Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 33.9s

Alternatives: 21

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -1.612487490106591e-45
  2. Ec = 5.5261073071940405e+296
  3. Vef = -7.556933177572977e+26
  4. EDonor = -9.758936286294145e+254
  5. mu = 3.265439872445571e+51
  6. KbT = 0.036204497301283285
  7. NaChar = -1.5119642002744746e-46
  8. Ev = -1.2869651308707446e-241
  9. EAccept = 4.7281821564301035e-147

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: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ t_2 := t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;Ec \leq -4.5 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Ec \leq -1.7 \cdot 10^{-49}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ec \leq 4.6 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Ec \leq 3 \cdot 10^{-14}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;Ec \leq 2.9 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))))
        (t_2 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= Ec -4.5e+157)
     t_1
     (if (<= Ec -1.7e-49)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
       (if (<= Ec 4.6e-97)
         t_2
         (if (<= Ec 3e-14)
           (+
            (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
            (/
             NaChar
             (-
              1.0
              (*
               mu
               (+
                (/ (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) mu)
                (/ 1.0 KbT))))))
           (if (<= Ec 2.9e+119) t_2 t_1)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((Ec / -KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (Ec <= -4.5e+157) {
		tmp = t_1;
	} else if (Ec <= -1.7e-49) {
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	} else if (Ec <= 4.6e-97) {
		tmp = t_2;
	} else if (Ec <= 3e-14) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))));
	} else if (Ec <= 2.9e+119) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((ec / -kbt))))
    t_2 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (ec <= (-4.5d+157)) then
        tmp = t_1
    else if (ec <= (-1.7d-49)) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    else if (ec <= 4.6d-97) then
        tmp = t_2
    else if (ec <= 3d-14) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / (1.0d0 - (mu * ((((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) / mu) + (1.0d0 / kbt)))))
    else if (ec <= 2.9d+119) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((Ec / -KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (Ec <= -4.5e+157) {
		tmp = t_1;
	} else if (Ec <= -1.7e-49) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	} else if (Ec <= 4.6e-97) {
		tmp = t_2;
	} else if (Ec <= 3e-14) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))));
	} else if (Ec <= 2.9e+119) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((Ec / -KbT))))
	t_2 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if Ec <= -4.5e+157:
		tmp = t_1
	elif Ec <= -1.7e-49:
		tmp = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	elif Ec <= 4.6e-97:
		tmp = t_2
	elif Ec <= 3e-14:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))))
	elif Ec <= 2.9e+119:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))))
	t_2 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (Ec <= -4.5e+157)
		tmp = t_1;
	elseif (Ec <= -1.7e-49)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	elseif (Ec <= 4.6e-97)
		tmp = t_2;
	elseif (Ec <= 3e-14)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 - Float64(mu * Float64(Float64(Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) / mu) + Float64(1.0 / KbT))))));
	elseif (Ec <= 2.9e+119)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((Ec / -KbT))));
	t_2 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (Ec <= -4.5e+157)
		tmp = t_1;
	elseif (Ec <= -1.7e-49)
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	elseif (Ec <= 4.6e-97)
		tmp = t_2;
	elseif (Ec <= 3e-14)
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))));
	elseif (Ec <= 2.9e+119)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(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[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ec, -4.5e+157], t$95$1, If[LessEqual[Ec, -1.7e-49], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 4.6e-97], t$95$2, If[LessEqual[Ec, 3e-14], 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[(mu * N[(N[(N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 2.9e+119], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ec < -4.49999999999999985e157 or 2.90000000000000007e119 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 93.3%

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

      1. associate-*r/ 43.1%

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

      2. mul-1-neg 43.1%

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

   7. Simplified 93.3%

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

   if -4.49999999999999985e157 < Ec < -1.70000000000000002e-49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 81.3%

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

   if -1.70000000000000002e-49 < Ec < 4.59999999999999988e-97 or 2.9999999999999998e-14 < Ec < 2.90000000000000007e119

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 82.0%

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

   if 4.59999999999999988e-97 < Ec < 2.9999999999999998e-14

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 55.5%

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

   6. Taylor expanded in mu around -inf 75.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -4.5 \cdot 10^{+157}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;Ec \leq -1.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ec \leq 4.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ec \leq 3 \cdot 10^{-14}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;Ec \leq 2.9 \cdot 10^{+119}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{Vef}{KbT} + \frac{Ev}{KbT}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -6.5 \cdot 10^{+202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -9.5 \cdot 10^{-130}:\\ \;\;\;\;t\_3 - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right)\right)}\\ \mathbf{elif}\;mu \leq -6.5 \cdot 10^{-225}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.1 \cdot 10^{-196}:\\ \;\;\;\;t\_3 + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + t\_0\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 3.2 \cdot 10^{-110}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.04 \cdot 10^{+154}:\\ \;\;\;\;t\_3 + \frac{NaChar}{1 + EAccept \cdot \left(\frac{1}{KbT} + \frac{\left(1 + t\_0\right) - \frac{mu}{KbT}}{EAccept}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ Vef KbT) (/ Ev KbT)))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT))))))
        (t_3 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= mu -6.5e+202)
     t_2
     (if (<= mu -9.5e-130)
       (-
        t_3
        (/
         NaChar
         (+
          -1.0
          (+
           (/ mu KbT)
           (+
            -1.0
            (*
             EAccept
             (-
              (/ -1.0 KbT)
              (+ (/ Vef (* KbT EAccept)) (/ Ev (* KbT EAccept))))))))))
       (if (<= mu -6.5e-225)
         (+
          t_1
          (/
           NdChar
           (+
            1.0
            (-
             (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
             (/ Ec KbT)))))
         (if (<= mu 1.1e-196)
           (+
            t_3
            (/
             NaChar
             (-
              1.0
              (* mu (+ (/ (- -1.0 (+ (/ EAccept KbT) t_0)) mu) (/ 1.0 KbT))))))
           (if (<= mu 3.2e-110)
             (+ t_1 (/ NdChar (+ 1.0 (+ 1.0 (/ Vef KbT)))))
             (if (<= mu 1.04e+154)
               (+
                t_3
                (/
                 NaChar
                 (+
                  1.0
                  (*
                   EAccept
                   (+ (/ 1.0 KbT) (/ (- (+ 1.0 t_0) (/ mu KbT)) EAccept))))))
               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 = (Vef / KbT) + (Ev / KbT);
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	double t_3 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (mu <= -6.5e+202) {
		tmp = t_2;
	} else if (mu <= -9.5e-130) {
		tmp = t_3 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	} else if (mu <= -6.5e-225) {
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))));
	} else if (mu <= 1.1e-196) {
		tmp = t_3 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + t_0)) / mu) + (1.0 / KbT)))));
	} else if (mu <= 3.2e-110) {
		tmp = t_1 + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	} else if (mu <= 1.04e+154) {
		tmp = t_3 + (NaChar / (1.0 + (EAccept * ((1.0 / KbT) + (((1.0 + t_0) - (mu / KbT)) / EAccept)))));
	} 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) :: t_3
    real(8) :: tmp
    t_0 = (vef / kbt) + (ev / kbt)
    t_1 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    t_2 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    t_3 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (mu <= (-6.5d+202)) then
        tmp = t_2
    else if (mu <= (-9.5d-130)) then
        tmp = t_3 - (nachar / ((-1.0d0) + ((mu / kbt) + ((-1.0d0) + (eaccept * (((-1.0d0) / kbt) - ((vef / (kbt * eaccept)) + (ev / (kbt * eaccept)))))))))
    else if (mu <= (-6.5d-225)) then
        tmp = t_1 + (ndchar / (1.0d0 + ((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt))))
    else if (mu <= 1.1d-196) then
        tmp = t_3 + (nachar / (1.0d0 - (mu * ((((-1.0d0) - ((eaccept / kbt) + t_0)) / mu) + (1.0d0 / kbt)))))
    else if (mu <= 3.2d-110) then
        tmp = t_1 + (ndchar / (1.0d0 + (1.0d0 + (vef / kbt))))
    else if (mu <= 1.04d+154) then
        tmp = t_3 + (nachar / (1.0d0 + (eaccept * ((1.0d0 / kbt) + (((1.0d0 + t_0) - (mu / kbt)) / eaccept)))))
    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 = (Vef / KbT) + (Ev / KbT);
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	double t_3 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (mu <= -6.5e+202) {
		tmp = t_2;
	} else if (mu <= -9.5e-130) {
		tmp = t_3 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	} else if (mu <= -6.5e-225) {
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))));
	} else if (mu <= 1.1e-196) {
		tmp = t_3 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + t_0)) / mu) + (1.0 / KbT)))));
	} else if (mu <= 3.2e-110) {
		tmp = t_1 + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	} else if (mu <= 1.04e+154) {
		tmp = t_3 + (NaChar / (1.0 + (EAccept * ((1.0 / KbT) + (((1.0 + t_0) - (mu / KbT)) / EAccept)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (Vef / KbT) + (Ev / KbT)
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	t_2 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	t_3 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if mu <= -6.5e+202:
		tmp = t_2
	elif mu <= -9.5e-130:
		tmp = t_3 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))))
	elif mu <= -6.5e-225:
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))))
	elif mu <= 1.1e-196:
		tmp = t_3 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + t_0)) / mu) + (1.0 / KbT)))))
	elif mu <= 3.2e-110:
		tmp = t_1 + (NdChar / (1.0 + (1.0 + (Vef / KbT))))
	elif mu <= 1.04e+154:
		tmp = t_3 + (NaChar / (1.0 + (EAccept * ((1.0 / KbT) + (((1.0 + t_0) - (mu / KbT)) / EAccept)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(Vef / KbT) + Float64(Ev / KbT))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))))
	t_3 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (mu <= -6.5e+202)
		tmp = t_2;
	elseif (mu <= -9.5e-130)
		tmp = Float64(t_3 - Float64(NaChar / Float64(-1.0 + Float64(Float64(mu / KbT) + Float64(-1.0 + Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(KbT * EAccept)) + Float64(Ev / Float64(KbT * EAccept))))))))));
	elseif (mu <= -6.5e-225)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT)))));
	elseif (mu <= 1.1e-196)
		tmp = Float64(t_3 + Float64(NaChar / Float64(1.0 - Float64(mu * Float64(Float64(Float64(-1.0 - Float64(Float64(EAccept / KbT) + t_0)) / mu) + Float64(1.0 / KbT))))));
	elseif (mu <= 3.2e-110)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(Vef / KbT)))));
	elseif (mu <= 1.04e+154)
		tmp = Float64(t_3 + Float64(NaChar / Float64(1.0 + Float64(EAccept * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(1.0 + t_0) - Float64(mu / KbT)) / EAccept))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (Vef / KbT) + (Ev / KbT);
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	t_3 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (mu <= -6.5e+202)
		tmp = t_2;
	elseif (mu <= -9.5e-130)
		tmp = t_3 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	elseif (mu <= -6.5e-225)
		tmp = t_1 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))));
	elseif (mu <= 1.1e-196)
		tmp = t_3 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + t_0)) / mu) + (1.0 / KbT)))));
	elseif (mu <= 3.2e-110)
		tmp = t_1 + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	elseif (mu <= 1.04e+154)
		tmp = t_3 + (NaChar / (1.0 + (EAccept * ((1.0 / KbT) + (((1.0 + t_0) - (mu / KbT)) / EAccept)))));
	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[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $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[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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[mu, -6.5e+202], t$95$2, If[LessEqual[mu, -9.5e-130], N[(t$95$3 - N[(NaChar / N[(-1.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 + N[(EAccept * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(Vef / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision] + N[(Ev / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -6.5e-225], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.1e-196], N[(t$95$3 + N[(NaChar / N[(1.0 - N[(mu * N[(N[(N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 3.2e-110], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.04e+154], N[(t$95$3 + N[(NaChar / N[(1.0 + N[(EAccept * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(1.0 + t$95$0), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision] / EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if mu < -6.4999999999999996e202 or 1.04e154 < 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 98.0%

