Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 37.7s

Alternatives: 22

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 75.4% accurate, 0.9× speedup

Math

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) 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 + (EAccept - mu))) / 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 + (eaccept - mu))) / 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 + (EAccept - mu))) / 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 + (EAccept - mu))) / 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(EAccept - mu))) / 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 + (EAccept - mu))) / 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[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(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/ 93.3%

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

      2. mul-1-neg 93.3%

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

   7. Simplified 93.3%

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

   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%

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

Alternative 3: 65.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\\ t_1 := \frac{Vef}{KbT} + \frac{Ev}{KbT}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -6.5 \cdot 10^{+202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -3.2 \cdot 10^{-133}:\\ \;\;\;\;t\_3 + \frac{NaChar}{1 + \left(\left(1 - EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -1.4 \cdot 10^{-225}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} - \frac{NaChar}{-1 - t\_0}\\ \mathbf{elif}\;mu \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;t\_3 + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + t\_1\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 3.4 \cdot 10^{-94}:\\ \;\;\;\;\frac{NaChar}{1 + t\_0} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.8 \cdot 10^{+154}:\\ \;\;\;\;t\_3 - \frac{NaChar}{-1 + EAccept \cdot \left(\frac{\frac{mu}{KbT} + \left(-1 - t\_1\right)}{EAccept} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))
        (t_1 (+ (/ Vef KbT) (/ Ev 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 -3.2e-133)
       (+
        t_3
        (/
         NaChar
         (+
          1.0
          (-
           (-
            1.0
            (*
             EAccept
             (-
              (/ -1.0 KbT)
              (+ (/ Vef (* KbT EAccept)) (/ Ev (* KbT EAccept))))))
           (/ mu KbT)))))
       (if (<= mu -1.4e-225)
         (-
          (/
           NdChar
           (+
            1.0
            (-
             (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
             (/ Ec KbT))))
          (/ NaChar (- -1.0 t_0)))
         (if (<= mu 1.1e-194)
           (+
            t_3
            (/
             NaChar
             (-
              1.0
              (* mu (+ (/ (- -1.0 (+ (/ EAccept KbT) t_1)) mu) (/ 1.0 KbT))))))
           (if (<= mu 3.4e-94)
             (+ (/ NaChar (+ 1.0 t_0)) (/ NdChar (+ 1.0 (+ 1.0 (/ Vef KbT)))))
             (if (<= mu 1.8e+154)
               (-
                t_3
                (/
                 NaChar
                 (+
                  -1.0
                  (*
                   EAccept
                   (+ (/ (+ (/ mu KbT) (- -1.0 t_1)) EAccept) (/ -1.0 KbT))))))
               t_2))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_1 = (Vef / KbT) + (Ev / 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 <= -3.2e-133) {
		tmp = t_3 + (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT))));
	} else if (mu <= -1.4e-225) {
		tmp = (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))) - (NaChar / (-1.0 - t_0));
	} else if (mu <= 1.1e-194) {
		tmp = t_3 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + t_1)) / mu) + (1.0 / KbT)))));
	} else if (mu <= 3.4e-94) {
		tmp = (NaChar / (1.0 + t_0)) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	} else if (mu <= 1.8e+154) {
		tmp = t_3 - (NaChar / (-1.0 + (EAccept * ((((mu / KbT) + (-1.0 - t_1)) / EAccept) + (-1.0 / KbT)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = exp(((vef + (ev + (eaccept - mu))) / kbt))
    t_1 = (vef / kbt) + (ev / 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 <= (-3.2d-133)) then
        tmp = t_3 + (nachar / (1.0d0 + ((1.0d0 - (eaccept * (((-1.0d0) / kbt) - ((vef / (kbt * eaccept)) + (ev / (kbt * eaccept)))))) - (mu / kbt))))
    else if (mu <= (-1.4d-225)) then
        tmp = (ndchar / (1.0d0 + ((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))) - (nachar / ((-1.0d0) - t_0))
    else if (mu <= 1.1d-194) then
        tmp = t_3 + (nachar / (1.0d0 - (mu * ((((-1.0d0) - ((eaccept / kbt) + t_1)) / mu) + (1.0d0 / kbt)))))
    else if (mu <= 3.4d-94) then
        tmp = (nachar / (1.0d0 + t_0)) + (ndchar / (1.0d0 + (1.0d0 + (vef / kbt))))
    else if (mu <= 1.8d+154) then
        tmp = t_3 - (nachar / ((-1.0d0) + (eaccept * ((((mu / kbt) + ((-1.0d0) - t_1)) / eaccept) + ((-1.0d0) / kbt)))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_1 = (Vef / KbT) + (Ev / 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 <= -3.2e-133) {
		tmp = t_3 + (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT))));
	} else if (mu <= -1.4e-225) {
		tmp = (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))) - (NaChar / (-1.0 - t_0));
	} else if (mu <= 1.1e-194) {
		tmp = t_3 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + t_1)) / mu) + (1.0 / KbT)))));
	} else if (mu <= 3.4e-94) {
		tmp = (NaChar / (1.0 + t_0)) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	} else if (mu <= 1.8e+154) {
		tmp = t_3 - (NaChar / (-1.0 + (EAccept * ((((mu / KbT) + (-1.0 - t_1)) / EAccept) + (-1.0 / KbT)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))
	t_1 = (Vef / KbT) + (Ev / 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 <= -3.2e-133:
		tmp = t_3 + (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT))))
	elif mu <= -1.4e-225:
		tmp = (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))) - (NaChar / (-1.0 - t_0))
	elif mu <= 1.1e-194:
		tmp = t_3 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + t_1)) / mu) + (1.0 / KbT)))))
	elif mu <= 3.4e-94:
		tmp = (NaChar / (1.0 + t_0)) + (NdChar / (1.0 + (1.0 + (Vef / KbT))))
	elif mu <= 1.8e+154:
		tmp = t_3 - (NaChar / (-1.0 + (EAccept * ((((mu / KbT) + (-1.0 - t_1)) / EAccept) + (-1.0 / KbT)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))
	t_1 = Float64(Float64(Vef / KbT) + Float64(Ev / 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 <= -3.2e-133)
		tmp = Float64(t_3 + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(KbT * EAccept)) + Float64(Ev / Float64(KbT * EAccept)))))) - Float64(mu / KbT)))));
	elseif (mu <= -1.4e-225)
		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 - t_0)));
	elseif (mu <= 1.1e-194)
		tmp = Float64(t_3 + Float64(NaChar / Float64(1.0 - Float64(mu * Float64(Float64(Float64(-1.0 - Float64(Float64(EAccept / KbT) + t_1)) / mu) + Float64(1.0 / KbT))))));
	elseif (mu <= 3.4e-94)
		tmp = Float64(Float64(NaChar / Float64(1.0 + t_0)) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(Vef / KbT)))));
	elseif (mu <= 1.8e+154)
		tmp = Float64(t_3 - Float64(NaChar / Float64(-1.0 + Float64(EAccept * Float64(Float64(Float64(Float64(mu / KbT) + Float64(-1.0 - t_1)) / EAccept) + Float64(-1.0 / KbT))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	t_1 = (Vef / KbT) + (Ev / 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 <= -3.2e-133)
		tmp = t_3 + (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT))));
	elseif (mu <= -1.4e-225)
		tmp = (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))) - (NaChar / (-1.0 - t_0));
	elseif (mu <= 1.1e-194)
		tmp = t_3 + (NaChar / (1.0 - (mu * (((-1.0 - ((EAccept / KbT) + t_1)) / mu) + (1.0 / KbT)))));
	elseif (mu <= 3.4e-94)
		tmp = (NaChar / (1.0 + t_0)) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	elseif (mu <= 1.8e+154)
		tmp = t_3 - (NaChar / (-1.0 + (EAccept * ((((mu / KbT) + (-1.0 - t_1)) / EAccept) + (-1.0 / KbT)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $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, -3.2e-133], N[(t$95$3 + N[(NaChar / N[(1.0 + N[(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] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -1.4e-225], 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 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.1e-194], N[(t$95$3 + N[(NaChar / N[(1.0 - N[(mu * N[(N[(N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 3.4e-94], N[(N[(NaChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.8e+154], N[(t$95$3 - N[(NaChar / N[(-1.0 + N[(EAccept * N[(N[(N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision] / EAccept), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if mu < -6.4999999999999996e202 or 1.8e154 < 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 < -3.20000000000000013e-133

