Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 39.5s

Alternatives: 24

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = 2.7271909216903848e-42
  2. Ec = 4.466996980998811e-230
  3. Vef = 9.673793758040852e-52
  4. EDonor = 5.615147326983197e-12
  5. mu = 1.2657195631132388e+47
  6. KbT = -1.0111026027514435e-60
  7. NaChar = -1.218760995368923e-41
  8. Ev = 1.1289686027260533e+221
  9. EAccept = 4.1200819771760135e-109

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

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

FPCore

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

5. Final simplification 100.0%

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

Alternative 2: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := 2 + \frac{EAccept}{KbT}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_4 := \frac{NdChar}{t_0}\\ t_5 := t_4 + \frac{NaChar}{t_0}\\ t_6 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_7 := t_6 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+183}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq -6 \cdot 10^{+30}:\\ \;\;\;\;t_3 + \frac{NaChar}{t_2}\\ \mathbf{elif}\;Vef \leq -1.4 \cdot 10^{-207}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;Vef \leq 2.05 \cdot 10^{-222}:\\ \;\;\;\;t_3 + \frac{NaChar}{\left(t_2 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 7.5 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 5.1 \cdot 10^{-133}:\\ \;\;\;\;t_4 + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;Vef \leq 6.4 \cdot 10^{+27}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;Vef \leq 4.6 \cdot 10^{+137}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq 9.5 \cdot 10^{+148}:\\ \;\;\;\;t_6 + t_1\\ \mathbf{elif}\;Vef \leq 2.65 \cdot 10^{+193}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
        (t_2 (+ 2.0 (/ EAccept KbT)))
        (t_3 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_4 (/ NdChar t_0))
        (t_5 (+ t_4 (/ NaChar t_0)))
        (t_6 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
        (t_7 (+ t_6 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))))
   (if (<= Vef -4.2e+183)
     t_5
     (if (<= Vef -6e+30)
       (+ t_3 (/ NaChar t_2))
       (if (<= Vef -1.4e-207)
         t_7
         (if (<= Vef 2.05e-222)
           (+ t_3 (/ NaChar (- (+ t_2 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT))))
           (if (<= Vef 7.5e-176)
             t_1
             (if (<= Vef 5.1e-133)
               (+ t_4 (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
               (if (<= Vef 1.5e-10)
                 (+
                  (/
                   NaChar
                   (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
                  (/ NdChar (+ 2.0 (/ EDonor KbT))))
                 (if (<= Vef 6.4e+27)
                   t_7
                   (if (<= Vef 4.6e+137)
                     t_5
                     (if (<= Vef 9.5e+148)
                       (+ t_6 t_1)
                       (if (<= Vef 2.65e+193) (+ t_4 t_1) t_5)))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + exp((Ev / KbT)));
	double t_2 = 2.0 + (EAccept / KbT);
	double t_3 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_4 = NdChar / t_0;
	double t_5 = t_4 + (NaChar / t_0);
	double t_6 = NdChar / (1.0 + exp((EDonor / KbT)));
	double t_7 = t_6 + (NaChar / (1.0 + exp((EAccept / KbT))));
	double tmp;
	if (Vef <= -4.2e+183) {
		tmp = t_5;
	} else if (Vef <= -6e+30) {
		tmp = t_3 + (NaChar / t_2);
	} else if (Vef <= -1.4e-207) {
		tmp = t_7;
	} else if (Vef <= 2.05e-222) {
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 7.5e-176) {
		tmp = t_1;
	} else if (Vef <= 5.1e-133) {
		tmp = t_4 + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (Vef <= 1.5e-10) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)));
	} else if (Vef <= 6.4e+27) {
		tmp = t_7;
	} else if (Vef <= 4.6e+137) {
		tmp = t_5;
	} else if (Vef <= 9.5e+148) {
		tmp = t_6 + t_1;
	} else if (Vef <= 2.65e+193) {
		tmp = t_4 + t_1;
	} else {
		tmp = t_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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = nachar / (1.0d0 + exp((ev / kbt)))
    t_2 = 2.0d0 + (eaccept / kbt)
    t_3 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_4 = ndchar / t_0
    t_5 = t_4 + (nachar / t_0)
    t_6 = ndchar / (1.0d0 + exp((edonor / kbt)))
    t_7 = t_6 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    if (vef <= (-4.2d+183)) then
        tmp = t_5
    else if (vef <= (-6d+30)) then
        tmp = t_3 + (nachar / t_2)
    else if (vef <= (-1.4d-207)) then
        tmp = t_7
    else if (vef <= 2.05d-222) then
        tmp = t_3 + (nachar / ((t_2 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    else if (vef <= 7.5d-176) then
        tmp = t_1
    else if (vef <= 5.1d-133) then
        tmp = t_4 + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (vef <= 1.5d-10) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (2.0d0 + (edonor / kbt)))
    else if (vef <= 6.4d+27) then
        tmp = t_7
    else if (vef <= 4.6d+137) then
        tmp = t_5
    else if (vef <= 9.5d+148) then
        tmp = t_6 + t_1
    else if (vef <= 2.65d+193) then
        tmp = t_4 + t_1
    else
        tmp = t_5
    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 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + Math.exp((Ev / KbT)));
	double t_2 = 2.0 + (EAccept / KbT);
	double t_3 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_4 = NdChar / t_0;
	double t_5 = t_4 + (NaChar / t_0);
	double t_6 = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	double t_7 = t_6 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	double tmp;
	if (Vef <= -4.2e+183) {
		tmp = t_5;
	} else if (Vef <= -6e+30) {
		tmp = t_3 + (NaChar / t_2);
	} else if (Vef <= -1.4e-207) {
		tmp = t_7;
	} else if (Vef <= 2.05e-222) {
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 7.5e-176) {
		tmp = t_1;
	} else if (Vef <= 5.1e-133) {
		tmp = t_4 + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (Vef <= 1.5e-10) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)));
	} else if (Vef <= 6.4e+27) {
		tmp = t_7;
	} else if (Vef <= 4.6e+137) {
		tmp = t_5;
	} else if (Vef <= 9.5e+148) {
		tmp = t_6 + t_1;
	} else if (Vef <= 2.65e+193) {
		tmp = t_4 + t_1;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = NaChar / (1.0 + math.exp((Ev / KbT)))
	t_2 = 2.0 + (EAccept / KbT)
	t_3 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_4 = NdChar / t_0
	t_5 = t_4 + (NaChar / t_0)
	t_6 = NdChar / (1.0 + math.exp((EDonor / KbT)))
	t_7 = t_6 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	tmp = 0
	if Vef <= -4.2e+183:
		tmp = t_5
	elif Vef <= -6e+30:
		tmp = t_3 + (NaChar / t_2)
	elif Vef <= -1.4e-207:
		tmp = t_7
	elif Vef <= 2.05e-222:
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	elif Vef <= 7.5e-176:
		tmp = t_1
	elif Vef <= 5.1e-133:
		tmp = t_4 + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif Vef <= 1.5e-10:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)))
	elif Vef <= 6.4e+27:
		tmp = t_7
	elif Vef <= 4.6e+137:
		tmp = t_5
	elif Vef <= 9.5e+148:
		tmp = t_6 + t_1
	elif Vef <= 2.65e+193:
		tmp = t_4 + t_1
	else:
		tmp = t_5
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT))))
	t_2 = Float64(2.0 + Float64(EAccept / KbT))
	t_3 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_4 = Float64(NdChar / t_0)
	t_5 = Float64(t_4 + Float64(NaChar / t_0))
	t_6 = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))))
	t_7 = Float64(t_6 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))))
	tmp = 0.0
	if (Vef <= -4.2e+183)
		tmp = t_5;
	elseif (Vef <= -6e+30)
		tmp = Float64(t_3 + Float64(NaChar / t_2));
	elseif (Vef <= -1.4e-207)
		tmp = t_7;
	elseif (Vef <= 2.05e-222)
		tmp = Float64(t_3 + Float64(NaChar / Float64(Float64(t_2 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	elseif (Vef <= 7.5e-176)
		tmp = t_1;
	elseif (Vef <= 5.1e-133)
		tmp = Float64(t_4 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (Vef <= 1.5e-10)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(2.0 + Float64(EDonor / KbT))));
	elseif (Vef <= 6.4e+27)
		tmp = t_7;
	elseif (Vef <= 4.6e+137)
		tmp = t_5;
	elseif (Vef <= 9.5e+148)
		tmp = Float64(t_6 + t_1);
	elseif (Vef <= 2.65e+193)
		tmp = Float64(t_4 + t_1);
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = NaChar / (1.0 + exp((Ev / KbT)));
	t_2 = 2.0 + (EAccept / KbT);
	t_3 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_4 = NdChar / t_0;
	t_5 = t_4 + (NaChar / t_0);
	t_6 = NdChar / (1.0 + exp((EDonor / KbT)));
	t_7 = t_6 + (NaChar / (1.0 + exp((EAccept / KbT))));
	tmp = 0.0;
	if (Vef <= -4.2e+183)
		tmp = t_5;
	elseif (Vef <= -6e+30)
		tmp = t_3 + (NaChar / t_2);
	elseif (Vef <= -1.4e-207)
		tmp = t_7;
	elseif (Vef <= 2.05e-222)
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	elseif (Vef <= 7.5e-176)
		tmp = t_1;
	elseif (Vef <= 5.1e-133)
		tmp = t_4 + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (Vef <= 1.5e-10)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)));
	elseif (Vef <= 6.4e+27)
		tmp = t_7;
	elseif (Vef <= 4.6e+137)
		tmp = t_5;
	elseif (Vef <= 9.5e+148)
		tmp = t_6 + t_1;
	elseif (Vef <= 2.65e+193)
		tmp = t_4 + t_1;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(NdChar / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -4.2e+183], t$95$5, If[LessEqual[Vef, -6e+30], N[(t$95$3 + N[(NaChar / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -1.4e-207], t$95$7, If[LessEqual[Vef, 2.05e-222], N[(t$95$3 + N[(NaChar / N[(N[(t$95$2 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 7.5e-176], t$95$1, If[LessEqual[Vef, 5.1e-133], N[(t$95$4 + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.5e-10], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 6.4e+27], t$95$7, If[LessEqual[Vef, 4.6e+137], t$95$5, If[LessEqual[Vef, 9.5e+148], N[(t$95$6 + t$95$1), $MachinePrecision], If[LessEqual[Vef, 2.65e+193], N[(t$95$4 + t$95$1), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if Vef < -4.2e183 or 6.4000000000000003e27 < Vef < 4.59999999999999999e137 or 2.6499999999999999e193 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 92.8%