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

   6. Taylor expanded in mu around inf 93.3%

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

      1. neg-mul-1 93.3%

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

      2. distribute-neg-frac2 93.3%

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

   8. Simplified 93.3%

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

   if -6.4999999999999996e202 < mu < -9.49999999999999962e-130

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.8%

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

   6. Taylor expanded in EAccept around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. *-commutative 76.1%

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

   8. Simplified 76.1%

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

   if -9.49999999999999962e-130 < mu < -6.5000000000000005e-225

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 86.9%

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

   if -6.5000000000000005e-225 < mu < 1.10000000000000007e-196

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.7%

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

   6. Taylor expanded in mu around -inf 73.8%

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

   if 1.10000000000000007e-196 < mu < 3.20000000000000028e-110

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 88.9%

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

   6. Taylor expanded in Vef around 0 83.2%

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

   if 3.20000000000000028e-110 < mu < 1.04e154

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.8%

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

   6. Taylor expanded in EAccept around -inf 69.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -6.5 \cdot 10^{+202}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -9.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right)\right)}\\ \mathbf{elif}\;mu \leq -6.5 \cdot 10^{-225}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.1 \cdot 10^{-196}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 3.2 \cdot 10^{-110}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.04 \cdot 10^{+154}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + EAccept \cdot \left(\frac{1}{KbT} + \frac{\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}{EAccept}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -4 \cdot 10^{-10}:\\ \;\;\;\;t\_1 - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -1.16 \cdot 10^{-290}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 4.2 \cdot 10^{-167}:\\ \;\;\;\;t\_1 + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 4.3 \cdot 10^{+23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 2.05 \cdot 10^{+55}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= KbT -4e-10)
     (-
      t_1
      (/
       NaChar
       (+
        -1.0
        (+
         (/ mu KbT)
         (+
          -1.0
          (/ (* EAccept (- -1.0 (+ (/ Ev EAccept) (/ Vef EAccept)))) KbT))))))
     (if (<= KbT -1.16e-290)
       t_0
       (if (<= KbT 4.2e-167)
         (+
          t_1
          (/
           (* KbT NaChar)
           (- (* Ev (- 1.0 (* EAccept (/ (- -1.0 (/ Vef EAccept)) Ev)))) mu)))
         (if (<= KbT 4.3e+23)
           t_0
           (if (<= KbT 2.05e+55)
             (+
              t_1
              (/
               NaChar
               (-
                1.0
                (*
                 mu
                 (+
                  (/
                   (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
                   mu)
                  (/ 1.0 KbT))))))
             (+
              (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
              (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (KbT <= -4e-10) {
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -1.16e-290) {
		tmp = t_0;
	} else if (KbT <= 4.2e-167) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 4.3e+23) {
		tmp = t_0;
	} else if (KbT <= 2.05e+55) {
		tmp = t_1 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))));
	} else {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (kbt <= (-4d-10)) then
        tmp = t_1 - (nachar / ((-1.0d0) + ((mu / kbt) + ((-1.0d0) + ((eaccept * ((-1.0d0) - ((ev / eaccept) + (vef / eaccept)))) / kbt)))))
    else if (kbt <= (-1.16d-290)) then
        tmp = t_0
    else if (kbt <= 4.2d-167) then
        tmp = t_1 + ((kbt * nachar) / ((ev * (1.0d0 - (eaccept * (((-1.0d0) - (vef / eaccept)) / ev)))) - mu))
    else if (kbt <= 4.3d+23) then
        tmp = t_0
    else if (kbt <= 2.05d+55) then
        tmp = t_1 + (nachar / (1.0d0 - (mu * ((((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) / mu) + (1.0d0 / kbt)))))
    else
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (KbT <= -4e-10) {
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -1.16e-290) {
		tmp = t_0;
	} else if (KbT <= 4.2e-167) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 4.3e+23) {
		tmp = t_0;
	} else if (KbT <= 2.05e+55) {
		tmp = t_1 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if KbT <= -4e-10:
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))))
	elif KbT <= -1.16e-290:
		tmp = t_0
	elif KbT <= 4.2e-167:
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu))
	elif KbT <= 4.3e+23:
		tmp = t_0
	elif KbT <= 2.05e+55:
		tmp = t_1 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))))
	else:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (KbT <= -4e-10)
		tmp = Float64(t_1 - Float64(NaChar / Float64(-1.0 + Float64(Float64(mu / KbT) + Float64(-1.0 + Float64(Float64(EAccept * Float64(-1.0 - Float64(Float64(Ev / EAccept) + Float64(Vef / EAccept)))) / KbT))))));
	elseif (KbT <= -1.16e-290)
		tmp = t_0;
	elseif (KbT <= 4.2e-167)
		tmp = Float64(t_1 + Float64(Float64(KbT * NaChar) / Float64(Float64(Ev * Float64(1.0 - Float64(EAccept * Float64(Float64(-1.0 - Float64(Vef / EAccept)) / Ev)))) - mu)));
	elseif (KbT <= 4.3e+23)
		tmp = t_0;
	elseif (KbT <= 2.05e+55)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 - Float64(mu * Float64(Float64(Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) / mu) + Float64(1.0 / KbT))))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (KbT <= -4e-10)
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	elseif (KbT <= -1.16e-290)
		tmp = t_0;
	elseif (KbT <= 4.2e-167)
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	elseif (KbT <= 4.3e+23)
		tmp = t_0;
	elseif (KbT <= 2.05e+55)
		tmp = t_1 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))));
	else
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -4e-10], N[(t$95$1 - N[(NaChar / N[(-1.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 + N[(N[(EAccept * N[(-1.0 - N[(N[(Ev / EAccept), $MachinePrecision] + N[(Vef / EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -1.16e-290], t$95$0, If[LessEqual[KbT, 4.2e-167], N[(t$95$1 + N[(N[(KbT * NaChar), $MachinePrecision] / N[(N[(Ev * N[(1.0 - N[(EAccept * N[(N[(-1.0 - N[(Vef / EAccept), $MachinePrecision]), $MachinePrecision] / Ev), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4.3e+23], t$95$0, If[LessEqual[KbT, 2.05e+55], N[(t$95$1 + N[(NaChar / N[(1.0 - N[(mu * N[(N[(N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if KbT < -4.00000000000000015e-10