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 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 -3.20000000000000013e-133 < mu < -1.4e-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 -1.4e-225 < mu < 1.1000000000000001e-194

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 1.1000000000000001e-194 < mu < 3.3999999999999998e-94

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in 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 3.3999999999999998e-94 < mu < 1.8e154

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -6.5 \cdot 10^{+202}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -3.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 - EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -1.4 \cdot 10^{-225}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 3.4 \cdot 10^{-94}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} - \frac{NaChar}{-1 + EAccept \cdot \left(\frac{\frac{mu}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{EAccept} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -4 \cdot 10^{-8}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -1.95 \cdot 10^{-292}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.65 \cdot 10^{-167}:\\ \;\;\;\;t\_1 + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 6.5 \cdot 10^{+25}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.9 \cdot 10^{+51}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

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-8)
     (+
      t_1
      (/
       NaChar
       (-
        1.0
        (+
         (/ mu KbT)
         (+
          -1.0
          (/ (* EAccept (- -1.0 (+ (/ Ev EAccept) (/ Vef EAccept)))) KbT))))))
     (if (<= KbT -1.95e-292)
       t_0
       (if (<= KbT 1.65e-167)
         (+
          t_1
          (/
           (* KbT NaChar)
           (- (* Ev (- 1.0 (* EAccept (/ (- -1.0 (/ Vef EAccept)) Ev)))) mu)))
         (if (<= KbT 6.5e+25)
           t_0
           (if (<= KbT 1.9e+51)
             (+
              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-8) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -1.95e-292) {
		tmp = t_0;
	} else if (KbT <= 1.65e-167) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 6.5e+25) {
		tmp = t_0;
	} else if (KbT <= 1.9e+51) {
		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-8)) then
        tmp = t_1 + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) + ((eaccept * ((-1.0d0) - ((ev / eaccept) + (vef / eaccept)))) / kbt)))))
    else if (kbt <= (-1.95d-292)) then
        tmp = t_0
    else if (kbt <= 1.65d-167) then
        tmp = t_1 + ((kbt * nachar) / ((ev * (1.0d0 - (eaccept * (((-1.0d0) - (vef / eaccept)) / ev)))) - mu))
    else if (kbt <= 6.5d+25) then
        tmp = t_0
    else if (kbt <= 1.9d+51) 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-8) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -1.95e-292) {
		tmp = t_0;
	} else if (KbT <= 1.65e-167) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 6.5e+25) {
		tmp = t_0;
	} else if (KbT <= 1.9e+51) {
		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-8:
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))))
	elif KbT <= -1.95e-292:
		tmp = t_0
	elif KbT <= 1.65e-167:
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu))
	elif KbT <= 6.5e+25:
		tmp = t_0
	elif KbT <= 1.9e+51:
		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-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 <= -1.95e-292)
		tmp = t_0;
	elseif (KbT <= 1.65e-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 <= 6.5e+25)
		tmp = t_0;
	elseif (KbT <= 1.9e+51)
		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-8)
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	elseif (KbT <= -1.95e-292)
		tmp = t_0;
	elseif (KbT <= 1.65e-167)
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	elseif (KbT <= 6.5e+25)
		tmp = t_0;
	elseif (KbT <= 1.9e+51)
		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-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, -1.95e-292], t$95$0, If[LessEqual[KbT, 1.65e-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, 6.5e+25], t$95$0, If[LessEqual[KbT, 1.9e+51], 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 < -4.0000000000000001e-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 -4.0000000000000001e-8 < KbT < -1.95e-292 or 1.64999999999999998e-167 < KbT < 6.50000000000000005e25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -1.95e-292 < KbT < 1.64999999999999998e-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 6.50000000000000005e25 < KbT < 1.8999999999999999e51

   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 1.8999999999999999e51 < 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/ 85.0%

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

      2. mul-1-neg 85.0%

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

   7. Simplified 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -1.95 \cdot 10^{-292}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.65 \cdot 10^{-167}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 6.5 \cdot 10^{+25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.9 \cdot 10^{+51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -6.5 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -4.7 \cdot 10^{+114}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq -3.5 \cdot 10^{+55} \lor \neg \left(mu \leq 8.8 \cdot 10^{+55}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) 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 8.8e+55)))
         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 + (EAccept - mu))) / 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 <= 8.8e+55)) {
		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 + (eaccept - mu))) / 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 <= 8.8d+55))) 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 + (EAccept - mu))) / 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 <= 8.8e+55)) {
		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 + (EAccept - mu))) / 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 <= 8.8e+55):
		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(EAccept - mu))) / 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 <= 8.8e+55))
		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 + (EAccept - mu))) / 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 <= 8.8e+55)))
		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[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, 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, 8.8e+55]], $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 8.80000000000000042e55 < 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 90.5%