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

   6. Taylor expanded in EAccept around 0 89.1%

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

      1. +-commutative 31.4%

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

   8. Simplified 89.1%

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

   9. Taylor expanded in Vef around inf 87.0%

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

   if -4.2e183 < Vef < -5.99999999999999956e30

   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%

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

   5. Taylor expanded in EAccept around inf 72.3%

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

   6. Taylor expanded in EAccept around 0 65.2%

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

   if -5.99999999999999956e30 < Vef < -1.39999999999999996e-207 or 1.5e-10 < Vef < 6.4000000000000003e27

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 84.6%

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

   6. Taylor expanded in EAccept around inf 60.4%

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

   if -1.39999999999999996e-207 < Vef < 2.0500000000000002e-222

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.5%

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

      1. associate-+r+ 31.0%

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

      2. +-commutative 31.0%

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

   7. Simplified 73.5%

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

   if 2.0500000000000002e-222 < Vef < 7.5e-176

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 70.8%

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

   6. Taylor expanded in Ev around inf 52.9%

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

   7. Taylor expanded in NdChar around 0 72.4%

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

   if 7.5e-176 < Vef < 5.0999999999999999e-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%

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

   5. Taylor expanded in Vef around inf 77.7%

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

   6. Taylor expanded in mu around inf 77.7%

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

      1. associate-*r/ 77.7%

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

      2. mul-1-neg 77.7%

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

   8. Simplified 77.7%

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

   if 5.0999999999999999e-133 < Vef < 1.5e-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%