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.4%

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

   6. Taylor expanded in EAccept around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

   8. Simplified 71.4%

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

   9. Taylor expanded in KbT around 0 70.1%

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

   if -4.00000000000000015e-10 < KbT < -1.16000000000000001e-290 or 4.20000000000000035e-167 < KbT < 4.2999999999999999e23

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.7%

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

      1. *-commutative 31.7%

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

   7. Simplified 31.7%

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

   8. Taylor expanded in NdChar around 0 76.6%

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

   if -1.16000000000000001e-290 < KbT < 4.20000000000000035e-167

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 33.6%

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

   6. Taylor expanded in EAccept around inf 52.3%

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

      1. *-commutative 52.3%

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

      2. *-commutative 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in KbT around 0 64.9%

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

       1. +-commutative 64.9%

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

       2. +-commutative 64.9%

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

       3. associate-+l+ 64.9%

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

   11. Simplified 64.9%

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

   12. Taylor expanded in Ev around inf 71.2%

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

       1. associate-/l* 74.2%

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

   14. Simplified 74.2%

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

   if 4.2999999999999999e23 < KbT < 2.04999999999999991e55

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 88.8%

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

   6. Taylor expanded in mu around -inf 99.8%

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

   if 2.04999999999999991e55 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 85.0%

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

      1. associate-*r/ 53.2%

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

      2. mul-1-neg 53.2%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in EAccept around 0 81.8%

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

      1. +-commutative 81.8%

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

   10. Simplified 81.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4 \cdot 10^{-10}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -1.16 \cdot 10^{-290}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 4.2 \cdot 10^{-167}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 4.3 \cdot 10^{+23}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.05 \cdot 10^{+55}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -6.5 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -4.7 \cdot 10^{+114}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq -3.5 \cdot 10^{+55} \lor \neg \left(mu \leq 3.2 \cdot 10^{+59}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))))
   (if (<= mu -6.5e+202)
     t_1
     (if (<= mu -4.7e+114)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
        (/
         NaChar
         (-
          (- 2.0 (* EAccept (- (/ -1.0 KbT) (/ Vef (* KbT EAccept)))))
          (/ mu KbT))))
       (if (or (<= mu -3.5e+55) (not (<= mu 3.2e+59)))
         t_1
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	double tmp;
	if (mu <= -6.5e+202) {
		tmp = t_1;
	} else if (mu <= -4.7e+114) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else if ((mu <= -3.5e+55) || !(mu <= 3.2e+59)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: 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 <= (-6.5d+202)) then
        tmp = t_1
    else if (mu <= (-4.7d+114)) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / ((2.0d0 - (eaccept * (((-1.0d0) / kbt) - (vef / (kbt * eaccept))))) - (mu / kbt)))
    else if ((mu <= (-3.5d+55)) .or. (.not. (mu <= 3.2d+59))) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double tmp;
	if (mu <= -6.5e+202) {
		tmp = t_1;
	} else if (mu <= -4.7e+114) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else if ((mu <= -3.5e+55) || !(mu <= 3.2e+59)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	tmp = 0
	if mu <= -6.5e+202:
		tmp = t_1
	elif mu <= -4.7e+114:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)))
	elif (mu <= -3.5e+55) or not (mu <= 3.2e+59):
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	tmp = 0.0
	if (mu <= -6.5e+202)
		tmp = t_1;
	elseif (mu <= -4.7e+114)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(2.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Vef / Float64(KbT * EAccept))))) - Float64(mu / KbT))));
	elseif ((mu <= -3.5e+55) || !(mu <= 3.2e+59))
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	tmp = 0.0;
	if (mu <= -6.5e+202)
		tmp = t_1;
	elseif (mu <= -4.7e+114)
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	elseif ((mu <= -3.5e+55) || ~((mu <= 3.2e+59)))
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(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, -6.5e+202], t$95$1, If[LessEqual[mu, -4.7e+114], 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[(2.0 - N[(EAccept * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(Vef / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[mu, -3.5e+55], N[Not[LessEqual[mu, 3.2e+59]], $MachinePrecision]], t$95$1, N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -6.4999999999999996e202 or -4.7000000000000001e114 < mu < -3.5000000000000001e55 or 3.19999999999999982e59 < 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 91.4%

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

   if -6.4999999999999996e202 < mu < -4.7000000000000001e114

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.6%

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

   6. Taylor expanded in EAccept around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. *-commutative 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in Ev around 0 84.0%

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

       1. *-commutative 84.0%

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

   11. Simplified 84.0%

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

   if -3.5000000000000001e55 < mu < 3.19999999999999982e59

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 77.0%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -6.5 \cdot 10^{+202}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -4.7 \cdot 10^{+114}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq -3.5 \cdot 10^{+55} \lor \neg \left(mu \leq 3.2 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{if}\;mu \leq -6.8 \cdot 10^{+202}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq -2.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right)\right)}\\ \mathbf{elif}\;mu \leq 7.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))))
   (if (<= mu -6.8e+202)
     t_0
     (if (<= mu -2.5e-117)
       (-
        (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
        (/
         NaChar
         (+
          -1.0
          (+
           (/ mu KbT)
           (+
            -1.0
            (*
             EAccept
             (-
              (/ -1.0 KbT)
              (+ (/ Vef (* KbT EAccept)) (/ Ev (* KbT EAccept))))))))))
       (if (<= mu 7.8e+87)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	double tmp;
	if (mu <= -6.8e+202) {
		tmp = t_0;
	} else if (mu <= -2.5e-117) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	} else if (mu <= 7.8e+87) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    if (mu <= (-6.8d+202)) then
        tmp = t_0
    else if (mu <= (-2.5d-117)) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) - (nachar / ((-1.0d0) + ((mu / kbt) + ((-1.0d0) + (eaccept * (((-1.0d0) / kbt) - ((vef / (kbt * eaccept)) + (ev / (kbt * eaccept)))))))))
    else if (mu <= 7.8d+87) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	double tmp;
	if (mu <= -6.8e+202) {
		tmp = t_0;
	} else if (mu <= -2.5e-117) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	} else if (mu <= 7.8e+87) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	tmp = 0
	if mu <= -6.8e+202:
		tmp = t_0
	elif mu <= -2.5e-117:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))))
	elif mu <= 7.8e+87:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))))
	tmp = 0.0
	if (mu <= -6.8e+202)
		tmp = t_0;
	elseif (mu <= -2.5e-117)
		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(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(KbT * EAccept)) + Float64(Ev / Float64(KbT * EAccept))))))))));
	elseif (mu <= 7.8e+87)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	tmp = 0.0;
	if (mu <= -6.8e+202)
		tmp = t_0;
	elseif (mu <= -2.5e-117)
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	elseif (mu <= 7.8e+87)
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -6.8e+202], t$95$0, If[LessEqual[mu, -2.5e-117], 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[(EAccept * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(Vef / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision] + N[(Ev / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 7.8e+87], 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[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -6.8e202 or 7.80000000000000039e87 < 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 91.0%