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

   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 < 8.80000000000000042e55

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 77.3%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -6.5 \cdot 10^{+202}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -4.7 \cdot 10^{+114}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq -3.5 \cdot 10^{+55} \lor \neg \left(mu \leq 8.8 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{if}\;mu \leq -7 \cdot 10^{+202}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq -1.95 \cdot 10^{-115}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 - EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 2.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -7e+202)
     t_0
     (if (<= mu -1.95e-115)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
        (/
         NaChar
         (+
          1.0
          (-
           (-
            1.0
            (*
             EAccept
             (-
              (/ -1.0 KbT)
              (+ (/ Vef (* KbT EAccept)) (/ Ev (* KbT EAccept))))))
           (/ mu KbT)))))
       (if (<= mu 2.4e+86)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) 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 <= -7e+202) {
		tmp = t_0;
	} else if (mu <= -1.95e-115) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT))));
	} else if (mu <= 2.4e+86) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / 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 <= (-7d+202)) then
        tmp = t_0
    else if (mu <= (-1.95d-115)) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + ((1.0d0 - (eaccept * (((-1.0d0) / kbt) - ((vef / (kbt * eaccept)) + (ev / (kbt * eaccept)))))) - (mu / kbt))))
    else if (mu <= 2.4d+86) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / 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 <= -7e+202) {
		tmp = t_0;
	} else if (mu <= -1.95e-115) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT))));
	} else if (mu <= 2.4e+86) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / 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 <= -7e+202:
		tmp = t_0
	elif mu <= -1.95e-115:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT))))
	elif mu <= 2.4e+86:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / 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 <= -7e+202)
		tmp = t_0;
	elseif (mu <= -1.95e-115)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(KbT * EAccept)) + Float64(Ev / Float64(KbT * EAccept)))))) - Float64(mu / KbT)))));
	elseif (mu <= 2.4e+86)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	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 <= -7e+202)
		tmp = t_0;
	elseif (mu <= -1.95e-115)
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT))));
	elseif (mu <= 2.4e+86)
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / 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, -7e+202], t$95$0, If[LessEqual[mu, -1.95e-115], 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[(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] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 2.4e+86], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -6.99999999999999975e202 or 2.4e86 < 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 -6.99999999999999975e202 < mu < -1.9499999999999999e-115

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -1.9499999999999999e-115 < mu < 2.4e86

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -7 \cdot 10^{+202}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.95 \cdot 10^{-115}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 - EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 2.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -8.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -2.2 \cdot 10^{-292}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.65 \cdot 10^{-167}:\\ \;\;\;\;t\_1 + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 3.1 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.9 \cdot 10^{+86}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \end{array} \]

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 -8.5e-11)
     (+
      t_1
      (/
       NaChar
       (-
        1.0
        (+
         (/ mu KbT)
         (+
          -1.0
          (/ (* EAccept (- -1.0 (+ (/ Ev EAccept) (/ Vef EAccept)))) KbT))))))
     (if (<= KbT -2.2e-292)
       t_0
       (if (<= KbT 1.65e-167)
         (+
          t_1
          (/
           (* KbT NaChar)
           (- (* Ev (- 1.0 (* EAccept (/ (- -1.0 (/ Vef EAccept)) Ev)))) mu)))
         (if (<= KbT 3.1e+27)
           t_0
           (if (<= KbT 1.9e+86)
             (+
              t_1
              (/
               NaChar
               (-
                1.0
                (*
                 mu
                 (+
                  (/
                   (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
                   mu)
                  (/ 1.0 KbT))))))
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) 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 <= -8.5e-11) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -2.2e-292) {
		tmp = t_0;
	} else if (KbT <= 1.65e-167) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 3.1e+27) {
		tmp = t_0;
	} else if (KbT <= 1.9e+86) {
		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 + (EAccept - mu))) / 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 <= (-8.5d-11)) then
        tmp = t_1 + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) + ((eaccept * ((-1.0d0) - ((ev / eaccept) + (vef / eaccept)))) / kbt)))))
    else if (kbt <= (-2.2d-292)) then
        tmp = t_0
    else if (kbt <= 1.65d-167) then
        tmp = t_1 + ((kbt * nachar) / ((ev * (1.0d0 - (eaccept * (((-1.0d0) - (vef / eaccept)) / ev)))) - mu))
    else if (kbt <= 3.1d+27) then
        tmp = t_0
    else if (kbt <= 1.9d+86) 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 + (eaccept - mu))) / 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 <= -8.5e-11) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -2.2e-292) {
		tmp = t_0;
	} else if (KbT <= 1.65e-167) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 3.1e+27) {
		tmp = t_0;
	} else if (KbT <= 1.9e+86) {
		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 + (EAccept - mu))) / 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 <= -8.5e-11:
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))))
	elif KbT <= -2.2e-292:
		tmp = t_0
	elif KbT <= 1.65e-167:
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu))
	elif KbT <= 3.1e+27:
		tmp = t_0
	elif KbT <= 1.9e+86:
		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 + (EAccept - mu))) / 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 <= -8.5e-11)
		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 <= -2.2e-292)
		tmp = t_0;
	elseif (KbT <= 1.65e-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 <= 3.1e+27)
		tmp = t_0;
	elseif (KbT <= 1.9e+86)
		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(EAccept - mu))) / 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 <= -8.5e-11)
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	elseif (KbT <= -2.2e-292)
		tmp = t_0;
	elseif (KbT <= 1.65e-167)
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	elseif (KbT <= 3.1e+27)
		tmp = t_0;
	elseif (KbT <= 1.9e+86)
		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 + (EAccept - mu))) / 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, -8.5e-11], 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, -2.2e-292], t$95$0, If[LessEqual[KbT, 1.65e-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, 3.1e+27], t$95$0, If[LessEqual[KbT, 1.9e+86], 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[(EAccept - mu), $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 < -8.50000000000000037e-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%

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

   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 -8.50000000000000037e-11 < KbT < -2.20000000000000011e-292 or 1.64999999999999998e-167 < KbT < 3.09999999999999996e27

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -2.20000000000000011e-292 < KbT < 1.64999999999999998e-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 3.09999999999999996e27 < KbT < 1.89999999999999989e86

   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 1.89999999999999989e86 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -2.2 \cdot 10^{-292}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.65 \cdot 10^{-167}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 3.1 \cdot 10^{+27}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.9 \cdot 10^{+86}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - mu \cdot \left(\frac{-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -2.4 \cdot 10^{-292}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.9 \cdot 10^{-166}:\\ \;\;\;\;t\_1 + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 1.66 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.65 \cdot 10^{+86}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \end{array} \]