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

   5. Taylor expanded in EDonor around inf 77.0%

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

   6. Taylor expanded in EDonor around 0 68.9%

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

   if 4.59999999999999999e137 < Vef < 9.5000000000000002e148

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 100.0%

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

   6. Taylor expanded in Ev around inf 76.1%

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

   if 9.5000000000000002e148 < Vef < 2.6499999999999999e193

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 100.0%

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

   6. Taylor expanded in Ev around inf 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+183}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -6 \cdot 10^{+30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;Vef \leq -1.4 \cdot 10^{-207}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.05 \cdot 10^{-222}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 7.5 \cdot 10^{-176}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 5.1 \cdot 10^{-133}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;Vef \leq 6.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.6 \cdot 10^{+137}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 9.5 \cdot 10^{+148}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.65 \cdot 10^{+193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := 2 + \frac{EAccept}{KbT}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_3 := \frac{NdChar}{t_0} + \frac{NaChar}{t_0}\\ t_4 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{if}\;Vef \leq -8.6 \cdot 10^{+186}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -4 \cdot 10^{+40}:\\ \;\;\;\;t_2 + \frac{NaChar}{t_1}\\ \mathbf{elif}\;Vef \leq -3 \cdot 10^{-41}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -5.6 \cdot 10^{-210}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 1.15 \cdot 10^{-268}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.3 \cdot 10^{-221}:\\ \;\;\;\;t_2 + \frac{NaChar}{\left(t_1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 1.82 \cdot 10^{+196}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1 (+ 2.0 (/ EAccept KbT)))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_3 (+ (/ NdChar t_0) (/ NaChar t_0)))
        (t_4
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))))
   (if (<= Vef -8.6e+186)
     t_3
     (if (<= Vef -4e+40)
       (+ t_2 (/ NaChar t_1))
       (if (<= Vef -3e-41)
         t_4
         (if (<= Vef -5.6e-210)
           (+
            (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT))))
            (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
           (if (<= Vef -1.4e-260)
             t_4
             (if (<= Vef 1.15e-268)
               (+
                (/ NdChar (+ 1.0 (exp (/ mu KbT))))
                (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
               (if (<= Vef 4.3e-221)
                 (+
                  t_2
                  (/ NaChar (- (+ t_1 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT))))
                 (if (<= Vef 1.82e+196) t_4 t_3))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + exp((Vef / KbT));
	double t_1 = 2.0 + (EAccept / KbT);
	double t_2 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_3 = (NdChar / t_0) + (NaChar / t_0);
	double t_4 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	double tmp;
	if (Vef <= -8.6e+186) {
		tmp = t_3;
	} else if (Vef <= -4e+40) {
		tmp = t_2 + (NaChar / t_1);
	} else if (Vef <= -3e-41) {
		tmp = t_4;
	} else if (Vef <= -5.6e-210) {
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (Vef <= -1.4e-260) {
		tmp = t_4;
	} else if (Vef <= 1.15e-268) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (Vef <= 4.3e-221) {
		tmp = t_2 + (NaChar / ((t_1 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 1.82e+196) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = 2.0d0 + (eaccept / kbt)
    t_2 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_3 = (ndchar / t_0) + (nachar / t_0)
    t_4 = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    if (vef <= (-8.6d+186)) then
        tmp = t_3
    else if (vef <= (-4d+40)) then
        tmp = t_2 + (nachar / t_1)
    else if (vef <= (-3d-41)) then
        tmp = t_4
    else if (vef <= (-5.6d-210)) then
        tmp = (ndchar / (1.0d0 + exp((-ec / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (vef <= (-1.4d-260)) then
        tmp = t_4
    else if (vef <= 1.15d-268) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (vef <= 4.3d-221) then
        tmp = t_2 + (nachar / ((t_1 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    else if (vef <= 1.82d+196) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = 2.0 + (EAccept / KbT);
	double t_2 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_3 = (NdChar / t_0) + (NaChar / t_0);
	double t_4 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	double tmp;
	if (Vef <= -8.6e+186) {
		tmp = t_3;
	} else if (Vef <= -4e+40) {
		tmp = t_2 + (NaChar / t_1);
	} else if (Vef <= -3e-41) {
		tmp = t_4;
	} else if (Vef <= -5.6e-210) {
		tmp = (NdChar / (1.0 + Math.exp((-Ec / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (Vef <= -1.4e-260) {
		tmp = t_4;
	} else if (Vef <= 1.15e-268) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (Vef <= 4.3e-221) {
		tmp = t_2 + (NaChar / ((t_1 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 1.82e+196) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = 2.0 + (EAccept / KbT)
	t_2 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_3 = (NdChar / t_0) + (NaChar / t_0)
	t_4 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	tmp = 0
	if Vef <= -8.6e+186:
		tmp = t_3
	elif Vef <= -4e+40:
		tmp = t_2 + (NaChar / t_1)
	elif Vef <= -3e-41:
		tmp = t_4
	elif Vef <= -5.6e-210:
		tmp = (NdChar / (1.0 + math.exp((-Ec / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif Vef <= -1.4e-260:
		tmp = t_4
	elif Vef <= 1.15e-268:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif Vef <= 4.3e-221:
		tmp = t_2 + (NaChar / ((t_1 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	elif Vef <= 1.82e+196:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(2.0 + Float64(EAccept / KbT))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_3 = Float64(Float64(NdChar / t_0) + Float64(NaChar / t_0))
	t_4 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))))
	tmp = 0.0
	if (Vef <= -8.6e+186)
		tmp = t_3;
	elseif (Vef <= -4e+40)
		tmp = Float64(t_2 + Float64(NaChar / t_1));
	elseif (Vef <= -3e-41)
		tmp = t_4;
	elseif (Vef <= -5.6e-210)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (Vef <= -1.4e-260)
		tmp = t_4;
	elseif (Vef <= 1.15e-268)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (Vef <= 4.3e-221)
		tmp = Float64(t_2 + Float64(NaChar / Float64(Float64(t_1 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	elseif (Vef <= 1.82e+196)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = 2.0 + (EAccept / KbT);
	t_2 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_3 = (NdChar / t_0) + (NaChar / t_0);
	t_4 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	tmp = 0.0;
	if (Vef <= -8.6e+186)
		tmp = t_3;
	elseif (Vef <= -4e+40)
		tmp = t_2 + (NaChar / t_1);
	elseif (Vef <= -3e-41)
		tmp = t_4;
	elseif (Vef <= -5.6e-210)
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (Vef <= -1.4e-260)
		tmp = t_4;
	elseif (Vef <= 1.15e-268)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (Vef <= 4.3e-221)
		tmp = t_2 + (NaChar / ((t_1 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	elseif (Vef <= 1.82e+196)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NdChar / t$95$0), $MachinePrecision] + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / 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]}, If[LessEqual[Vef, -8.6e+186], t$95$3, If[LessEqual[Vef, -4e+40], N[(t$95$2 + N[(NaChar / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -3e-41], t$95$4, If[LessEqual[Vef, -5.6e-210], N[(N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -1.4e-260], t$95$4, If[LessEqual[Vef, 1.15e-268], 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[Vef, 4.3e-221], N[(t$95$2 + N[(NaChar / N[(N[(t$95$1 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.82e+196], t$95$4, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if Vef < -8.6e186 or 1.82e196 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 100.0%

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

   6. Taylor expanded in EAccept around 0 100.0%

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

      1. +-commutative 30.7%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in Vef around inf 96.6%

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

   if -8.6e186 < Vef < -4.00000000000000012e40

   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%

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

   5. Taylor expanded in EAccept around inf 77.4%

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

   6. Taylor expanded in EAccept around 0 69.7%

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

   if -4.00000000000000012e40 < Vef < -2.99999999999999989e-41 or -5.6e-210 < Vef < -1.3999999999999999e-260 or 4.2999999999999998e-221 < Vef < 1.82e196

