (EAccept <= 6.2e-20) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - exp((mu / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= 8.5d-282) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else if (eaccept <= 6.2d-20) then
        tmp = (nachar / 2.0d0) - (ndchar / ((-1.0d0) - exp((mu / kbt))))
    else
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 8.5e-282) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (EAccept <= 6.2e-20) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - Math.exp((mu / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 8.5e-282:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	elif EAccept <= 6.2e-20:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - math.exp((mu / KbT))))
	else:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 8.5e-282)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	elseif (EAccept <= 6.2e-20)
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 - exp(Float64(mu / KbT)))));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 8.5e-282)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	elseif (EAccept <= 6.2e-20)
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - exp((mu / KbT))));
	else
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 8.5e-282], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 6.2e-20], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 8.499999999999999e-282

   1. Initial program 100.0%

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

   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 50.4%

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

   6. Taylor expanded in Ev around inf 35.8%

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

   if 8.499999999999999e-282 < EAccept < 6.19999999999999999e-20

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 72.4%

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

   6. Taylor expanded in KbT around inf 42.2%

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

   if 6.19999999999999999e-20 < 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 KbT around inf 57.6%

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

   6. Taylor expanded in EAccept around inf 47.0%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 8.5 \cdot 10^{-282}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;EAccept \leq 6.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 36.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ec -3.8e-59)
   (+
    (/ NaChar (+ (/ EAccept KbT) 2.0))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
   (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ EAccept KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -3.8e-59) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ec <= (-3.8d-59)) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -3.8e-59) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ec <= -3.8e-59:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ec <= -3.8e-59)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ec <= -3.8e-59)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ec, -3.8e-59], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < -3.79999999999999983e-59

   1. Initial program 100.0%

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

   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 73.4%

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

   6. Taylor expanded in EAccept around 0 52.4%

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

   7. Taylor expanded in EDonor around inf 44.0%

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

   if -3.79999999999999983e-59 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.1%

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

   6. Taylor expanded in EAccept around inf 40.7%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 37.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -1.55 \cdot 10^{+93}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -1.55e+93)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ EAccept KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -1.55e+93) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-1.55d+93)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -1.55e+93) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -1.55e+93:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -1.55e+93)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -1.55e+93)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -1.55e+93], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -1.5500000000000001e93

   1. Initial program 100.0%

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

   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 44.7%

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

   6. Taylor expanded in Ev around inf 38.3%

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

   if -1.5500000000000001e93 < Ev

   1. Initial program 100.0%

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

   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 53.4%

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

   6. Taylor expanded in EAccept around inf 40.8%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.55 \cdot 10^{+93}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 36.2% accurate, 2.1× speedup

Math

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ EAccept KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / 2.0) - (NaChar / (-1.0 - exp((EAccept / 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 / 2.0d0) - (nachar / ((-1.0d0) - exp((eaccept / 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 / 2.0) - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / 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. 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 39.3%

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

7. Final simplification 39.3%

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

Alternative 32: 28.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq -1.3 \cdot 10^{-189}:\\ \;\;\;\;\frac{NdChar}{2 + EDonor \cdot \left(\frac{1}{KbT} - \frac{\frac{Ec}{KbT} - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{EDonor}\right)} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ec -1.3e-189)
   (+
    (/
     NdChar
     (+
      2.0
      (*
       EDonor
       (- (/ 1.0 KbT) (/ (- (/ Ec KbT) (+ (/ Vef KbT) (/ mu KbT))) EDonor)))))
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT))))
   (+ (/ NdChar 2.0) (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -1.3e-189) {
		tmp = (NdChar / (2.0 + (EDonor * ((1.0 / KbT) - (((Ec / KbT) - ((Vef / KbT) + (mu / KbT))) / EDonor))))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ec <= (-1.3d-189)) then
        tmp = (ndchar / (2.0d0 + (edonor * ((1.0d0 / kbt) - (((ec / kbt) - ((vef / kbt) + (mu / kbt))) / edonor))))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else
        tmp = (ndchar / 2.0d0) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -1.3e-189) {
		tmp = (NdChar / (2.0 + (EDonor * ((1.0 / KbT) - (((Ec / KbT) - ((Vef / KbT) + (mu / KbT))) / EDonor))))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ec <= -1.3e-189:
		tmp = (NdChar / (2.0 + (EDonor * ((1.0 / KbT) - (((Ec / KbT) - ((Vef / KbT) + (mu / KbT))) / EDonor))))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	else:
		tmp = (NdChar / 2.0) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ec <= -1.3e-189)
		tmp = Float64(Float64(NdChar / Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(Ec / KbT) - Float64(Float64(Vef / KbT) + Float64(mu / KbT))) / EDonor))))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	else
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ec <= -1.3e-189)
		tmp = (NdChar / (2.0 + (EDonor * ((1.0 / KbT) - (((Ec / KbT) - ((Vef / KbT) + (mu / KbT))) / EDonor))))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	else
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ec, -1.3e-189], N[(N[(NdChar / N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(Ec / KbT), $MachinePrecision] - N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < -1.2999999999999999e-189