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 -1.15e-10)
     (+
      t_1
      (/
       NaChar
       (-
        1.0
        (+
         (/ mu KbT)
         (+
          -1.0
          (/ (* EAccept (- -1.0 (+ (/ Ev EAccept) (/ Vef EAccept)))) KbT))))))
     (if (<= KbT -2.4e-292)
       t_0
       (if (<= KbT 1.9e-166)
         (+
          t_1
          (/
           (* KbT NaChar)
           (- (* Ev (- 1.0 (* EAccept (/ (- -1.0 (/ Vef EAccept)) Ev)))) mu)))
         (if (<= KbT 1.66e+27)
           t_0
           (if (<= KbT 1.65e+86)
             (+
              t_1
              (/
               NaChar
               (-
                (- 2.0 (* EAccept (- (/ -1.0 KbT) (/ Vef (* KbT EAccept)))))
                (/ mu KbT))))
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) 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 <= -1.15e-10) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -2.4e-292) {
		tmp = t_0;
	} else if (KbT <= 1.9e-166) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 1.66e+27) {
		tmp = t_0;
	} else if (KbT <= 1.65e+86) {
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / 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 <= (-1.15d-10)) then
        tmp = t_1 + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) + ((eaccept * ((-1.0d0) - ((ev / eaccept) + (vef / eaccept)))) / kbt)))))
    else if (kbt <= (-2.4d-292)) then
        tmp = t_0
    else if (kbt <= 1.9d-166) then
        tmp = t_1 + ((kbt * nachar) / ((ev * (1.0d0 - (eaccept * (((-1.0d0) - (vef / eaccept)) / ev)))) - mu))
    else if (kbt <= 1.66d+27) then
        tmp = t_0
    else if (kbt <= 1.65d+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 + (eaccept - mu))) / 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 <= -1.15e-10) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	} else if (KbT <= -2.4e-292) {
		tmp = t_0;
	} else if (KbT <= 1.9e-166) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 1.66e+27) {
		tmp = t_0;
	} else if (KbT <= 1.65e+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 + (EAccept - mu))) / 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 <= -1.15e-10:
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))))
	elif KbT <= -2.4e-292:
		tmp = t_0
	elif KbT <= 1.9e-166:
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu))
	elif KbT <= 1.66e+27:
		tmp = t_0
	elif KbT <= 1.65e+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 + (EAccept - mu))) / 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 <= -1.15e-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 <= -2.4e-292)
		tmp = t_0;
	elseif (KbT <= 1.9e-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 <= 1.66e+27)
		tmp = t_0;
	elseif (KbT <= 1.65e+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(EAccept - mu))) / 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 <= -1.15e-10)
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 + ((EAccept * (-1.0 - ((Ev / EAccept) + (Vef / EAccept)))) / KbT)))));
	elseif (KbT <= -2.4e-292)
		tmp = t_0;
	elseif (KbT <= 1.9e-166)
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	elseif (KbT <= 1.66e+27)
		tmp = t_0;
	elseif (KbT <= 1.65e+86)
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / 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, -1.15e-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, -2.4e-292], t$95$0, If[LessEqual[KbT, 1.9e-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, 1.66e+27], t$95$0, If[LessEqual[KbT, 1.65e+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[(EAccept - mu), $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 < -1.15000000000000004e-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 -1.15000000000000004e-10 < KbT < -2.4000000000000001e-292 or 1.89999999999999991e-166 < KbT < 1.65999999999999986e27

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -2.4000000000000001e-292 < KbT < 1.89999999999999991e-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 1.65999999999999986e27 < KbT < 1.65e86

   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 1.65e86 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 + \frac{EAccept \cdot \left(-1 - \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -2.4 \cdot 10^{-292}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.9 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 1.66 \cdot 10^{+27}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.65 \cdot 10^{+86}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.45 \cdot 10^{-8}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;KbT \leq -1.35 \cdot 10^{-291}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 5.5 \cdot 10^{-167}:\\ \;\;\;\;t\_1 + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 7.2 \cdot 10^{+25}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 2.05 \cdot 10^{+86}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \end{array} \]

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 -1.45e-8)
     (+
      t_1
      (/
       NaChar
       (-
        1.0
        (+
         (/ mu KbT)
         (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))))))
     (if (<= KbT -1.35e-291)
       t_0
       (if (<= KbT 5.5e-167)
         (+
          t_1
          (/
           (* KbT NaChar)
           (- (* Ev (- 1.0 (* EAccept (/ (- -1.0 (/ Vef EAccept)) Ev)))) mu)))
         (if (<= KbT 7.2e+25)
           t_0
           (if (<= KbT 2.05e+86)
             (+
              t_1
              (/
               NaChar
               (-
                (- 2.0 (* EAccept (- (/ -1.0 KbT) (/ Vef (* KbT EAccept)))))
                (/ mu KbT))))
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) 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 <= -1.45e-8) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (KbT <= -1.35e-291) {
		tmp = t_0;
	} else if (KbT <= 5.5e-167) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 7.2e+25) {
		tmp = t_0;
	} else if (KbT <= 2.05e+86) {
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / 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 <= (-1.45d-8)) then
        tmp = t_1 + (nachar / (1.0d0 - ((mu / kbt) + ((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))))))
    else if (kbt <= (-1.35d-291)) then
        tmp = t_0
    else if (kbt <= 5.5d-167) then
        tmp = t_1 + ((kbt * nachar) / ((ev * (1.0d0 - (eaccept * (((-1.0d0) - (vef / eaccept)) / ev)))) - mu))
    else if (kbt <= 7.2d+25) then
        tmp = t_0
    else if (kbt <= 2.05d+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 + (eaccept - mu))) / 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 <= -1.45e-8) {
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	} else if (KbT <= -1.35e-291) {
		tmp = t_0;
	} else if (KbT <= 5.5e-167) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 7.2e+25) {
		tmp = t_0;
	} else if (KbT <= 2.05e+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 + (EAccept - mu))) / 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 <= -1.45e-8:
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))))
	elif KbT <= -1.35e-291:
		tmp = t_0
	elif KbT <= 5.5e-167:
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu))
	elif KbT <= 7.2e+25:
		tmp = t_0
	elif KbT <= 2.05e+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 + (EAccept - mu))) / 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 <= -1.45e-8)
		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 <= -1.35e-291)
		tmp = t_0;
	elseif (KbT <= 5.5e-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 <= 7.2e+25)
		tmp = t_0;
	elseif (KbT <= 2.05e+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(EAccept - mu))) / 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 <= -1.45e-8)
		tmp = t_1 + (NaChar / (1.0 - ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	elseif (KbT <= -1.35e-291)
		tmp = t_0;
	elseif (KbT <= 5.5e-167)
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	elseif (KbT <= 7.2e+25)
		tmp = t_0;
	elseif (KbT <= 2.05e+86)
		tmp = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / 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, -1.45e-8], 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, -1.35e-291], t$95$0, If[LessEqual[KbT, 5.5e-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, 7.2e+25], t$95$0, If[LessEqual[KbT, 2.05e+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[(EAccept - mu), $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 < -1.4500000000000001e-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%

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

   if -1.4500000000000001e-8 < KbT < -1.34999999999999996e-291 or 5.5000000000000003e-167 < KbT < 7.20000000000000031e25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -1.34999999999999996e-291 < KbT < 5.5000000000000003e-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 7.20000000000000031e25 < KbT < 2.05e86

   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 2.05e86 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.45 \cdot 10^{-8}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 - \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;KbT \leq -1.35 \cdot 10^{-291}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 5.5 \cdot 10^{-167}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 7.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.05 \cdot 10^{+86}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{if}\;KbT \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;KbT \leq -1.25 \cdot 10^{-290}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 7.5 \cdot 10^{-164}:\\ \;\;\;\;t\_1 + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 5.7 \cdot 10^{+28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \end{array} \]