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 78.2%

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

   6. Taylor expanded in EAccept around 0 67.0%

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

      1. +-commutative 45.8%

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

   8. Simplified 67.0%

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

   if -2.99999999999999989e-41 < Vef < -5.6e-210

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 69.5%

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

   6. Taylor expanded in Ec around inf 59.5%

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

      1. associate-*r/ 59.5%

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

      2. mul-1-neg 59.5%

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

   8. Simplified 59.5%

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

   if -1.3999999999999999e-260 < Vef < 1.15000000000000005e-268

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 86.1%

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

   6. Taylor expanded in mu around inf 82.0%

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

      1. associate-*r/ 36.6%

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

      2. mul-1-neg 36.6%

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

   8. Simplified 82.0%

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

   if 1.15000000000000005e-268 < Vef < 4.2999999999999998e-221

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.3%

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

      1. associate-+r+ 28.4%

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

      2. +-commutative 28.4%

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

   7. Simplified 76.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -8.6 \cdot 10^{+186}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -4 \cdot 10^{+40}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;Vef \leq -3 \cdot 10^{-41}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -5.6 \cdot 10^{-210}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.15 \cdot 10^{-268}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.3 \cdot 10^{-221}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 1.82 \cdot 10^{+196}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ t_2 := 2 + \frac{EAccept}{KbT}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_4 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_1\\ t_5 := \frac{NdChar}{t_0}\\ \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+183}:\\ \;\;\;\;t_5 + \frac{NaChar}{t_0}\\ \mathbf{elif}\;Vef \leq -4.3 \cdot 10^{+40}:\\ \;\;\;\;t_3 + \frac{NaChar}{t_2}\\ \mathbf{elif}\;Vef \leq -3 \cdot 10^{-41}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq -2 \cdot 10^{-257}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 1.06 \cdot 10^{-268}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.6 \cdot 10^{-221}:\\ \;\;\;\;t_3 + \frac{NaChar}{\left(t_2 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 2.3 \cdot 10^{+149}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
        (t_2 (+ 2.0 (/ EAccept KbT)))
        (t_3 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_4 (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) t_1))
        (t_5 (/ NdChar t_0)))
   (if (<= Vef -4.2e+183)
     (+ t_5 (/ NaChar t_0))
     (if (<= Vef -4.3e+40)
       (+ t_3 (/ NaChar t_2))
       (if (<= Vef -3e-41)
         t_4
         (if (<= Vef -3.8e-210)
           (+
            (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT))))
            (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
           (if (<= Vef -2e-257)
             t_4
             (if (<= Vef 1.06e-268)
               (+
                (/ NdChar (+ 1.0 (exp (/ mu KbT))))
                (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
               (if (<= Vef 1.6e-221)
                 (+
                  t_3
                  (/ NaChar (- (+ t_2 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT))))
                 (if (<= Vef 2.3e+149) t_4 (+ t_5 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 = 1.0 + exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)));
	double t_2 = 2.0 + (EAccept / KbT);
	double t_3 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_4 = (NdChar / (1.0 + exp((EDonor / KbT)))) + t_1;
	double t_5 = NdChar / t_0;
	double tmp;
	if (Vef <= -4.2e+183) {
		tmp = t_5 + (NaChar / t_0);
	} else if (Vef <= -4.3e+40) {
		tmp = t_3 + (NaChar / t_2);
	} else if (Vef <= -3e-41) {
		tmp = t_4;
	} else if (Vef <= -3.8e-210) {
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (Vef <= -2e-257) {
		tmp = t_4;
	} else if (Vef <= 1.06e-268) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (Vef <= 1.6e-221) {
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 2.3e+149) {
		tmp = t_4;
	} else {
		tmp = t_5 + 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))
    t_2 = 2.0d0 + (eaccept / kbt)
    t_3 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_4 = (ndchar / (1.0d0 + exp((edonor / kbt)))) + t_1
    t_5 = ndchar / t_0
    if (vef <= (-4.2d+183)) then
        tmp = t_5 + (nachar / t_0)
    else if (vef <= (-4.3d+40)) then
        tmp = t_3 + (nachar / t_2)
    else if (vef <= (-3d-41)) then
        tmp = t_4
    else if (vef <= (-3.8d-210)) then
        tmp = (ndchar / (1.0d0 + exp((-ec / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (vef <= (-2d-257)) then
        tmp = t_4
    else if (vef <= 1.06d-268) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (vef <= 1.6d-221) then
        tmp = t_3 + (nachar / ((t_2 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    else if (vef <= 2.3d+149) then
        tmp = t_4
    else
        tmp = t_5 + 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 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)));
	double t_2 = 2.0 + (EAccept / KbT);
	double t_3 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_4 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + t_1;
	double t_5 = NdChar / t_0;
	double tmp;
	if (Vef <= -4.2e+183) {
		tmp = t_5 + (NaChar / t_0);
	} else if (Vef <= -4.3e+40) {
		tmp = t_3 + (NaChar / t_2);
	} else if (Vef <= -3e-41) {
		tmp = t_4;
	} else if (Vef <= -3.8e-210) {
		tmp = (NdChar / (1.0 + Math.exp((-Ec / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (Vef <= -2e-257) {
		tmp = t_4;
	} else if (Vef <= 1.06e-268) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (Vef <= 1.6e-221) {
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 2.3e+149) {
		tmp = t_4;
	} else {
		tmp = t_5 + t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))
	t_2 = 2.0 + (EAccept / KbT)
	t_3 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_4 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + t_1
	t_5 = NdChar / t_0
	tmp = 0
	if Vef <= -4.2e+183:
		tmp = t_5 + (NaChar / t_0)
	elif Vef <= -4.3e+40:
		tmp = t_3 + (NaChar / t_2)
	elif Vef <= -3e-41:
		tmp = t_4
	elif Vef <= -3.8e-210:
		tmp = (NdChar / (1.0 + math.exp((-Ec / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif Vef <= -2e-257:
		tmp = t_4
	elif Vef <= 1.06e-268:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif Vef <= 1.6e-221:
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	elif Vef <= 2.3e+149:
		tmp = t_4
	else:
		tmp = t_5 + t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT))))
	t_2 = Float64(2.0 + Float64(EAccept / KbT))
	t_3 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_4 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + t_1)
	t_5 = Float64(NdChar / t_0)
	tmp = 0.0
	if (Vef <= -4.2e+183)
		tmp = Float64(t_5 + Float64(NaChar / t_0));
	elseif (Vef <= -4.3e+40)
		tmp = Float64(t_3 + Float64(NaChar / t_2));
	elseif (Vef <= -3e-41)
		tmp = t_4;
	elseif (Vef <= -3.8e-210)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (Vef <= -2e-257)
		tmp = t_4;
	elseif (Vef <= 1.06e-268)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (Vef <= 1.6e-221)
		tmp = Float64(t_3 + Float64(NaChar / Float64(Float64(t_2 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	elseif (Vef <= 2.3e+149)
		tmp = t_4;
	else
		tmp = Float64(t_5 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)));
	t_2 = 2.0 + (EAccept / KbT);
	t_3 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_4 = (NdChar / (1.0 + exp((EDonor / KbT)))) + t_1;
	t_5 = NdChar / t_0;
	tmp = 0.0;
	if (Vef <= -4.2e+183)
		tmp = t_5 + (NaChar / t_0);
	elseif (Vef <= -4.3e+40)
		tmp = t_3 + (NaChar / t_2);
	elseif (Vef <= -3e-41)
		tmp = t_4;
	elseif (Vef <= -3.8e-210)
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (Vef <= -2e-257)
		tmp = t_4;
	elseif (Vef <= 1.06e-268)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (Vef <= 1.6e-221)
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	elseif (Vef <= 2.3e+149)
		tmp = t_4;
	else
		tmp = t_5 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(NdChar / t$95$0), $MachinePrecision]}, If[LessEqual[Vef, -4.2e+183], N[(t$95$5 + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -4.3e+40], N[(t$95$3 + N[(NaChar / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -3e-41], t$95$4, If[LessEqual[Vef, -3.8e-210], N[(N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -2e-257], t$95$4, If[LessEqual[Vef, 1.06e-268], 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[Vef, 1.6e-221], N[(t$95$3 + N[(NaChar / N[(N[(t$95$2 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 2.3e+149], t$95$4, N[(t$95$5 + t$95$1), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if Vef < -4.2e183

   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%

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

   5. Taylor expanded in Vef around inf 99.9%

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

   6. Taylor expanded in EAccept around 0 99.9%

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

      1. +-commutative 31.5%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in Vef around inf 99.9%

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

   if -4.2e183 < Vef < -4.3000000000000002e40

   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%

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

   5. Taylor expanded in EAccept around inf 77.4%

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

   6. Taylor expanded in EAccept around 0 69.7%

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

   if -4.3000000000000002e40 < Vef < -2.99999999999999989e-41 or -3.80000000000000003e-210 < Vef < -2e-257 or 1.60000000000000008e-221 < Vef < 2.2999999999999998e149

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 80.2%

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

   6. Taylor expanded in EAccept around 0 68.2%

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

      1. +-commutative 46.5%

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

   8. Simplified 68.2%

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

   if -2.99999999999999989e-41 < Vef < -3.80000000000000003e-210

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 69.5%

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

   6. Taylor expanded in Ec around inf 59.5%

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

      1. associate-*r/ 59.5%

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

      2. mul-1-neg 59.5%

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

   8. Simplified 59.5%

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

   if -2e-257 < Vef < 1.06e-268

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 86.1%

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

   6. Taylor expanded in mu around inf 82.0%

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

      1. associate-*r/ 36.6%

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

      2. mul-1-neg 36.6%

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

   8. Simplified 82.0%

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

   if 1.06e-268 < Vef < 1.60000000000000008e-221

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.3%

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

      1. associate-+r+ 28.4%

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

      2. +-commutative 28.4%

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

   7. Simplified 76.3%

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

   if 2.2999999999999998e149 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 97.4%