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

   6. Taylor expanded in mu around inf 84.5%

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

      1. neg-mul-1 84.5%

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

      2. distribute-neg-frac2 84.5%

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

   8. Simplified 84.5%

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

   if -6.8e202 < mu < -2.5e-117

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.9%

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

   6. Taylor expanded in EAccept around inf 76.2%

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

      1. *-commutative 76.2%

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

      2. *-commutative 76.2%

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

   8. Simplified 76.2%

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

   if -2.5e-117 < mu < 7.80000000000000039e87

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 78.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -6.8 \cdot 10^{+202}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -2.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right)\right)}\\ \mathbf{elif}\;mu \leq 7.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.9 \cdot 10^{-9}:\\ \;\;\;\;t\_1 - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -9 \cdot 10^{-292}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 6.3 \cdot 10^{-164}:\\ \;\;\;\;t\_1 + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 2.9 \cdot 10^{+28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 6.6 \cdot 10^{+85}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= KbT -1.9e-9)
     (-
      t_1
      (/
       NaChar
       (+
        -1.0
        (+
         (/ mu KbT)
         (+
          -1.0
          (/ (* EAccept (- -1.0 (+ (/ Ev EAccept) (/ Vef EAccept)))) KbT))))))
     (if (<= KbT -9e-292)
       t_0
       (if (<= KbT 6.3e-164)
         (+
          t_1
          (/
           (* KbT NaChar)
           (- (* Ev (- 1.0 (* EAccept (/ (- -1.0 (/ Vef EAccept)) Ev)))) mu)))
         (if (<= KbT 2.9e+28)
           t_0
           (if (<= KbT 6.6e+85)
             (+
              t_1
              (/
               NaChar
               (-
                1.0
                (*
                 mu
                 (+
                  (/
                   (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
                   mu)
                  (/ 1.0 KbT))))))
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
              (/ NdChar (+ 1.0 (+ 1.0 (/ Vef KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (KbT <= -1.9e-9) {
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -9e-292) {
		tmp = t_0;
	} else if (KbT <= 6.3e-164) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 2.9e+28) {
		tmp = t_0;
	} else if (KbT <= 6.6e+85) {
		tmp = t_1 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (kbt <= (-1.9d-9)) then
        tmp = t_1 - (nachar / ((-1.0d0) + ((mu / kbt) + ((-1.0d0) + ((eaccept * ((-1.0d0) - ((ev / eaccept) + (vef / eaccept)))) / kbt)))))
    else if (kbt <= (-9d-292)) then
        tmp = t_0
    else if (kbt <= 6.3d-164) then
        tmp = t_1 + ((kbt * nachar) / ((ev * (1.0d0 - (eaccept * (((-1.0d0) - (vef / eaccept)) / ev)))) - mu))
    else if (kbt <= 2.9d+28) then
        tmp = t_0
    else if (kbt <= 6.6d+85) then
        tmp = t_1 + (nachar / (1.0d0 - (mu * ((((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) / mu) + (1.0d0 / kbt)))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (1.0d0 + (1.0d0 + (vef / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (KbT <= -1.9e-9) {
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -9e-292) {
		tmp = t_0;
	} else if (KbT <= 6.3e-164) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 2.9e+28) {
		tmp = t_0;
	} else if (KbT <= 6.6e+85) {
		tmp = t_1 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if KbT <= -1.9e-9:
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))))
	elif KbT <= -9e-292:
		tmp = t_0
	elif KbT <= 6.3e-164:
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu))
	elif KbT <= 2.9e+28:
		tmp = t_0
	elif KbT <= 6.6e+85:
		tmp = t_1 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (KbT <= -1.9e-9)
		tmp = Float64(t_1 - Float64(NaChar / Float64(-1.0 + Float64(Float64(mu / KbT) + Float64(-1.0 + Float64(Float64(EAccept * Float64(-1.0 - Float64(Float64(Ev / EAccept) + Float64(Vef / EAccept)))) / KbT))))));
	elseif (KbT <= -9e-292)
		tmp = t_0;
	elseif (KbT <= 6.3e-164)
		tmp = Float64(t_1 + Float64(Float64(KbT * NaChar) / Float64(Float64(Ev * Float64(1.0 - Float64(EAccept * Float64(Float64(-1.0 - Float64(Vef / EAccept)) / Ev)))) - mu)));
	elseif (KbT <= 2.9e+28)
		tmp = t_0;
	elseif (KbT <= 6.6e+85)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 - Float64(mu * Float64(Float64(Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) / mu) + Float64(1.0 / KbT))))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(Vef / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (KbT <= -1.9e-9)
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	elseif (KbT <= -9e-292)
		tmp = t_0;
	elseif (KbT <= 6.3e-164)
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	elseif (KbT <= 2.9e+28)
		tmp = t_0;
	elseif (KbT <= 6.6e+85)
		tmp = t_1 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) / mu) + (1.0 / KbT)))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -1.9e-9], N[(t$95$1 - N[(NaChar / N[(-1.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 + N[(N[(EAccept * N[(-1.0 - N[(N[(Ev / EAccept), $MachinePrecision] + N[(Vef / EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -9e-292], t$95$0, If[LessEqual[KbT, 6.3e-164], N[(t$95$1 + N[(N[(KbT * NaChar), $MachinePrecision] / N[(N[(Ev * N[(1.0 - N[(EAccept * N[(N[(-1.0 - N[(Vef / EAccept), $MachinePrecision]), $MachinePrecision] / Ev), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.9e+28], t$95$0, If[LessEqual[KbT, 6.6e+85], N[(t$95$1 + N[(NaChar / N[(1.0 - N[(mu * N[(N[(N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if KbT < -1.90000000000000006e-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 KbT around inf 71.4%

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

   6. Taylor expanded in EAccept around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

   8. Simplified 71.4%

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

   9. Taylor expanded in KbT around 0 70.1%

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

   if -1.90000000000000006e-9 < KbT < -8.99999999999999913e-292 or 6.30000000000000009e-164 < KbT < 2.9000000000000001e28

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.7%

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

      1. *-commutative 31.7%

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

   7. Simplified 31.7%

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

   8. Taylor expanded in NdChar around 0 76.6%

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

   if -8.99999999999999913e-292 < KbT < 6.30000000000000009e-164

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 33.6%

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

   6. Taylor expanded in EAccept around inf 52.3%

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

      1. *-commutative 52.3%

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

      2. *-commutative 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in KbT around 0 64.9%

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

       1. +-commutative 64.9%

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

       2. +-commutative 64.9%

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

       3. associate-+l+ 64.9%

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

   11. Simplified 64.9%

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

   12. Taylor expanded in Ev around inf 71.2%

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

       1. associate-/l* 74.2%

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

   14. Simplified 74.2%

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

   if 2.9000000000000001e28 < KbT < 6.5999999999999998e85

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 76.9%

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

   6. Taylor expanded in mu around -inf 81.6%

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

   if 6.5999999999999998e85 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 78.7%

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

   6. Taylor expanded in Vef around 0 73.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.9 \cdot 10^{-9}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -9 \cdot 10^{-292}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 6.3 \cdot 10^{-164}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 2.9 \cdot 10^{+28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 6.6 \cdot 10^{+85}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.2 \cdot 10^{-11}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;KbT \leq -8.5 \cdot 10^{-292}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 3.6 \cdot 10^{-166}:\\ \;\;\;\;t\_1 + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.85 \cdot 10^{+86}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= KbT -1.2e-11)
     (+
      t_1
      (/
       NaChar
       (-
        1.0
        (+
         (/ mu KbT)
         (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))))))
     (if (<= KbT -8.5e-292)
       t_0
       (if (<= KbT 3.6e-166)
         (+
          t_1
          (/
           (* KbT NaChar)
           (- (* Ev (- 1.0 (* EAccept (/ (- -1.0 (/ Vef EAccept)) Ev)))) mu)))
         (if (<= KbT 9.5e+26)
           t_0
           (if (<= KbT 1.85e+86)
             (+
              t_1
              (/
               NaChar
               (-
                (- 2.0 (* EAccept (- (/ -1.0 KbT) (/ Vef (* KbT EAccept)))))
                (/ mu KbT))))
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
              (/ NdChar (+ 1.0 (+ 1.0 (/ Vef KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (KbT <= -1.2e-11) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (KbT <= -8.5e-292) {
		tmp = t_0;
	} else if (KbT <= 3.6e-166) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 9.5e+26) {
		tmp = t_0;
	} else if (KbT <= 1.85e+86) {
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (kbt <= (-1.2d-11)) then
        tmp = t_1 + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))))))
    else if (kbt <= (-8.5d-292)) then
        tmp = t_0
    else if (kbt <= 3.6d-166) then
        tmp = t_1 + ((kbt * nachar) / ((ev * (1.0d0 - (eaccept * (((-1.0d0) - (vef / eaccept)) / ev)))) - mu))
    else if (kbt <= 9.5d+26) then
        tmp = t_0
    else if (kbt <= 1.85d+86) then
        tmp = t_1 + (nachar / ((2.0d0 - (eaccept * (((-1.0d0) / kbt) - (vef / (kbt * eaccept))))) - (mu / kbt)))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (1.0d0 + (1.0d0 + (vef / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (KbT <= -1.2e-11) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (KbT <= -8.5e-292) {
		tmp = t_0;
	} else if (KbT <= 3.6e-166) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 9.5e+26) {
		tmp = t_0;
	} else if (KbT <= 1.85e+86) {
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if KbT <= -1.2e-11:
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))))
	elif KbT <= -8.5e-292:
		tmp = t_0
	elif KbT <= 3.6e-166:
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu))
	elif KbT <= 9.5e+26:
		tmp = t_0
	elif KbT <= 1.85e+86:
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (KbT <= -1.2e-11)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 - Float64(Float64(mu / KbT) + Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))))))));
	elseif (KbT <= -8.5e-292)
		tmp = t_0;
	elseif (KbT <= 3.6e-166)
		tmp = Float64(t_1 + Float64(Float64(KbT * NaChar) / Float64(Float64(Ev * Float64(1.0 - Float64(EAccept * Float64(Float64(-1.0 - Float64(Vef / EAccept)) / Ev)))) - mu)));
	elseif (KbT <= 9.5e+26)
		tmp = t_0;
	elseif (KbT <= 1.85e+86)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(2.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Vef / Float64(KbT * EAccept))))) - Float64(mu / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(Vef / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (KbT <= -1.2e-11)
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	elseif (KbT <= -8.5e-292)
		tmp = t_0;
	elseif (KbT <= 3.6e-166)
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	elseif (KbT <= 9.5e+26)
		tmp = t_0;
	elseif (KbT <= 1.85e+86)
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -1.2e-11], N[(t$95$1 + 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[KbT, -8.5e-292], t$95$0, If[LessEqual[KbT, 3.6e-166], N[(t$95$1 + N[(N[(KbT * NaChar), $MachinePrecision] / N[(N[(Ev * N[(1.0 - N[(EAccept * N[(N[(-1.0 - N[(Vef / EAccept), $MachinePrecision]), $MachinePrecision] / Ev), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 9.5e+26], t$95$0, If[LessEqual[KbT, 1.85e+86], N[(t$95$1 + N[(NaChar / N[(N[(2.0 - N[(EAccept * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(Vef / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $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[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if KbT < -1.2000000000000001e-11