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)))))
        (t_2
         (+
          t_1
          (/
           NaChar
           (-
            (- 2.0 (* EAccept (- (/ -1.0 KbT) (/ Vef (* KbT EAccept)))))
            (/ mu KbT))))))
   (if (<= KbT -1.15e-10)
     t_2
     (if (<= KbT -1.25e-290)
       t_0
       (if (<= KbT 7.5e-164)
         (+
          t_1
          (/
           (* KbT NaChar)
           (- (* Ev (- 1.0 (* EAccept (/ (- -1.0 (/ Vef EAccept)) Ev)))) mu)))
         (if (<= KbT 5.7e+28)
           t_0
           (if (<= KbT 2.1e+86)
             t_2
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) 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 t_2 = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	double tmp;
	if (KbT <= -1.15e-10) {
		tmp = t_2;
	} else if (KbT <= -1.25e-290) {
		tmp = t_0;
	} else if (KbT <= 7.5e-164) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 5.7e+28) {
		tmp = t_0;
	} else if (KbT <= 2.1e+86) {
		tmp = t_2;
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / 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) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_2 = t_1 + (nachar / ((2.0d0 - (eaccept * (((-1.0d0) / kbt) - (vef / (kbt * eaccept))))) - (mu / kbt)))
    if (kbt <= (-1.15d-10)) then
        tmp = t_2
    else if (kbt <= (-1.25d-290)) then
        tmp = t_0
    else if (kbt <= 7.5d-164) then
        tmp = t_1 + ((kbt * nachar) / ((ev * (1.0d0 - (eaccept * (((-1.0d0) - (vef / eaccept)) / ev)))) - mu))
    else if (kbt <= 5.7d+28) then
        tmp = t_0
    else if (kbt <= 2.1d+86) then
        tmp = t_2
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / 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 t_2 = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	double tmp;
	if (KbT <= -1.15e-10) {
		tmp = t_2;
	} else if (KbT <= -1.25e-290) {
		tmp = t_0;
	} else if (KbT <= 7.5e-164) {
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	} else if (KbT <= 5.7e+28) {
		tmp = t_0;
	} else if (KbT <= 2.1e+86) {
		tmp = t_2;
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / 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)))
	t_2 = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)))
	tmp = 0
	if KbT <= -1.15e-10:
		tmp = t_2
	elif KbT <= -1.25e-290:
		tmp = t_0
	elif KbT <= 7.5e-164:
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu))
	elif KbT <= 5.7e+28:
		tmp = t_0
	elif KbT <= 2.1e+86:
		tmp = t_2
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / 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))))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(Float64(2.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Vef / Float64(KbT * EAccept))))) - Float64(mu / KbT))))
	tmp = 0.0
	if (KbT <= -1.15e-10)
		tmp = t_2;
	elseif (KbT <= -1.25e-290)
		tmp = t_0;
	elseif (KbT <= 7.5e-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 <= 5.7e+28)
		tmp = t_0;
	elseif (KbT <= 2.1e+86)
		tmp = t_2;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / 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)));
	t_2 = t_1 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	tmp = 0.0;
	if (KbT <= -1.15e-10)
		tmp = t_2;
	elseif (KbT <= -1.25e-290)
		tmp = t_0;
	elseif (KbT <= 7.5e-164)
		tmp = t_1 + ((KbT * NaChar) / ((Ev * (1.0 - (EAccept * ((-1.0 - (Vef / EAccept)) / Ev)))) - mu));
	elseif (KbT <= 5.7e+28)
		tmp = t_0;
	elseif (KbT <= 2.1e+86)
		tmp = t_2;
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / 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]}, Block[{t$95$2 = 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]}, If[LessEqual[KbT, -1.15e-10], t$95$2, If[LessEqual[KbT, -1.25e-290], t$95$0, If[LessEqual[KbT, 7.5e-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, 5.7e+28], t$95$0, If[LessEqual[KbT, 2.1e+86], t$95$2, N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -1.15000000000000004e-10 or 5.7000000000000003e28 < KbT < 2.0999999999999999e86

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 72.5%

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

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in Ev around 0 73.7%

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

       1. *-commutative 73.7%

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

   11. Simplified 73.7%

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

   if -1.15000000000000004e-10 < KbT < -1.25e-290 or 7.5000000000000006e-164 < KbT < 5.7000000000000003e28