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

   6. Taylor expanded in EAccept around 0 94.8%

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

      1. +-commutative 31.0%

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

   8. Simplified 94.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{\left(Vef + Ev\right) - mu}{KbT}}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+183}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -4.3 \cdot 10^{+40}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;Vef \leq -3 \cdot 10^{-41}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq -2 \cdot 10^{-257}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.06 \cdot 10^{-268}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.6 \cdot 10^{-221}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 2.3 \cdot 10^{+149}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := 2 + \frac{EAccept}{KbT}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_4 := \frac{NdChar}{t_0} + \frac{NaChar}{t_0}\\ t_5 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;Vef \leq -2.65 \cdot 10^{+184}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -6.5 \cdot 10^{+33}:\\ \;\;\;\;t_3 + \frac{NaChar}{t_2}\\ \mathbf{elif}\;Vef \leq -1.6 \cdot 10^{-207}:\\ \;\;\;\;t_5 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.05 \cdot 10^{-222}:\\ \;\;\;\;t_3 + \frac{NaChar}{\left(t_2 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 6.8 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 1.55 \cdot 10^{-103}:\\ \;\;\;\;t_5 + t_1\\ \mathbf{elif}\;Vef \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
        (t_2 (+ 2.0 (/ EAccept KbT)))
        (t_3 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_4 (+ (/ NdChar t_0) (/ NaChar t_0)))
        (t_5 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
   (if (<= Vef -2.65e+184)
     t_4
     (if (<= Vef -6.5e+33)
       (+ t_3 (/ NaChar t_2))
       (if (<= Vef -1.6e-207)
         (+ t_5 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
         (if (<= Vef 2.05e-222)
           (+ t_3 (/ NaChar (- (+ t_2 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT))))
           (if (<= Vef 6.8e-177)
             t_1
             (if (<= Vef 1.55e-103)
               (+ t_5 t_1)
               (if (<= Vef 7.5e+14) t_1 t_4)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + exp((Ev / KbT)));
	double t_2 = 2.0 + (EAccept / KbT);
	double t_3 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_4 = (NdChar / t_0) + (NaChar / t_0);
	double t_5 = NdChar / (1.0 + exp((EDonor / KbT)));
	double tmp;
	if (Vef <= -2.65e+184) {
		tmp = t_4;
	} else if (Vef <= -6.5e+33) {
		tmp = t_3 + (NaChar / t_2);
	} else if (Vef <= -1.6e-207) {
		tmp = t_5 + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (Vef <= 2.05e-222) {
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 6.8e-177) {
		tmp = t_1;
	} else if (Vef <= 1.55e-103) {
		tmp = t_5 + t_1;
	} else if (Vef <= 7.5e+14) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = nachar / (1.0d0 + exp((ev / kbt)))
    t_2 = 2.0d0 + (eaccept / kbt)
    t_3 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_4 = (ndchar / t_0) + (nachar / t_0)
    t_5 = ndchar / (1.0d0 + exp((edonor / kbt)))
    if (vef <= (-2.65d+184)) then
        tmp = t_4
    else if (vef <= (-6.5d+33)) then
        tmp = t_3 + (nachar / t_2)
    else if (vef <= (-1.6d-207)) then
        tmp = t_5 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (vef <= 2.05d-222) then
        tmp = t_3 + (nachar / ((t_2 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    else if (vef <= 6.8d-177) then
        tmp = t_1
    else if (vef <= 1.55d-103) then
        tmp = t_5 + t_1
    else if (vef <= 7.5d+14) then
        tmp = t_1
    else
        tmp = t_4
    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 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + Math.exp((Ev / KbT)));
	double t_2 = 2.0 + (EAccept / KbT);
	double t_3 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_4 = (NdChar / t_0) + (NaChar / t_0);
	double t_5 = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	double tmp;
	if (Vef <= -2.65e+184) {
		tmp = t_4;
	} else if (Vef <= -6.5e+33) {
		tmp = t_3 + (NaChar / t_2);
	} else if (Vef <= -1.6e-207) {
		tmp = t_5 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (Vef <= 2.05e-222) {
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 6.8e-177) {
		tmp = t_1;
	} else if (Vef <= 1.55e-103) {
		tmp = t_5 + t_1;
	} else if (Vef <= 7.5e+14) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = NaChar / (1.0 + math.exp((Ev / KbT)))
	t_2 = 2.0 + (EAccept / KbT)
	t_3 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_4 = (NdChar / t_0) + (NaChar / t_0)
	t_5 = NdChar / (1.0 + math.exp((EDonor / KbT)))
	tmp = 0
	if Vef <= -2.65e+184:
		tmp = t_4
	elif Vef <= -6.5e+33:
		tmp = t_3 + (NaChar / t_2)
	elif Vef <= -1.6e-207:
		tmp = t_5 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif Vef <= 2.05e-222:
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	elif Vef <= 6.8e-177:
		tmp = t_1
	elif Vef <= 1.55e-103:
		tmp = t_5 + t_1
	elif Vef <= 7.5e+14:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT))))
	t_2 = Float64(2.0 + Float64(EAccept / KbT))
	t_3 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_4 = Float64(Float64(NdChar / t_0) + Float64(NaChar / t_0))
	t_5 = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))))
	tmp = 0.0
	if (Vef <= -2.65e+184)
		tmp = t_4;
	elseif (Vef <= -6.5e+33)
		tmp = Float64(t_3 + Float64(NaChar / t_2));
	elseif (Vef <= -1.6e-207)
		tmp = Float64(t_5 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (Vef <= 2.05e-222)
		tmp = Float64(t_3 + Float64(NaChar / Float64(Float64(t_2 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	elseif (Vef <= 6.8e-177)
		tmp = t_1;
	elseif (Vef <= 1.55e-103)
		tmp = Float64(t_5 + t_1);
	elseif (Vef <= 7.5e+14)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = NaChar / (1.0 + exp((Ev / KbT)));
	t_2 = 2.0 + (EAccept / KbT);
	t_3 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_4 = (NdChar / t_0) + (NaChar / t_0);
	t_5 = NdChar / (1.0 + exp((EDonor / KbT)));
	tmp = 0.0;
	if (Vef <= -2.65e+184)
		tmp = t_4;
	elseif (Vef <= -6.5e+33)
		tmp = t_3 + (NaChar / t_2);
	elseif (Vef <= -1.6e-207)
		tmp = t_5 + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (Vef <= 2.05e-222)
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	elseif (Vef <= 6.8e-177)
		tmp = t_1;
	elseif (Vef <= 1.55e-103)
		tmp = t_5 + t_1;
	elseif (Vef <= 7.5e+14)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(NdChar / t$95$0), $MachinePrecision] + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -2.65e+184], t$95$4, If[LessEqual[Vef, -6.5e+33], N[(t$95$3 + N[(NaChar / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -1.6e-207], N[(t$95$5 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 2.05e-222], N[(t$95$3 + N[(NaChar / N[(N[(t$95$2 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 6.8e-177], t$95$1, If[LessEqual[Vef, 1.55e-103], N[(t$95$5 + t$95$1), $MachinePrecision], If[LessEqual[Vef, 7.5e+14], t$95$1, t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if Vef < -2.65000000000000011e184 or 7.5e14 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 89.7%