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.4%

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

   if -1.2000000000000001e-11 < KbT < -8.50000000000000066e-292 or 3.6000000000000001e-166 < KbT < 9.50000000000000054e26

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.7%

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

      1. *-commutative 31.7%

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

   7. Simplified 31.7%

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

   8. Taylor expanded in NdChar around 0 76.6%

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

   if -8.50000000000000066e-292 < KbT < 3.6000000000000001e-166

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 33.6%

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

   6. Taylor expanded in EAccept around inf 52.3%

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

      1. *-commutative 52.3%

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

      2. *-commutative 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in KbT around 0 64.9%

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

       1. +-commutative 64.9%

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

       2. +-commutative 64.9%

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

       3. associate-+l+ 64.9%

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

   11. Simplified 64.9%

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

   12. Taylor expanded in Ev around inf 71.2%

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

       1. associate-/l* 74.2%

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

   14. Simplified 74.2%

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

   if 9.50000000000000054e26 < KbT < 1.84999999999999996e86

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 76.9%

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

   6. Taylor expanded in EAccept around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. *-commutative 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in Ev around 0 77.5%

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

       1. *-commutative 77.5%

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

   11. Simplified 77.5%

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

   if 1.84999999999999996e86 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 78.7%

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

   6. Taylor expanded in Vef around 0 73.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;KbT \leq -8.5 \cdot 10^{-292}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 3.6 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.85 \cdot 10^{+86}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;t\_1 - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -6.4 \cdot 10^{-291}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 6.6 \cdot 10^{-164}:\\ \;\;\;\;t\_1 + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 2.8 \cdot 10^{+25}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 7.2 \cdot 10^{+85}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= KbT -4.2e-8)
     (-
      t_1
      (/
       NaChar
       (+
        -1.0
        (+
         (/ mu KbT)
         (+
          -1.0
          (/ (* EAccept (- -1.0 (+ (/ Ev EAccept) (/ Vef EAccept)))) KbT))))))
     (if (<= KbT -6.4e-291)
       t_0
       (if (<= KbT 6.6e-164)
         (+
          t_1
          (/
           (* KbT NaChar)
           (- (* Ev (- 1.0 (* EAccept (/ (- -1.0 (/ Vef EAccept)) Ev)))) mu)))
         (if (<= KbT 2.8e+25)
           t_0
           (if (<= KbT 7.2e+85)
             (+
              t_1
              (/
               NaChar
               (-
                (- 2.0 (* EAccept (- (/ -1.0 KbT) (/ Vef (* KbT EAccept)))))
                (/ mu KbT))))
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
              (/ NdChar (+ 1.0 (+ 1.0 (/ Vef KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (KbT <= -4.2e-8) {
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -6.4e-291) {
		tmp = t_0;
	} else if (KbT <= 6.6e-164) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 2.8e+25) {
		tmp = t_0;
	} else if (KbT <= 7.2e+85) {
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (kbt <= (-4.2d-8)) then
        tmp = t_1 - (nachar / ((-1.0d0) + ((mu / kbt) + ((-1.0d0) + ((eaccept * ((-1.0d0) - ((ev / eaccept) + (vef / eaccept)))) / kbt)))))
    else if (kbt <= (-6.4d-291)) then
        tmp = t_0
    else if (kbt <= 6.6d-164) then
        tmp = t_1 + ((kbt * nachar) / ((ev * (1.0d0 - (eaccept * (((-1.0d0) - (vef / eaccept)) / ev)))) - mu))
    else if (kbt <= 2.8d+25) then
        tmp = t_0
    else if (kbt <= 7.2d+85) then
        tmp = t_1 + (nachar / ((2.0d0 - (eaccept * (((-1.0d0) / kbt) - (vef / (kbt * eaccept))))) - (mu / kbt)))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (1.0d0 + (1.0d0 + (vef / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (KbT <= -4.2e-8) {
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -6.4e-291) {
		tmp = t_0;
	} else if (KbT <= 6.6e-164) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 2.8e+25) {
		tmp = t_0;
	} else if (KbT <= 7.2e+85) {
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if KbT <= -4.2e-8:
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))))
	elif KbT <= -6.4e-291:
		tmp = t_0
	elif KbT <= 6.6e-164:
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu))
	elif KbT <= 2.8e+25:
		tmp = t_0
	elif KbT <= 7.2e+85:
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (KbT <= -4.2e-8)
		tmp = Float64(t_1 - Float64(NaChar / Float64(-1.0 + Float64(Float64(mu / KbT) + Float64(-1.0 + Float64(Float64(EAccept * Float64(-1.0 - Float64(Float64(Ev / EAccept) + Float64(Vef / EAccept)))) / KbT))))));
	elseif (KbT <= -6.4e-291)
		tmp = t_0;
	elseif (KbT <= 6.6e-164)
		tmp = Float64(t_1 + Float64(Float64(KbT * NaChar) / Float64(Float64(Ev * Float64(1.0 - Float64(EAccept * Float64(Float64(-1.0 - Float64(Vef / EAccept)) / Ev)))) - mu)));
	elseif (KbT <= 2.8e+25)
		tmp = t_0;
	elseif (KbT <= 7.2e+85)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(2.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Vef / Float64(KbT * EAccept))))) - Float64(mu / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(Vef / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (KbT <= -4.2e-8)
		tmp = t_1 - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	elseif (KbT <= -6.4e-291)
		tmp = t_0;
	elseif (KbT <= 6.6e-164)
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	elseif (KbT <= 2.8e+25)
		tmp = t_0;
	elseif (KbT <= 7.2e+85)
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -4.2e-8], N[(t$95$1 - N[(NaChar / N[(-1.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 + N[(N[(EAccept * N[(-1.0 - N[(N[(Ev / EAccept), $MachinePrecision] + N[(Vef / EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -6.4e-291], t$95$0, If[LessEqual[KbT, 6.6e-164], N[(t$95$1 + N[(N[(KbT * NaChar), $MachinePrecision] / N[(N[(Ev * N[(1.0 - N[(EAccept * N[(N[(-1.0 - N[(Vef / EAccept), $MachinePrecision]), $MachinePrecision] / Ev), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.8e+25], t$95$0, If[LessEqual[KbT, 7.2e+85], N[(t$95$1 + N[(NaChar / N[(N[(2.0 - N[(EAccept * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(Vef / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $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[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if KbT < -4.19999999999999989e-8

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.4%

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

   6. Taylor expanded in EAccept around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

   8. Simplified 71.4%

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

   9. Taylor expanded in KbT around 0 70.1%

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

   if -4.19999999999999989e-8 < KbT < -6.4000000000000003e-291 or 6.6e-164 < KbT < 2.8000000000000002e25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.7%

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

      1. *-commutative 31.7%

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

   7. Simplified 31.7%

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

   8. Taylor expanded in NdChar around 0 76.6%

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

   if -6.4000000000000003e-291 < KbT < 6.6e-164

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 33.6%

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

   6. Taylor expanded in EAccept around inf 52.3%

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

      1. *-commutative 52.3%

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

      2. *-commutative 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in KbT around 0 64.9%

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

       1. +-commutative 64.9%

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

       2. +-commutative 64.9%

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

       3. associate-+l+ 64.9%

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

   11. Simplified 64.9%

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

   12. Taylor expanded in Ev around inf 71.2%

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

       1. associate-/l* 74.2%

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

   14. Simplified 74.2%

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

   if 2.8000000000000002e25 < KbT < 7.1999999999999996e85

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 76.9%

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

   6. Taylor expanded in EAccept around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. *-commutative 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in Ev around 0 77.5%