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -1.25e-290 < KbT < 7.5000000000000006e-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 2.0999999999999999e86 < 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 4 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;KbT \leq -1.25 \cdot 10^{-290}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 7.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Ev \cdot \left(1 - EAccept \cdot \frac{-1 - \frac{Vef}{EAccept}}{Ev}\right) - mu}\\ \mathbf{elif}\;KbT \leq 5.7 \cdot 10^{+28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+86}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := Vef + \left(Ev + \left(EAccept - mu\right)\right)\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_3 := t\_2 + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{if}\;KbT \leq -2.3 \cdot 10^{-8}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;KbT \leq -1 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;KbT \leq 3 \cdot 10^{-167}:\\ \;\;\;\;t\_2 + KbT \cdot \frac{NaChar}{t\_0}\\ \mathbf{elif}\;KbT \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;KbT \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{t\_0}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ Vef (+ Ev (- EAccept mu))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_3
         (+
          t_2
          (/
           NaChar
           (-
            (- 2.0 (* EAccept (- (/ -1.0 KbT) (/ Vef (* KbT EAccept)))))
            (/ mu KbT))))))
   (if (<= KbT -2.3e-8)
     t_3
     (if (<= KbT -1e-293)
       t_1
       (if (<= KbT 3e-167)
         (+ t_2 (* KbT (/ NaChar t_0)))
         (if (<= KbT 3.8e+28)
           t_1
           (if (<= KbT 5.6e+85)
             t_3
             (+
              (/ NaChar (+ 1.0 (exp (/ t_0 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 = Vef + (Ev + (EAccept - mu));
	double t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_2 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_3 = t_2 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	double tmp;
	if (KbT <= -2.3e-8) {
		tmp = t_3;
	} else if (KbT <= -1e-293) {
		tmp = t_1;
	} else if (KbT <= 3e-167) {
		tmp = t_2 + (KbT * (NaChar / t_0));
	} else if (KbT <= 3.8e+28) {
		tmp = t_1;
	} else if (KbT <= 5.6e+85) {
		tmp = t_3;
	} else {
		tmp = (NaChar / (1.0 + exp((t_0 / 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = vef + (ev + (eaccept - mu))
    t_1 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_2 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_3 = t_2 + (nachar / ((2.0d0 - (eaccept * (((-1.0d0) / kbt) - (vef / (kbt * eaccept))))) - (mu / kbt)))
    if (kbt <= (-2.3d-8)) then
        tmp = t_3
    else if (kbt <= (-1d-293)) then
        tmp = t_1
    else if (kbt <= 3d-167) then
        tmp = t_2 + (kbt * (nachar / t_0))
    else if (kbt <= 3.8d+28) then
        tmp = t_1
    else if (kbt <= 5.6d+85) then
        tmp = t_3
    else
        tmp = (nachar / (1.0d0 + exp((t_0 / 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 = Vef + (Ev + (EAccept - mu));
	double t_1 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_2 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_3 = t_2 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	double tmp;
	if (KbT <= -2.3e-8) {
		tmp = t_3;
	} else if (KbT <= -1e-293) {
		tmp = t_1;
	} else if (KbT <= 3e-167) {
		tmp = t_2 + (KbT * (NaChar / t_0));
	} else if (KbT <= 3.8e+28) {
		tmp = t_1;
	} else if (KbT <= 5.6e+85) {
		tmp = t_3;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((t_0 / KbT)))) + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = Vef + (Ev + (EAccept - mu))
	t_1 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_2 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_3 = t_2 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)))
	tmp = 0
	if KbT <= -2.3e-8:
		tmp = t_3
	elif KbT <= -1e-293:
		tmp = t_1
	elif KbT <= 3e-167:
		tmp = t_2 + (KbT * (NaChar / t_0))
	elif KbT <= 3.8e+28:
		tmp = t_1
	elif KbT <= 5.6e+85:
		tmp = t_3
	else:
		tmp = (NaChar / (1.0 + math.exp((t_0 / 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(Vef + Float64(Ev + Float64(EAccept - mu)))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_3 = Float64(t_2 + Float64(NaChar / Float64(Float64(2.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Vef / Float64(KbT * EAccept))))) - Float64(mu / KbT))))
	tmp = 0.0
	if (KbT <= -2.3e-8)
		tmp = t_3;
	elseif (KbT <= -1e-293)
		tmp = t_1;
	elseif (KbT <= 3e-167)
		tmp = Float64(t_2 + Float64(KbT * Float64(NaChar / t_0)));
	elseif (KbT <= 3.8e+28)
		tmp = t_1;
	elseif (KbT <= 5.6e+85)
		tmp = t_3;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(t_0 / 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 = Vef + (Ev + (EAccept - mu));
	t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_2 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_3 = t_2 + (NaChar / ((2.0 - (EAccept * ((-1.0 / KbT) - (Vef / (KbT * EAccept))))) - (mu / KbT)));
	tmp = 0.0;
	if (KbT <= -2.3e-8)
		tmp = t_3;
	elseif (KbT <= -1e-293)
		tmp = t_1;
	elseif (KbT <= 3e-167)
		tmp = t_2 + (KbT * (NaChar / t_0));
	elseif (KbT <= 3.8e+28)
		tmp = t_1;
	elseif (KbT <= 5.6e+85)
		tmp = t_3;
	else
		tmp = (NaChar / (1.0 + exp((t_0 / 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[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + 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[LessEqual[KbT, -2.3e-8], t$95$3, If[LessEqual[KbT, -1e-293], t$95$1, If[LessEqual[KbT, 3e-167], N[(t$95$2 + N[(KbT * N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 3.8e+28], t$95$1, If[LessEqual[KbT, 5.6e+85], t$95$3, N[(N[(NaChar / N[(1.0 + N[Exp[N[(t$95$0 / 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 4 regimes

2. if KbT < -2.3000000000000001e-8 or 3.7999999999999999e28 < KbT < 5.5999999999999998e85

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 72.5%

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

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in Ev around 0 73.7%

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

       1. *-commutative 73.7%

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

   11. Simplified 73.7%

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

   if -2.3000000000000001e-8 < KbT < -1.0000000000000001e-293 or 2.9999999999999998e-167 < KbT < 3.7999999999999999e28

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.3%

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

      1. *-commutative 31.3%

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

   7. Simplified 31.3%

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

   8. Taylor expanded in NdChar around 0 76.9%

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

   if -1.0000000000000001e-293 < KbT < 2.9999999999999998e-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 34.5%

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

   6. Taylor expanded in KbT around 0 70.2%

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

      1. associate-/l* 70.2%

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

      2. +-commutative 70.2%

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

      3. +-commutative 70.2%

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

      4. associate-+r- 70.2%

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

      5. associate-+l+ 70.2%

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

   8. Simplified 70.2%

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

   if 5.5999999999999998e85 < 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 4 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.3 \cdot 10^{-8}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;KbT \leq -1 \cdot 10^{-293}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 3 \cdot 10^{-167}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + KbT \cdot \frac{NaChar}{Vef + \left(Ev + \left(EAccept - mu\right)\right)}\\ \mathbf{elif}\;KbT \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 - EAccept \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot EAccept}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t\_0 + NaChar \cdot 0.5\\ \mathbf{if}\;NdChar \leq -4.2 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.12 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NaChar}{EAccept \cdot \left(\frac{Vef}{EAccept} + \left(1 + \frac{Ev}{EAccept}\right)\right) - mu}\\ \end{array} \end{array} \]

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 -4.2e+92)
     t_1
     (if (<= NdChar 5.2e+53)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
       (if (<= NdChar 1.12e+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 <= -4.2e+92) {
		tmp = t_1;
	} else if (NdChar <= 5.2e+53) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (NdChar <= 1.12e+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 <= (-4.2d+92)) then
        tmp = t_1
    else if (ndchar <= 5.2d+53) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else if (ndchar <= 1.12d+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 <= -4.2e+92) {
		tmp = t_1;
	} else if (NdChar <= 5.2e+53) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (NdChar <= 1.12e+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 <= -4.2e+92:
		tmp = t_1
	elif NdChar <= 5.2e+53:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	elif NdChar <= 1.12e+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 <= -4.2e+92)
		tmp = t_1;
	elseif (NdChar <= 5.2e+53)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	elseif (NdChar <= 1.12e+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 <= -4.2e+92)
		tmp = t_1;
	elseif (NdChar <= 5.2e+53)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	elseif (NdChar <= 1.12e+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, -4.2e+92], t$95$1, If[LessEqual[NdChar, 5.2e+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, 1.12e+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 < -4.19999999999999972e92 or 5.19999999999999996e53 < NdChar < 1.11999999999999996e169