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.0%

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

      1. associate--l+ 60.0%

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

      2. associate--l+ 60.0%

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

      3. associate--l+ 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in EDonor around -inf 65.5%

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

   9. Taylor expanded in KbT around inf 37.7%

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

   if -1.2999999999999999e-189 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 53.3%

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

   6. Taylor expanded in KbT around inf 25.9%

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

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -1.3 \cdot 10^{-189}:\\ \;\;\;\;\frac{NdChar}{2 + EDonor \cdot \left(\frac{1}{KbT} - \frac{\frac{Ec}{KbT} - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{EDonor}\right)} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 27.3% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq -5.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \left(\frac{mu}{KbT} - \frac{Ec}{KbT}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ec -5.5e-188)
   (+
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT)))
    (/
     NdChar
     (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (- (/ mu KbT) (/ Ec KbT)))))))
   (+ (/ NdChar 2.0) (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -5.5e-188) {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / (2.0 + ((EDonor / KbT) + ((Vef / KbT) + ((mu / KbT) - (Ec / KbT))))));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ec <= (-5.5d-188)) then
        tmp = (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt))) + (ndchar / (2.0d0 + ((edonor / kbt) + ((vef / kbt) + ((mu / kbt) - (ec / kbt))))))
    else
        tmp = (ndchar / 2.0d0) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -5.5e-188) {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / (2.0 + ((EDonor / KbT) + ((Vef / KbT) + ((mu / KbT) - (Ec / KbT))))));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ec <= -5.5e-188:
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / (2.0 + ((EDonor / KbT) + ((Vef / KbT) + ((mu / KbT) - (Ec / KbT))))))
	else:
		tmp = (NdChar / 2.0) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ec <= -5.5e-188)
		tmp = Float64(Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))) + Float64(NdChar / Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(Float64(mu / KbT) - Float64(Ec / KbT)))))));
	else
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ec <= -5.5e-188)
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / (2.0 + ((EDonor / KbT) + ((Vef / KbT) + ((mu / KbT) - (Ec / KbT))))));
	else
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ec, -5.5e-188], N[(N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(mu / KbT), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < -5.5000000000000002e-188

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.0%

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

      1. associate--l+ 60.0%

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

      2. associate--l+ 60.0%

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

      3. associate--l+ 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in KbT around inf 36.8%

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

   if -5.5000000000000002e-188 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 53.3%

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

   6. Taylor expanded in KbT around inf 25.9%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -5.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \left(\frac{mu}{KbT} - \frac{Ec}{KbT}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 27.2% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq -5 \cdot 10^{-176}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{\frac{Ec}{KbT} - \left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ec -5e-176)
   (-
    (/ NaChar (+ (/ EAccept KbT) 2.0))
    (/
     NdChar
     (- (/ Ec KbT) (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))))))
   (+ (/ NdChar 2.0) (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -5e-176) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / ((Ec / KbT) - (2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT))))));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ec <= (-5d-176)) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((ec / kbt) - (2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt))))))
    else
        tmp = (ndchar / 2.0d0) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -5e-176) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / ((Ec / KbT) - (2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT))))));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ec <= -5e-176:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / ((Ec / KbT) - (2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT))))))
	else:
		tmp = (NdChar / 2.0) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ec <= -5e-176)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(Float64(Ec / KbT) - Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))))));
	else
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ec <= -5e-176)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / ((Ec / KbT) - (2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT))))));
	else
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ec, -5e-176], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(N[(Ec / KbT), $MachinePrecision] - N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < -5e-176

   1. Initial program 100.0%

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

   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 71.0%

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

   6. Taylor expanded in EAccept around 0 51.5%

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

   7. Taylor expanded in KbT around inf 34.1%

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

   if -5e-176 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 53.7%

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

   6. Taylor expanded in KbT around inf 26.5%

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

4. Final simplification 29.5%

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

Alternative 35: 27.6% accurate, 32.7× speedup

Math

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

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / 2.0) + (NaChar / 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 = (ndchar / 2.0d0) + (nachar / 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 (NdChar / 2.0) + (NaChar / 2.0);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / 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 KbT around inf 28.0%

   \[\leadsto \frac{NdChar}{2} + \frac{NaChar}{\color{blue}{2}} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024103 
(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))))))