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

       1. *-commutative 77.5%

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

   11. Simplified 77.5%

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

   if 7.1999999999999996e85 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 78.7%

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

   6. Taylor expanded in Vef around 0 73.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -6.4 \cdot 10^{-291}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 6.6 \cdot 10^{-164}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 2.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 7.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t\_0 + NaChar \cdot 0.5\\ \mathbf{if}\;NdChar \leq -2.5 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 8.2 \cdot 10^{+53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.9 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NaChar}{EAccept \cdot \left(\frac{Vef}{EAccept} + \left(1 + \frac{Ev}{EAccept}\right)\right) - mu}\\ \end{array} \end{array} \]

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 0.5))))
   (if (<= NdChar -2.5e+89)
     t_1
     (if (<= NdChar 8.2e+53)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
       (if (<= NdChar 1.9e+169)
         t_1
         (+
          t_0
          (*
           KbT
           (/
            NaChar
            (-
             (* EAccept (+ (/ Vef EAccept) (+ 1.0 (/ Ev EAccept))))
             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 = t_0 + (NaChar * 0.5);
	double tmp;
	if (NdChar <= -2.5e+89) {
		tmp = t_1;
	} else if (NdChar <= 8.2e+53) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (NdChar <= 1.9e+169) {
		tmp = t_1;
	} else {
		tmp = t_0 + (KbT * (NaChar / ((EAccept * ((Vef / EAccept) + (1.0 + (Ev / EAccept)))) - 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) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = t_0 + (nachar * 0.5d0)
    if (ndchar <= (-2.5d+89)) then
        tmp = t_1
    else if (ndchar <= 8.2d+53) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else if (ndchar <= 1.9d+169) then
        tmp = t_1
    else
        tmp = t_0 + (kbt * (nachar / ((eaccept * ((vef / eaccept) + (1.0d0 + (ev / eaccept)))) - 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 = t_0 + (NaChar * 0.5);
	double tmp;
	if (NdChar <= -2.5e+89) {
		tmp = t_1;
	} else if (NdChar <= 8.2e+53) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (NdChar <= 1.9e+169) {
		tmp = t_1;
	} else {
		tmp = t_0 + (KbT * (NaChar / ((EAccept * ((Vef / EAccept) + (1.0 + (Ev / EAccept)))) - 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 = t_0 + (NaChar * 0.5)
	tmp = 0
	if NdChar <= -2.5e+89:
		tmp = t_1
	elif NdChar <= 8.2e+53:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	elif NdChar <= 1.9e+169:
		tmp = t_1
	else:
		tmp = t_0 + (KbT * (NaChar / ((EAccept * ((Vef / EAccept) + (1.0 + (Ev / EAccept)))) - 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(t_0 + Float64(NaChar * 0.5))
	tmp = 0.0
	if (NdChar <= -2.5e+89)
		tmp = t_1;
	elseif (NdChar <= 8.2e+53)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	elseif (NdChar <= 1.9e+169)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(KbT * Float64(NaChar / Float64(Float64(EAccept * Float64(Float64(Vef / EAccept) + Float64(1.0 + Float64(Ev / EAccept)))) - 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 = t_0 + (NaChar * 0.5);
	tmp = 0.0;
	if (NdChar <= -2.5e+89)
		tmp = t_1;
	elseif (NdChar <= 8.2e+53)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	elseif (NdChar <= 1.9e+169)
		tmp = t_1;
	else
		tmp = t_0 + (KbT * (NaChar / ((EAccept * ((Vef / EAccept) + (1.0 + (Ev / EAccept)))) - 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[(t$95$0 + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -2.5e+89], t$95$1, If[LessEqual[NdChar, 8.2e+53], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.9e+169], t$95$1, N[(t$95$0 + N[(KbT * N[(NaChar / N[(N[(EAccept * N[(N[(Vef / EAccept), $MachinePrecision] + N[(1.0 + N[(Ev / EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -2.49999999999999992e89 or 8.20000000000000037e53 < NdChar < 1.89999999999999996e169

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 69.6%

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

   6. Taylor expanded in KbT around inf 69.3%

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

   if -2.49999999999999992e89 < NdChar < 8.20000000000000037e53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 52.0%

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

      1. *-commutative 52.0%

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

   7. Simplified 52.0%

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

   8. Taylor expanded in NdChar around 0 68.3%

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

   if 1.89999999999999996e169 < 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 72.6%

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

   6. Taylor expanded in EAccept around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. *-commutative 82.4%

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

   8. Simplified 82.4%

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

   9. Taylor expanded in KbT around 0 71.9%

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

       1. +-commutative 71.9%

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

       2. +-commutative 71.9%

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

       3. associate-+l+ 71.9%

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

   11. Simplified 71.9%

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

       1. associate-/l* 71.9%

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

       2. +-commutative 71.9%

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

   13. Applied egg-rr 71.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 8.2 \cdot 10^{+53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.9 \cdot 10^{+169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + KbT \cdot \frac{NaChar}{EAccept \cdot \left(\frac{Vef}{EAccept} + \left(1 + \frac{Ev}{EAccept}\right)\right) - mu}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -2.3 \cdot 10^{+85} \lor \neg \left(NdChar \leq 1.25 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -2.3e+85) (not (<= NdChar 1.25e+53)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/
     NaChar
     (-
      (- 2.0 (* EAccept (- (/ -1.0 KbT) (/ Vef (* KbT EAccept)))))
      (/ mu KbT))))
   (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -2.3e+85) || !(NdChar <= 1.25e+53)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-2.3d+85)) .or. (.not. (ndchar <= 1.25d+53))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / ((2.0d0 - (eaccept * (((-1.0d0) / kbt) - (vef / (kbt * eaccept))))) - (mu / kbt)))
    else
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -2.3e+85) || !(NdChar <= 1.25e+53)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -2.3e+85) or not (NdChar <= 1.25e+53):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)))
	else:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -2.3e+85) || !(NdChar <= 1.25e+53))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(2.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Vef / Float64(KbT * EAccept))))) - Float64(mu / KbT))));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -2.3e+85) || ~((NdChar <= 1.25e+53)))
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	else
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -2.3e+85], N[Not[LessEqual[NdChar, 1.25e+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 / N[(N[(2.0 - N[(EAccept * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(Vef / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -2.2999999999999999e85 or 1.2500000000000001e53 < 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 70.4%

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

   6. Taylor expanded in EAccept around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. *-commutative 76.1%

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

   8. Simplified 76.1%

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

   9. Taylor expanded in Ev around 0 79.9%

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

       1. *-commutative 79.9%

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

   11. Simplified 79.9%

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

   if -2.2999999999999999e85 < NdChar < 1.2500000000000001e53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 52.0%

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

      1. *-commutative 52.0%

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

   7. Simplified 52.0%

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

   8. Taylor expanded in NdChar around 0 68.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.3 \cdot 10^{+85} \lor \neg \left(NdChar \leq 1.25 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -8.5 \cdot 10^{+289} \lor \neg \left(NdChar \leq -2.8 \cdot 10^{+204}\right) \land \left(NdChar \leq -3 \cdot 10^{+97} \lor \neg \left(NdChar \leq 5.2 \cdot 10^{+53}\right)\right):\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -8.5e+289)
         (and (not (<= NdChar -2.8e+204))
              (or (<= NdChar -3e+97) (not (<= NdChar 5.2e+53)))))
   (+ (* NaChar 0.5) (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
   (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -8.5e+289) || (!(NdChar <= -2.8e+204) && ((NdChar <= -3e+97) || !(NdChar <= 5.2e+53)))) {
		tmp = (NaChar * 0.5) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-8.5d+289)) .or. (.not. (ndchar <= (-2.8d+204))) .and. (ndchar <= (-3d+97)) .or. (.not. (ndchar <= 5.2d+53))) then
        tmp = (nachar * 0.5d0) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -8.5e+289) || (!(NdChar <= -2.8e+204) && ((NdChar <= -3e+97) || !(NdChar <= 5.2e+53)))) {
		tmp = (NaChar * 0.5) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -8.5e+289) or (not (NdChar <= -2.8e+204) and ((NdChar <= -3e+97) or not (NdChar <= 5.2e+53))):
		tmp = (NaChar * 0.5) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -8.5e+289) || (!(NdChar <= -2.8e+204) && ((NdChar <= -3e+97) || !(NdChar <= 5.2e+53))))
		tmp = Float64(Float64(NaChar * 0.5) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -8.5e+289) || (~((NdChar <= -2.8e+204)) && ((NdChar <= -3e+97) || ~((NdChar <= 5.2e+53)))))
		tmp = (NaChar * 0.5) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -8.5e+289], And[N[Not[LessEqual[NdChar, -2.8e+204]], $MachinePrecision], Or[LessEqual[NdChar, -3e+97], N[Not[LessEqual[NdChar, 5.2e+53]], $MachinePrecision]]]], N[(N[(NaChar * 0.5), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -8.4999999999999992e289 or -2.80000000000000025e204 < NdChar < -2.9999999999999998e97 or 5.19999999999999996e53 < 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 70.6%