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -4.19999999999999972e92 < 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 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 1.11999999999999996e169 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.12 \cdot 10^{+169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + KbT \cdot \frac{NaChar}{EAccept \cdot \left(\frac{Vef}{EAccept} + \left(1 + \frac{Ev}{EAccept}\right)\right) - mu}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -9 \cdot 10^{+289} \lor \neg \left(NdChar \leq -6.2 \cdot 10^{+207}\right) \land \left(NdChar \leq -2.85 \cdot 10^{+97} \lor \neg \left(NdChar \leq 1.12 \cdot 10^{+54}\right)\right):\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -9e+289)
         (and (not (<= NdChar -6.2e+207))
              (or (<= NdChar -2.85e+97) (not (<= NdChar 1.12e+54)))))
   (+ (* 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 <= -9e+289) || (!(NdChar <= -6.2e+207) && ((NdChar <= -2.85e+97) || !(NdChar <= 1.12e+54)))) {
		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 <= (-9d+289)) .or. (.not. (ndchar <= (-6.2d+207))) .and. (ndchar <= (-2.85d+97)) .or. (.not. (ndchar <= 1.12d+54))) 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 <= -9e+289) || (!(NdChar <= -6.2e+207) && ((NdChar <= -2.85e+97) || !(NdChar <= 1.12e+54)))) {
		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 <= -9e+289) or (not (NdChar <= -6.2e+207) and ((NdChar <= -2.85e+97) or not (NdChar <= 1.12e+54))):
		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 <= -9e+289) || (!(NdChar <= -6.2e+207) && ((NdChar <= -2.85e+97) || !(NdChar <= 1.12e+54))))
		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 <= -9e+289) || (~((NdChar <= -6.2e+207)) && ((NdChar <= -2.85e+97) || ~((NdChar <= 1.12e+54)))))
		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, -9e+289], And[N[Not[LessEqual[NdChar, -6.2e+207]], $MachinePrecision], Or[LessEqual[NdChar, -2.85e+97], N[Not[LessEqual[NdChar, 1.12e+54]], $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 < -8.99999999999999969e289 or -6.2000000000000005e207 < NdChar < -2.8500000000000001e97 or 1.12e54 < 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 -8.99999999999999969e289 < NdChar < -6.2000000000000005e207 or -2.8500000000000001e97 < NdChar < 1.12e54

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -9 \cdot 10^{+289} \lor \neg \left(NdChar \leq -6.2 \cdot 10^{+207}\right) \land \left(NdChar \leq -2.85 \cdot 10^{+97} \lor \neg \left(NdChar \leq 1.12 \cdot 10^{+54}\right)\right):\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.1 \cdot 10^{+107}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;KbT \leq -4.2 \cdot 10^{+83} \lor \neg \left(KbT \leq -85000\right) \land KbT \leq 2.3 \cdot 10^{+200}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.1e+107)
   (+ (* NdChar 0.5) (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
   (if (or (<= KbT -4.2e+83) (and (not (<= KbT -85000.0)) (<= KbT 2.3e+200)))
     (/ 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 <= -1.1e+107) {
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if ((KbT <= -4.2e+83) || (!(KbT <= -85000.0) && (KbT <= 2.3e+200))) {
		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 <= (-1.1d+107)) then
        tmp = (ndchar * 0.5d0) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if ((kbt <= (-4.2d+83)) .or. (.not. (kbt <= (-85000.0d0))) .and. (kbt <= 2.3d+200)) 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 <= -1.1e+107) {
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if ((KbT <= -4.2e+83) || (!(KbT <= -85000.0) && (KbT <= 2.3e+200))) {
		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 <= -1.1e+107:
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif (KbT <= -4.2e+83) or (not (KbT <= -85000.0) and (KbT <= 2.3e+200)):
		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 <= -1.1e+107)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif ((KbT <= -4.2e+83) || (!(KbT <= -85000.0) && (KbT <= 2.3e+200)))
		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 <= -1.1e+107)
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif ((KbT <= -4.2e+83) || (~((KbT <= -85000.0)) && (KbT <= 2.3e+200)))
		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, -1.1e+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, -85000.0]], $MachinePrecision], LessEqual[KbT, 2.3e+200]]], 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 < -1.1e107

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -1.1e107 < KbT < -4.20000000000000005e83 or -85000 < KbT < 2.30000000000000003e200

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 < -85000 or 2.30000000000000003e200 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.1 \cdot 10^{+107}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;KbT \leq -4.2 \cdot 10^{+83} \lor \neg \left(KbT \leq -85000\right) \land KbT \leq 2.3 \cdot 10^{+200}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -2.8 \cdot 10^{+95} \lor \neg \left(NdChar \leq 1.42 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -2.8e+95) (not (<= NdChar 1.42e+54)))
   (+
    (/ 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 <= -2.8e+95) || !(NdChar <= 1.42e+54)) {
		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 <= (-2.8d+95)) .or. (.not. (ndchar <= 1.42d+54))) 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 <= -2.8e+95) || !(NdChar <= 1.42e+54)) {
		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 <= -2.8e+95) or not (NdChar <= 1.42e+54):
		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 <= -2.8e+95) || !(NdChar <= 1.42e+54))
		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 <= -2.8e+95) || ~((NdChar <= 1.42e+54)))
		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, -2.8e+95], N[Not[LessEqual[NdChar, 1.42e+54]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 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 < -2.7999999999999998e95 or 1.41999999999999995e54 < 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 -2.7999999999999998e95 < NdChar < 1.41999999999999995e54

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.8 \cdot 10^{+95} \lor \neg \left(NdChar \leq 1.42 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 1.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.65e-16)
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
   (if (<= KbT 1.2e+25)
     (/ 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 <= -1.65e-16) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (KbT <= 1.2e+25) {
		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 <= (-1.65d-16)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else if (kbt <= 1.2d+25) 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 <= -1.65e-16) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (KbT <= 1.2e+25) {
		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 <= -1.65e-16:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	elif KbT <= 1.2e+25:
		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 <= -1.65e-16)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	elseif (KbT <= 1.2e+25)
		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 <= -1.65e-16)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	elseif (KbT <= 1.2e+25)
		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, -1.65e-16], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.2e+25], 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 < -1.64999999999999994e-16

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -1.64999999999999994e-16 < KbT < 1.19999999999999998e25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 1.19999999999999998e25 < 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/ 80.3%

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

      2. mul-1-neg 80.3%

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

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 1.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EAccept}{KbT}}\\ \mathbf{if}\;KbT \leq -5.2 \cdot 10^{-9} \lor \neg \left(KbT \leq 3 \cdot 10^{+49}\right):\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ EAccept KbT))))
   (if (or (<= KbT -5.2e-9) (not (<= KbT 3e+49)))
     (- (* NdChar 0.5) (/ NaChar (- -1.0 t_0)))
     (/ NaChar (+ 1.0 t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp((EAccept / KbT));
	double tmp;
	if ((KbT <= -5.2e-9) || !(KbT <= 3e+49)) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - t_0));
	} else {
		tmp = NaChar / (1.0 + t_0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp((eaccept / kbt))
    if ((kbt <= (-5.2d-9)) .or. (.not. (kbt <= 3d+49))) then
        tmp = (ndchar * 0.5d0) - (nachar / ((-1.0d0) - t_0))
    else
        tmp = nachar / (1.0d0 + t_0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp((EAccept / KbT));
	double tmp;
	if ((KbT <= -5.2e-9) || !(KbT <= 3e+49)) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - t_0));
	} else {
		tmp = NaChar / (1.0 + t_0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp((EAccept / KbT))
	tmp = 0
	if (KbT <= -5.2e-9) or not (KbT <= 3e+49):
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - t_0))
	else:
		tmp = NaChar / (1.0 + t_0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(EAccept / KbT))
	tmp = 0.0
	if ((KbT <= -5.2e-9) || !(KbT <= 3e+49))
		tmp = Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 - t_0)));
	else
		tmp = Float64(NaChar / Float64(1.0 + t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp((EAccept / KbT));
	tmp = 0.0;
	if ((KbT <= -5.2e-9) || ~((KbT <= 3e+49)))
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - t_0));
	else
		tmp = NaChar / (1.0 + t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[KbT, -5.2e-9], N[Not[LessEqual[KbT, 3e+49]], $MachinePrecision]], N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if KbT < -5.2000000000000002e-9 or 3.0000000000000002e49 < 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 -5.2000000000000002e-9 < KbT < 3.0000000000000002e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -5.2 \cdot 10^{-9} \lor \neg \left(KbT \leq 3 \cdot 10^{+49}\right):\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.55 \cdot 10^{-14}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 2.05 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2.55e-14)
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
   (if (<= KbT 2.05e+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 <= -2.55e-14) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (KbT <= 2.05e+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 <= (-2.55d-14)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else if (kbt <= 2.05d+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 <= -2.55e-14) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (KbT <= 2.05e+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 <= -2.55e-14:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	elif KbT <= 2.05e+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 <= -2.55e-14)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	elseif (KbT <= 2.05e+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 <= -2.55e-14)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	elseif (KbT <= 2.05e+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, -2.55e-14], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.05e+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 < -2.5499999999999999e-14