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

   6. Taylor expanded in EAccept around 0 85.5%

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

      1. +-commutative 32.3%

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

   8. Simplified 85.5%

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

   9. Taylor expanded in Vef around inf 80.7%

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

   if -2.65000000000000011e184 < Vef < -6.49999999999999993e33

   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%

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

   5. Taylor expanded in EAccept around inf 72.3%

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

   6. Taylor expanded in EAccept around 0 65.2%

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

   if -6.49999999999999993e33 < Vef < -1.6000000000000002e-207

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 85.5%

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

   6. Taylor expanded in EAccept around inf 59.0%

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

   if -1.6000000000000002e-207 < Vef < 2.0500000000000002e-222

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.5%

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

      1. associate-+r+ 31.0%

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

      2. +-commutative 31.0%

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

   7. Simplified 73.5%

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

   if 2.0500000000000002e-222 < Vef < 6.8000000000000001e-177 or 1.5500000000000001e-103 < Vef < 7.5e14

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 69.9%

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

   6. Taylor expanded in Ev around inf 45.1%

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

   7. Taylor expanded in NdChar around 0 43.3%

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

   if 6.8000000000000001e-177 < Vef < 1.5500000000000001e-103

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 88.4%

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

   6. Taylor expanded in Ev around inf 66.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.65 \cdot 10^{+184}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -6.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;Vef \leq -1.6 \cdot 10^{-207}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.05 \cdot 10^{-222}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 6.8 \cdot 10^{-177}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.55 \cdot 10^{-103}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ t_2 := 2 + \frac{EAccept}{KbT}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_4 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_1\\ t_5 := \frac{NdChar}{t_0}\\ \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+183}:\\ \;\;\;\;t_5 + \frac{NaChar}{t_0}\\ \mathbf{elif}\;Vef \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;t_3 + \frac{NaChar}{t_2}\\ \mathbf{elif}\;Vef \leq -8 \cdot 10^{-84}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_1\\ \mathbf{elif}\;Vef \leq 1.25 \cdot 10^{-268}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 1.2 \cdot 10^{-221}:\\ \;\;\;\;t_3 + \frac{NaChar}{\left(t_2 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
        (t_2 (+ 2.0 (/ EAccept KbT)))
        (t_3 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_4 (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_1))
        (t_5 (/ NdChar t_0)))
   (if (<= Vef -4.2e+183)
     (+ t_5 (/ NaChar t_0))
     (if (<= Vef -1.05e+41)
       (+ t_3 (/ NaChar t_2))
       (if (<= Vef -8e-84)
         (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) t_1)
         (if (<= Vef 1.25e-268)
           t_4
           (if (<= Vef 1.2e-221)
             (+
              t_3
              (/ NaChar (- (+ t_2 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT))))
             (if (<= Vef 2.1e+44) t_4 (+ t_5 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 = 1.0 + exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)));
	double t_2 = 2.0 + (EAccept / KbT);
	double t_3 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_4 = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	double t_5 = NdChar / t_0;
	double tmp;
	if (Vef <= -4.2e+183) {
		tmp = t_5 + (NaChar / t_0);
	} else if (Vef <= -1.05e+41) {
		tmp = t_3 + (NaChar / t_2);
	} else if (Vef <= -8e-84) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + t_1;
	} else if (Vef <= 1.25e-268) {
		tmp = t_4;
	} else if (Vef <= 1.2e-221) {
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 2.1e+44) {
		tmp = t_4;
	} else {
		tmp = t_5 + 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))
    t_2 = 2.0d0 + (eaccept / kbt)
    t_3 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_4 = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_1
    t_5 = ndchar / t_0
    if (vef <= (-4.2d+183)) then
        tmp = t_5 + (nachar / t_0)
    else if (vef <= (-1.05d+41)) then
        tmp = t_3 + (nachar / t_2)
    else if (vef <= (-8d-84)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + t_1
    else if (vef <= 1.25d-268) then
        tmp = t_4
    else if (vef <= 1.2d-221) then
        tmp = t_3 + (nachar / ((t_2 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    else if (vef <= 2.1d+44) then
        tmp = t_4
    else
        tmp = t_5 + 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 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)));
	double t_2 = 2.0 + (EAccept / KbT);
	double t_3 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_4 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_1;
	double t_5 = NdChar / t_0;
	double tmp;
	if (Vef <= -4.2e+183) {
		tmp = t_5 + (NaChar / t_0);
	} else if (Vef <= -1.05e+41) {
		tmp = t_3 + (NaChar / t_2);
	} else if (Vef <= -8e-84) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + t_1;
	} else if (Vef <= 1.25e-268) {
		tmp = t_4;
	} else if (Vef <= 1.2e-221) {
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 2.1e+44) {
		tmp = t_4;
	} else {
		tmp = t_5 + t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))
	t_2 = 2.0 + (EAccept / KbT)
	t_3 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_4 = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_1
	t_5 = NdChar / t_0
	tmp = 0
	if Vef <= -4.2e+183:
		tmp = t_5 + (NaChar / t_0)
	elif Vef <= -1.05e+41:
		tmp = t_3 + (NaChar / t_2)
	elif Vef <= -8e-84:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + t_1
	elif Vef <= 1.25e-268:
		tmp = t_4
	elif Vef <= 1.2e-221:
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	elif Vef <= 2.1e+44:
		tmp = t_4
	else:
		tmp = t_5 + t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT))))
	t_2 = Float64(2.0 + Float64(EAccept / KbT))
	t_3 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_4 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_1)
	t_5 = Float64(NdChar / t_0)
	tmp = 0.0
	if (Vef <= -4.2e+183)
		tmp = Float64(t_5 + Float64(NaChar / t_0));
	elseif (Vef <= -1.05e+41)
		tmp = Float64(t_3 + Float64(NaChar / t_2));
	elseif (Vef <= -8e-84)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + t_1);
	elseif (Vef <= 1.25e-268)
		tmp = t_4;
	elseif (Vef <= 1.2e-221)
		tmp = Float64(t_3 + Float64(NaChar / Float64(Float64(t_2 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	elseif (Vef <= 2.1e+44)
		tmp = t_4;
	else
		tmp = Float64(t_5 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)));
	t_2 = 2.0 + (EAccept / KbT);
	t_3 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_4 = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	t_5 = NdChar / t_0;
	tmp = 0.0;
	if (Vef <= -4.2e+183)
		tmp = t_5 + (NaChar / t_0);
	elseif (Vef <= -1.05e+41)
		tmp = t_3 + (NaChar / t_2);
	elseif (Vef <= -8e-84)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + t_1;
	elseif (Vef <= 1.25e-268)
		tmp = t_4;
	elseif (Vef <= 1.2e-221)
		tmp = t_3 + (NaChar / ((t_2 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	elseif (Vef <= 2.1e+44)
		tmp = t_4;
	else
		tmp = t_5 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(NdChar / t$95$0), $MachinePrecision]}, If[LessEqual[Vef, -4.2e+183], N[(t$95$5 + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -1.05e+41], N[(t$95$3 + N[(NaChar / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -8e-84], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[Vef, 1.25e-268], t$95$4, If[LessEqual[Vef, 1.2e-221], N[(t$95$3 + N[(NaChar / N[(N[(t$95$2 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 2.1e+44], t$95$4, N[(t$95$5 + t$95$1), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if Vef < -4.2e183