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

   6. Taylor expanded in KbT around inf 70.2%

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

   7. Taylor expanded in EDonor around 0 61.2%

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

   if -8.4999999999999992e289 < NdChar < -2.80000000000000025e204 or -2.9999999999999998e97 < NdChar < 5.19999999999999996e53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 48.6%

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

      1. *-commutative 48.6%

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

   7. Simplified 48.6%

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

   8. Taylor expanded in NdChar around 0 67.2%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -8.5 \cdot 10^{+289} \lor \neg \left(NdChar \leq -2.8 \cdot 10^{+204}\right) \land \left(NdChar \leq -3 \cdot 10^{+97} \lor \neg \left(NdChar \leq 5.2 \cdot 10^{+53}\right)\right):\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.06 \cdot 10^{+107}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;KbT \leq -4.2 \cdot 10^{+83} \lor \neg \left(KbT \leq -70000\right) \land KbT \leq 9.2 \cdot 10^{+204}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.06e+107)
   (- (* NdChar 0.5) (/ NaChar (- -1.0 (exp (/ Ev KbT)))))
   (if (or (<= KbT -4.2e+83) (and (not (<= KbT -70000.0)) (<= KbT 9.2e+204)))
     (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.06e+107) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / KbT))));
	} else if ((KbT <= -4.2e+83) || (!(KbT <= -70000.0) && (KbT <= 9.2e+204))) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-1.06d+107)) then
        tmp = (ndchar * 0.5d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    else if ((kbt <= (-4.2d+83)) .or. (.not. (kbt <= (-70000.0d0))) .and. (kbt <= 9.2d+204)) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.06e+107) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	} else if ((KbT <= -4.2e+83) || (!(KbT <= -70000.0) && (KbT <= 9.2e+204))) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -1.06e+107:
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	elif (KbT <= -4.2e+83) or (not (KbT <= -70000.0) and (KbT <= 9.2e+204)):
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -1.06e+107)
		tmp = Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	elseif ((KbT <= -4.2e+83) || (!(KbT <= -70000.0) && (KbT <= 9.2e+204)))
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -1.06e+107)
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / KbT))));
	elseif ((KbT <= -4.2e+83) || (~((KbT <= -70000.0)) && (KbT <= 9.2e+204)))
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	else
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -1.06e+107], N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[KbT, -4.2e+83], And[N[Not[LessEqual[KbT, -70000.0]], $MachinePrecision], LessEqual[KbT, 9.2e+204]]], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.06e107

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.8%

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

      1. *-commutative 76.8%

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

   7. Simplified 76.8%

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

   8. Taylor expanded in Ev around inf 65.1%

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

   if -1.06e107 < KbT < -4.20000000000000005e83 or -7e4 < KbT < 9.19999999999999962e204

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 37.0%

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

      1. *-commutative 37.0%

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

   7. Simplified 37.0%

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

   8. Taylor expanded in NdChar around 0 65.3%

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

   if -4.20000000000000005e83 < KbT < -7e4 or 9.19999999999999962e204 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 75.6%

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

   6. Taylor expanded in KbT around inf 59.3%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.06 \cdot 10^{+107}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;KbT \leq -4.2 \cdot 10^{+83} \lor \neg \left(KbT \leq -70000\right) \land KbT \leq 9.2 \cdot 10^{+204}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -6.5 \cdot 10^{+92} \lor \neg \left(NdChar \leq 8.5 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -6.5e+92) (not (<= NdChar 8.5e+53)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (* NaChar 0.5))
   (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -6.5e+92) || !(NdChar <= 8.5e+53)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-6.5d+92)) .or. (.not. (ndchar <= 8.5d+53))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar * 0.5d0)
    else
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -6.5e+92) || !(NdChar <= 8.5e+53)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -6.5e+92) or not (NdChar <= 8.5e+53):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar * 0.5)
	else:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -6.5e+92) || !(NdChar <= 8.5e+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(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / 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+92) || ~((NdChar <= 8.5e+53)))
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	else
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -6.5e+92], N[Not[LessEqual[NdChar, 8.5e+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[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -6.49999999999999999e92 or 8.5000000000000002e53 < 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 70.4%

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

   6. Taylor expanded in KbT around inf 66.9%

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

   if -6.49999999999999999e92 < NdChar < 8.5000000000000002e53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 52.0%

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

      1. *-commutative 52.0%

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

   7. Simplified 52.0%

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

   8. Taylor expanded in NdChar around 0 68.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6.5 \cdot 10^{+92} \lor \neg \left(NdChar \leq 8.5 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -4.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 6.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -4.2e-13)
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
   (if (<= KbT 6.2e+23)
     (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
     (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (* NaChar 0.5)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -4.2e-13) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (KbT <= 6.2e+23) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-4.2d-13)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else if (kbt <= 6.2d+23) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -4.2e-13) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (KbT <= 6.2e+23) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -4.2e-13:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	elif KbT <= 6.2e+23:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -4.2e-13)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	elseif (KbT <= 6.2e+23)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -4.2e-13)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	elseif (KbT <= 6.2e+23)
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	else
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -4.2e-13], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 6.2e+23], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -4.19999999999999977e-13

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 72.4%

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

   6. Taylor expanded in KbT around inf 55.3%

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

   if -4.19999999999999977e-13 < KbT < 6.19999999999999941e23

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 29.9%

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

      1. *-commutative 29.9%

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

   7. Simplified 29.9%

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

   8. Taylor expanded in EAccept around inf 19.3%

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

   9. Taylor expanded in NdChar around 0 37.5%

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

   if 6.19999999999999941e23 < KbT

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 67.2%

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

   6. Taylor expanded in KbT around inf 64.2%

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

   7. Taylor expanded in Ec around inf 53.1%

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

      1. associate-*r/ 53.1%

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

      2. mul-1-neg 53.1%

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

   9. Simplified 53.1%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 6.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;KbT \leq -2.5 \cdot 10^{-8} \lor \neg \left(KbT \leq 2.2 \cdot 10^{+49}\right):\\ \;\;\;\;NdChar \cdot 0.5 + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
   (if (or (<= KbT -2.5e-8) (not (<= KbT 2.2e+49)))
     (+ (* NdChar 0.5) t_0)
     t_0)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((EAccept / KbT)));
	double tmp;
	if ((KbT <= -2.5e-8) || !(KbT <= 2.2e+49)) {
		tmp = (NdChar * 0.5) + t_0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((eaccept / kbt)))
    if ((kbt <= (-2.5d-8)) .or. (.not. (kbt <= 2.2d+49))) then
        tmp = (ndchar * 0.5d0) + t_0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	double tmp;
	if ((KbT <= -2.5e-8) || !(KbT <= 2.2e+49)) {
		tmp = (NdChar * 0.5) + t_0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((EAccept / KbT)))
	tmp = 0
	if (KbT <= -2.5e-8) or not (KbT <= 2.2e+49):
		tmp = (NdChar * 0.5) + t_0
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))))
	tmp = 0.0
	if ((KbT <= -2.5e-8) || !(KbT <= 2.2e+49))
		tmp = Float64(Float64(NdChar * 0.5) + t_0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((EAccept / KbT)));
	tmp = 0.0;
	if ((KbT <= -2.5e-8) || ~((KbT <= 2.2e+49)))
		tmp = (NdChar * 0.5) + t_0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[KbT, -2.5e-8], N[Not[LessEqual[KbT, 2.2e+49]], $MachinePrecision]], N[(N[(NdChar * 0.5), $MachinePrecision] + t$95$0), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if KbT < -2.4999999999999999e-8 or 2.2000000000000001e49 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 61.5%

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

      1. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   8. Taylor expanded in EAccept around inf 52.7%

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

   if -2.4999999999999999e-8 < KbT < 2.2000000000000001e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 30.0%