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 -2.5499999999999999e-14 < KbT < 2.05e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   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 2.05e49 < 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. Add Preprocessing

Alternative 19: 42.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EAccept}{KbT}}\\ \mathbf{if}\;KbT \leq -5.6 \cdot 10^{-8}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - t\_0}\\ \mathbf{elif}\;KbT \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + t\_0}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ EAccept KbT))))
   (if (<= KbT -5.6e-8)
     (- (* NdChar 0.5) (/ NaChar (- -1.0 t_0)))
     (if (<= KbT 2.2e+49)
       (/ NaChar (+ 1.0 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 = exp((EAccept / KbT));
	double tmp;
	if (KbT <= -5.6e-8) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - t_0));
	} else if (KbT <= 2.2e+49) {
		tmp = NaChar / (1.0 + 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 = exp((eaccept / kbt))
    if (kbt <= (-5.6d-8)) then
        tmp = (ndchar * 0.5d0) - (nachar / ((-1.0d0) - t_0))
    else if (kbt <= 2.2d+49) then
        tmp = nachar / (1.0d0 + 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 = Math.exp((EAccept / KbT));
	double tmp;
	if (KbT <= -5.6e-8) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - t_0));
	} else if (KbT <= 2.2e+49) {
		tmp = NaChar / (1.0 + 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 = math.exp((EAccept / KbT))
	tmp = 0
	if KbT <= -5.6e-8:
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - t_0))
	elif KbT <= 2.2e+49:
		tmp = NaChar / (1.0 + 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 = exp(Float64(EAccept / KbT))
	tmp = 0.0
	if (KbT <= -5.6e-8)
		tmp = Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 - t_0)));
	elseif (KbT <= 2.2e+49)
		tmp = Float64(NaChar / Float64(1.0 + 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 = exp((EAccept / KbT));
	tmp = 0.0;
	if (KbT <= -5.6e-8)
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - t_0));
	elseif (KbT <= 2.2e+49)
		tmp = NaChar / (1.0 + 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[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[KbT, -5.6e-8], N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.2e+49], N[(NaChar / N[(1.0 + t$95$0), $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 < -5.5999999999999999e-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 -5.5999999999999999e-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%

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

   if 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 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -5.6 \cdot 10^{-8}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 - EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right) - \frac{mu}{KbT}\right)} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 3.75 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -6.5e-8)
   (+
    (/
     NaChar
     (+
      1.0
      (-
       (-
        1.0
        (*
         EAccept
         (- (/ -1.0 KbT) (+ (/ Vef (* KbT EAccept)) (/ Ev (* KbT EAccept))))))
       (/ mu KbT))))
    (* NdChar 0.5))
   (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 <= -6.5e-8) {
		tmp = (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT)))) + (NdChar * 0.5);
	} 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 <= (-6.5d-8)) then
        tmp = (nachar / (1.0d0 + ((1.0d0 - (eaccept * (((-1.0d0) / kbt) - ((vef / (kbt * eaccept)) + (ev / (kbt * eaccept)))))) - (mu / kbt)))) + (ndchar * 0.5d0)
    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 <= -6.5e-8) {
		tmp = (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT)))) + (NdChar * 0.5);
	} 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 <= -6.5e-8:
		tmp = (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT)))) + (NdChar * 0.5)
	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 <= -6.5e-8)
		tmp = Float64(Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(KbT * EAccept)) + Float64(Ev / Float64(KbT * EAccept)))))) - Float64(mu / KbT)))) + Float64(NdChar * 0.5));
	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 <= -6.5e-8)
		tmp = (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT)))) + (NdChar * 0.5);
	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, -6.5e-8], N[(N[(NaChar / N[(1.0 + N[(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] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $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 < -6.49999999999999997e-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 -6.49999999999999997e-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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 - EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right) - \frac{mu}{KbT}\right)} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 3.75 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 26.9% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq 1.15 \cdot 10^{-63}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 - EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right) - \frac{mu}{KbT}\right)} + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EDonor 1.15e-63)
   (+
    (/
     NaChar
     (+
      1.0
      (-
       (-
        1.0
        (*
         EAccept
         (- (/ -1.0 KbT) (+ (/ Vef (* KbT EAccept)) (/ Ev (* KbT EAccept))))))
       (/ mu KbT))))
    (/
     NdChar
     (+
      1.0
      (- (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) (/ Ec 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 (EDonor <= 1.15e-63) {
		tmp = (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT)))) + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / 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 (edonor <= 1.15d-63) then
        tmp = (nachar / (1.0d0 + ((1.0d0 - (eaccept * (((-1.0d0) / kbt) - ((vef / (kbt * eaccept)) + (ev / (kbt * eaccept)))))) - (mu / kbt)))) + (ndchar / (1.0d0 + ((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / 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 (EDonor <= 1.15e-63) {
		tmp = (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT)))) + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EDonor <= 1.15e-63:
		tmp = (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT)))) + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / 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 (EDonor <= 1.15e-63)
		tmp = Float64(Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 - Float64(EAccept * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(KbT * EAccept)) + Float64(Ev / Float64(KbT * EAccept)))))) - Float64(mu / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / 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 (EDonor <= 1.15e-63)
		tmp = (NaChar / (1.0 + ((1.0 - (EAccept * ((-1.0 / KbT) - ((Vef / (KbT * EAccept)) + (Ev / (KbT * EAccept)))))) - (mu / KbT)))) + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / 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[EDonor, 1.15e-63], N[(N[(NaChar / N[(1.0 + N[(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] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 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], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EDonor < 1.15e-63

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in 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 1.15e-63 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq 1.15 \cdot 10^{-63}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 - EAccept \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{KbT \cdot EAccept} + \frac{Ev}{KbT \cdot EAccept}\right)\right)\right) - \frac{mu}{KbT}\right)} + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 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))))))