   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%

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

   5. Taylor expanded in Vef around inf 99.9%

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

   6. Taylor expanded in EAccept around 0 99.9%

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

      1. +-commutative 31.5%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in Vef around inf 99.9%

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

   if -4.2e183 < Vef < -1.05e41

   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%

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

   5. Taylor expanded in EAccept around inf 77.4%

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

   6. Taylor expanded in EAccept around 0 69.7%

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

   if -1.05e41 < Vef < -8.0000000000000003e-84

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 92.7%

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

   6. Taylor expanded in EAccept around 0 89.7%

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

      1. +-commutative 61.7%

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

   8. Simplified 89.7%

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

   if -8.0000000000000003e-84 < Vef < 1.25e-268 or 1.20000000000000012e-221 < Vef < 2.09999999999999987e44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 81.9%

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

   6. Taylor expanded in EAccept around 0 74.2%

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

      1. +-commutative 47.1%

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

   8. Simplified 74.2%

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

   if 1.25e-268 < Vef < 1.20000000000000012e-221

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.3%

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

      1. associate-+r+ 28.4%

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

      2. +-commutative 28.4%

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

   7. Simplified 76.3%

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

   if 2.09999999999999987e44 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 86.3%

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

   6. Taylor expanded in EAccept around 0 81.6%

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

      1. +-commutative 33.3%

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

   8. Simplified 81.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+183}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;Vef \leq -8 \cdot 10^{-84}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.25 \cdot 10^{-268}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.2 \cdot 10^{-221}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_3 := \frac{NdChar}{t_0}\\ \mathbf{if}\;Vef \leq -7 \cdot 10^{+178}:\\ \;\;\;\;t_3 + \frac{NaChar}{t_0}\\ \mathbf{elif}\;Vef \leq -2.2 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 5 \cdot 10^{-265}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_1\\ \mathbf{elif}\;Vef \leq 6.3 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
        (t_2
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_3 (/ NdChar t_0)))
   (if (<= Vef -7e+178)
     (+ t_3 (/ NaChar t_0))
     (if (<= Vef -2.2e-259)
       t_2
       (if (<= Vef 5e-265)
         (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_1)
         (if (<= Vef 6.3e+149) t_2 (+ t_3 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 = 1.0 + exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)));
	double t_2 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_3 = NdChar / t_0;
	double tmp;
	if (Vef <= -7e+178) {
		tmp = t_3 + (NaChar / t_0);
	} else if (Vef <= -2.2e-259) {
		tmp = t_2;
	} else if (Vef <= 5e-265) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	} else if (Vef <= 6.3e+149) {
		tmp = t_2;
	} else {
		tmp = t_3 + 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) :: t_3
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))
    t_2 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_3 = ndchar / t_0
    if (vef <= (-7d+178)) then
        tmp = t_3 + (nachar / t_0)
    else if (vef <= (-2.2d-259)) then
        tmp = t_2
    else if (vef <= 5d-265) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_1
    else if (vef <= 6.3d+149) then
        tmp = t_2
    else
        tmp = t_3 + 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 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)));
	double t_2 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_3 = NdChar / t_0;
	double tmp;
	if (Vef <= -7e+178) {
		tmp = t_3 + (NaChar / t_0);
	} else if (Vef <= -2.2e-259) {
		tmp = t_2;
	} else if (Vef <= 5e-265) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_1;
	} else if (Vef <= 6.3e+149) {
		tmp = t_2;
	} else {
		tmp = t_3 + t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))
	t_2 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_3 = NdChar / t_0
	tmp = 0
	if Vef <= -7e+178:
		tmp = t_3 + (NaChar / t_0)
	elif Vef <= -2.2e-259:
		tmp = t_2
	elif Vef <= 5e-265:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_1
	elif Vef <= 6.3e+149:
		tmp = t_2
	else:
		tmp = t_3 + t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT))))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_3 = Float64(NdChar / t_0)
	tmp = 0.0
	if (Vef <= -7e+178)
		tmp = Float64(t_3 + Float64(NaChar / t_0));
	elseif (Vef <= -2.2e-259)
		tmp = t_2;
	elseif (Vef <= 5e-265)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_1);
	elseif (Vef <= 6.3e+149)
		tmp = t_2;
	else
		tmp = Float64(t_3 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)));
	t_2 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_3 = NdChar / t_0;
	tmp = 0.0;
	if (Vef <= -7e+178)
		tmp = t_3 + (NaChar / t_0);
	elseif (Vef <= -2.2e-259)
		tmp = t_2;
	elseif (Vef <= 5e-265)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	elseif (Vef <= 6.3e+149)
		tmp = t_2;
	else
		tmp = t_3 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar / t$95$0), $MachinePrecision]}, If[LessEqual[Vef, -7e+178], N[(t$95$3 + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -2.2e-259], t$95$2, If[LessEqual[Vef, 5e-265], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[Vef, 6.3e+149], t$95$2, N[(t$95$3 + t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -7.00000000000000001e178

   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%

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

   5. Taylor expanded in Vef around inf 96.3%

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

   6. Taylor expanded in EAccept around 0 96.3%

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

      1. +-commutative 29.9%

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

   8. Simplified 96.3%

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

   9. Taylor expanded in Vef around inf 96.3%

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

   if -7.00000000000000001e178 < Vef < -2.2000000000000001e-259 or 5.0000000000000001e-265 < Vef < 6.3e149

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 75.5%

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

   if -2.2000000000000001e-259 < Vef < 5.0000000000000001e-265

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 86.8%

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

   6. Taylor expanded in EAccept around 0 86.8%

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

      1. +-commutative 40.3%

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

   8. Simplified 86.8%

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

   if 6.3e149 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 97.4%

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

   6. Taylor expanded in EAccept around 0 94.8%

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

      1. +-commutative 31.0%

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

   8. Simplified 94.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -7 \cdot 10^{+178}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -2.2 \cdot 10^{-259}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 5 \cdot 10^{-265}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 6.3 \cdot 10^{+149}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;EDonor \leq -2.25 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq -64000000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -3.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= EDonor -2.25e+105)
     t_1
     (if (<= EDonor -64000000000.0)
       (+
        (/ NdChar (+ 1.0 (exp (/ mu KbT))))
        (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
       (if (<= EDonor -3.9e-37)
         (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
         (if (<= EDonor 2.3e+25)
           (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
           t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -2.25e+105) {
		tmp = t_1;
	} else if (EDonor <= -64000000000.0) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	} else if (EDonor <= -3.9e-37) {
		tmp = NaChar / (1.0 + exp((Ev / KbT)));
	} else if (EDonor <= 2.3e+25) {
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (edonor <= (-2.25d+105)) then
        tmp = t_1
    else if (edonor <= (-64000000000.0d0)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    else if (edonor <= (-3.9d-37)) then
        tmp = nachar / (1.0d0 + exp((ev / kbt)))
    else if (edonor <= 2.3d+25) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -2.25e+105) {
		tmp = t_1;
	} else if (EDonor <= -64000000000.0) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	} else if (EDonor <= -3.9e-37) {
		tmp = NaChar / (1.0 + Math.exp((Ev / KbT)));
	} else if (EDonor <= 2.3e+25) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if EDonor <= -2.25e+105:
		tmp = t_1
	elif EDonor <= -64000000000.0:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	elif EDonor <= -3.9e-37:
		tmp = NaChar / (1.0 + math.exp((Ev / KbT)))
	elif EDonor <= 2.3e+25:
		tmp = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (EDonor <= -2.25e+105)
		tmp = t_1;
	elseif (EDonor <= -64000000000.0)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	elseif (EDonor <= -3.9e-37)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT))));
	elseif (EDonor <= 2.3e+25)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (EDonor <= -2.25e+105)
		tmp = t_1;
	elseif (EDonor <= -64000000000.0)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	elseif (EDonor <= -3.9e-37)
		tmp = NaChar / (1.0 + exp((Ev / KbT)));
	elseif (EDonor <= 2.3e+25)
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - 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[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -2.25e+105], t$95$1, If[LessEqual[EDonor, -64000000000.0], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / 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], If[LessEqual[EDonor, -3.9e-37], N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 2.3e+25], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if EDonor < -2.2500000000000001e105 or 2.2999999999999998e25 < 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%