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

      1. *-commutative 30.0%

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

   7. Simplified 30.0%

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

   8. Taylor expanded in EAccept around inf 19.0%

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

   9. Taylor expanded in NdChar around 0 37.2%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.5 \cdot 10^{-8} \lor \neg \left(KbT \leq 2.2 \cdot 10^{+49}\right):\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.4 \cdot 10^{-8}:\\ \;\;\;\;NdChar \cdot 0.5 + t\_0\\ \mathbf{elif}\;KbT \leq 2.25 \cdot 10^{+49}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
   (if (<= KbT -1.4e-8)
     (+ (* NdChar 0.5) t_0)
     (if (<= KbT 2.25e+49)
       t_0
       (- (* NdChar 0.5) (/ NaChar (- -1.0 (exp (/ 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 = NaChar / (1.0 + exp((EAccept / KbT)));
	double tmp;
	if (KbT <= -1.4e-8) {
		tmp = (NdChar * 0.5) + t_0;
	} else if (KbT <= 2.25e+49) {
		tmp = t_0;
	} else {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((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 = nachar / (1.0d0 + exp((eaccept / kbt)))
    if (kbt <= (-1.4d-8)) then
        tmp = (ndchar * 0.5d0) + t_0
    else if (kbt <= 2.25d+49) then
        tmp = t_0
    else
        tmp = (ndchar * 0.5d0) - (nachar / ((-1.0d0) - exp((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 = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	double tmp;
	if (KbT <= -1.4e-8) {
		tmp = (NdChar * 0.5) + t_0;
	} else if (KbT <= 2.25e+49) {
		tmp = t_0;
	} else {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((EAccept / KbT)))
	tmp = 0
	if KbT <= -1.4e-8:
		tmp = (NdChar * 0.5) + t_0
	elif KbT <= 2.25e+49:
		tmp = t_0
	else:
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))))
	tmp = 0.0
	if (KbT <= -1.4e-8)
		tmp = Float64(Float64(NdChar * 0.5) + t_0);
	elseif (KbT <= 2.25e+49)
		tmp = t_0;
	else
		tmp = Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((EAccept / KbT)));
	tmp = 0.0;
	if (KbT <= -1.4e-8)
		tmp = (NdChar * 0.5) + t_0;
	elseif (KbT <= 2.25e+49)
		tmp = t_0;
	else
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / 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[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -1.4e-8], N[(N[(NdChar * 0.5), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[KbT, 2.25e+49], t$95$0, N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.4e-8

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.8%

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

      1. *-commutative 57.8%

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

   7. Simplified 57.8%

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

   8. Taylor expanded in EAccept around inf 54.7%

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

   if -1.4e-8 < KbT < 2.24999999999999991e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 30.0%

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

      1. *-commutative 30.0%

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

   7. Simplified 30.0%

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

   8. Taylor expanded in EAccept around inf 19.0%

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

   9. Taylor expanded in NdChar around 0 37.2%

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

   if 2.24999999999999991e49 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in Ev around inf 53.4%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.4 \cdot 10^{-8}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.25 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -3.9 \cdot 10^{-13}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -3.9e-13)
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
   (if (<= KbT 2.7e+49)
     (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
     (- (* NdChar 0.5) (/ NaChar (- -1.0 (exp (/ 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 (KbT <= -3.9e-13) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (KbT <= 2.7e+49) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((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 (kbt <= (-3.9d-13)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else if (kbt <= 2.7d+49) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else
        tmp = (ndchar * 0.5d0) - (nachar / ((-1.0d0) - exp((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 (KbT <= -3.9e-13) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (KbT <= 2.7e+49) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -3.9e-13:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	elif KbT <= 2.7e+49:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	else:
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -3.9e-13)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	elseif (KbT <= 2.7e+49)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	else
		tmp = Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 - exp(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 (KbT <= -3.9e-13)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	elseif (KbT <= 2.7e+49)
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	else
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -3.9e-13], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.7e+49], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -3.90000000000000004e-13

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 72.4%

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

   6. Taylor expanded in KbT around inf 55.3%

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

   if -3.90000000000000004e-13 < KbT < 2.7000000000000001e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 29.4%

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

      1. *-commutative 29.4%

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

   7. Simplified 29.4%

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

   8. Taylor expanded in EAccept around inf 19.2%

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

   9. Taylor expanded in NdChar around 0 37.5%

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

   if 2.7000000000000001e49 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in Ev around inf 53.4%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.9 \cdot 10^{-13}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 39.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2 \cdot 10^{-8}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right)\right)}\\ \mathbf{elif}\;KbT \leq 3.75 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2e-8)
   (-
    (* NdChar 0.5)
    (/
     NaChar
     (+
      -1.0
      (+
       (/ mu KbT)
       (+
        -1.0
        (*
         EAccept
         (-
          (/ -1.0 KbT)
          (+ (/ Vef (* KbT EAccept)) (/ Ev (* KbT EAccept))))))))))
   (if (<= KbT 3.75e+49)
     (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
     (* 0.5 (+ NdChar NaChar)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -2e-8) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	} else if (KbT <= 3.75e+49) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-2d-8)) then
        tmp = (ndchar * 0.5d0) - (nachar / ((-1.0d0) + ((mu / kbt) + ((-1.0d0) + (eaccept * (((-1.0d0) / kbt) - ((vef / (kbt * eaccept)) + (ev / (kbt * eaccept)))))))))
    else if (kbt <= 3.75d+49) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else
        tmp = 0.5d0 * (ndchar + nachar)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -2e-8) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	} else if (KbT <= 3.75e+49) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -2e-8:
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))))
	elif KbT <= 3.75e+49:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	else:
		tmp = 0.5 * (NdChar + NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -2e-8)
		tmp = Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 + Float64(Float64(mu / KbT) + Float64(-1.0 + Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(KbT * EAccept)) + Float64(Ev / Float64(KbT * EAccept))))))))));
	elseif (KbT <= 3.75e+49)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	else
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -2e-8)
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	elseif (KbT <= 3.75e+49)
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	else
		tmp = 0.5 * (NdChar + NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -2e-8], N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 + N[(EAccept * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(Vef / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision] + N[(Ev / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 3.75e+49], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -2e-8

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.4%

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

   6. Taylor expanded in EAccept around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

   8. Simplified 71.4%

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

   9. Taylor expanded in KbT around inf 49.0%

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

       1. *-commutative 57.8%

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

   11. Simplified 49.0%

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

   if -2e-8 < KbT < 3.7499999999999998e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 30.0%

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

      1. *-commutative 30.0%

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

   7. Simplified 30.0%

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

   8. Taylor expanded in EAccept around inf 19.0%

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

   9. Taylor expanded in NdChar around 0 37.2%

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

   if 3.7499999999999998e49 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in KbT around inf 45.3%

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

      1. distribute-lft-out 45.3%

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

   10. Simplified 45.3%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2 \cdot 10^{-8}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right)\right)}\\ \mathbf{elif}\;KbT \leq 3.75 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 26.9% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq 8.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EDonor 8.5e-64)
   (-
    (/
     NdChar
     (+
      1.0
      (- (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) (/ Ec KbT))))
    (/
     NaChar
     (+
      -1.0
      (+
       (/ mu KbT)
       (+
        -1.0
        (*
         EAccept
         (-
          (/ -1.0 KbT)
          (+ (/ Vef (* KbT EAccept)) (/ Ev (* KbT EAccept))))))))))
   (* 0.5 (+ NdChar NaChar))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EDonor <= 8.5e-64) {
		tmp = (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (edonor <= 8.5d-64) then
        tmp = (ndchar / (1.0d0 + ((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))) - (nachar / ((-1.0d0) + ((mu / kbt) + ((-1.0d0) + (eaccept * (((-1.0d0) / kbt) - ((vef / (kbt * eaccept)) + (ev / (kbt * eaccept)))))))))
    else
        tmp = 0.5d0 * (ndchar + nachar)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EDonor <= 8.5e-64) {
		tmp = (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EDonor <= 8.5e-64:
		tmp = (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))))
	else:
		tmp = 0.5 * (NdChar + NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EDonor <= 8.5e-64)
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT)))) - Float64(NaChar / Float64(-1.0 + Float64(Float64(mu / KbT) + Float64(-1.0 + Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(KbT * EAccept)) + Float64(Ev / Float64(KbT * EAccept))))))))));
	else
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EDonor <= 8.5e-64)
		tmp = (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 + (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))))));
	else
		tmp = 0.5 * (NdChar + NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EDonor, 8.5e-64], N[(N[(NdChar / N[(1.0 + N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 + N[(EAccept * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(Vef / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision] + N[(Ev / N[(KbT * EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EDonor < 8.49999999999999996e-64

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.9%

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

   6. Taylor expanded in EAccept around inf 62.1%

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

      1. *-commutative 62.1%

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

      2. *-commutative 62.1%

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

   8. Simplified 62.1%

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

   9. Taylor expanded in KbT around inf 39.5%

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

   if 8.49999999999999996e-64 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 41.5%

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

      1. *-commutative 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in KbT around inf 21.7%

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

      1. distribute-lft-out 21.7%

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

   10. Simplified 21.7%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq 8.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 + EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 27.2% accurate, 45.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 46.1%

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

   1. *-commutative 46.1%

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

7. Simplified 46.1%

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

8. Taylor expanded in KbT around inf 28.8%

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

   1. distribute-lft-out 28.8%

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

10. Simplified 28.8%

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

11. Final simplification 28.8%

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

Reproduce

herbie shell --seed 2024086 
(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))))))