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

   5. Taylor expanded in EDonor around inf 86.1%

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

   if -2.2500000000000001e105 < EDonor < -6.4e10

   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%

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

   5. Taylor expanded in mu around inf 92.9%

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

   6. Taylor expanded in EAccept around 0 86.0%

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

      1. +-commutative 37.2%

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

   8. Simplified 86.0%

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

   if -6.4e10 < EDonor < -3.8999999999999999e-37

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 63.3%

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

   6. Taylor expanded in Ev around inf 21.7%

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

   7. Taylor expanded in NdChar around 0 38.4%

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

   if -3.8999999999999999e-37 < EDonor < 2.2999999999999998e25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 78.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -2.25 \cdot 10^{+105}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -64000000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -3.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_2 := t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -5.3 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.2 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 6.2 \cdot 10^{-225}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT))))))
        (t_2 (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -5.3e+54)
     t_2
     (if (<= Vef 1.2e-268)
       t_1
       (if (<= Vef 6.2e-225)
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/
           NaChar
           (-
            (+ (+ 2.0 (/ EAccept KbT)) (+ (/ Vef KbT) (/ Ev KbT)))
            (/ mu KbT))))
         (if (<= Vef 1.05e+27) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -5.3e+54) {
		tmp = t_2;
	} else if (Vef <= 1.2e-268) {
		tmp = t_1;
	} else if (Vef <= 6.2e-225) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 1.05e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    t_2 = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-5.3d+54)) then
        tmp = t_2
    else if (vef <= 1.2d-268) then
        tmp = t_1
    else if (vef <= 6.2d-225) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (((2.0d0 + (eaccept / kbt)) + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    else if (vef <= 1.05d+27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -5.3e+54) {
		tmp = t_2;
	} else if (Vef <= 1.2e-268) {
		tmp = t_1;
	} else if (Vef <= 6.2e-225) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 1.05e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	t_2 = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -5.3e+54:
		tmp = t_2
	elif Vef <= 1.2e-268:
		tmp = t_1
	elif Vef <= 6.2e-225:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	elif Vef <= 1.05e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	t_2 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -5.3e+54)
		tmp = t_2;
	elseif (Vef <= 1.2e-268)
		tmp = t_1;
	elseif (Vef <= 6.2e-225)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(Float64(2.0 + Float64(EAccept / KbT)) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	elseif (Vef <= 1.05e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	t_2 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -5.3e+54)
		tmp = t_2;
	elseif (Vef <= 1.2e-268)
		tmp = t_1;
	elseif (Vef <= 6.2e-225)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	elseif (Vef <= 1.05e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -5.3e+54], t$95$2, If[LessEqual[Vef, 1.2e-268], t$95$1, If[LessEqual[Vef, 6.2e-225], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.05e+27], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -5.30000000000000018e54 or 1.04999999999999997e27 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 86.7%

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

   if -5.30000000000000018e54 < Vef < 1.1999999999999999e-268 or 6.19999999999999993e-225 < Vef < 1.04999999999999997e27

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 81.4%

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

   if 1.1999999999999999e-268 < Vef < 6.19999999999999993e-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%

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

   5. Taylor expanded in KbT around inf 86.2%

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

      1. associate-+r+ 31.6%

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

      2. +-commutative 31.6%

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

   7. Simplified 86.2%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -5.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.2 \cdot 10^{-268}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 6.2 \cdot 10^{-225}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := 2 + \frac{EAccept}{KbT}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_3 := \frac{NdChar}{t_0} + \frac{NaChar}{t_0}\\ \mathbf{if}\;Vef \leq -2.65 \cdot 10^{+184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -6.4 \cdot 10^{+34}:\\ \;\;\;\;t_2 + \frac{NaChar}{t_1}\\ \mathbf{elif}\;Vef \leq -2.45 \cdot 10^{-207}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.2 \cdot 10^{-222}:\\ \;\;\;\;t_2 + \frac{NaChar}{\left(t_1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 4.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1 (+ 2.0 (/ EAccept KbT)))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_3 (+ (/ NdChar t_0) (/ NaChar t_0))))
   (if (<= Vef -2.65e+184)
     t_3
     (if (<= Vef -6.4e+34)
       (+ t_2 (/ NaChar t_1))
       (if (<= Vef -2.45e-207)
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
         (if (<= Vef 8.2e-222)
           (+ t_2 (/ NaChar (- (+ t_1 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT))))
           (if (<= Vef 4.3e+15)
             (+
              (/ NdChar (+ 1.0 (exp (/ mu KbT))))
              (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
             t_3)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + exp((Vef / KbT));
	double t_1 = 2.0 + (EAccept / KbT);
	double t_2 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_3 = (NdChar / t_0) + (NaChar / t_0);
	double tmp;
	if (Vef <= -2.65e+184) {
		tmp = t_3;
	} else if (Vef <= -6.4e+34) {
		tmp = t_2 + (NaChar / t_1);
	} else if (Vef <= -2.45e-207) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (Vef <= 8.2e-222) {
		tmp = t_2 + (NaChar / ((t_1 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 4.3e+15) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = 2.0d0 + (eaccept / kbt)
    t_2 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_3 = (ndchar / t_0) + (nachar / t_0)
    if (vef <= (-2.65d+184)) then
        tmp = t_3
    else if (vef <= (-6.4d+34)) then
        tmp = t_2 + (nachar / t_1)
    else if (vef <= (-2.45d-207)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (vef <= 8.2d-222) then
        tmp = t_2 + (nachar / ((t_1 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    else if (vef <= 4.3d+15) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = 2.0 + (EAccept / KbT);
	double t_2 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_3 = (NdChar / t_0) + (NaChar / t_0);
	double tmp;
	if (Vef <= -2.65e+184) {
		tmp = t_3;
	} else if (Vef <= -6.4e+34) {
		tmp = t_2 + (NaChar / t_1);
	} else if (Vef <= -2.45e-207) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (Vef <= 8.2e-222) {
		tmp = t_2 + (NaChar / ((t_1 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (Vef <= 4.3e+15) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = 2.0 + (EAccept / KbT)
	t_2 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_3 = (NdChar / t_0) + (NaChar / t_0)
	tmp = 0
	if Vef <= -2.65e+184:
		tmp = t_3
	elif Vef <= -6.4e+34:
		tmp = t_2 + (NaChar / t_1)
	elif Vef <= -2.45e-207:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif Vef <= 8.2e-222:
		tmp = t_2 + (NaChar / ((t_1 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	elif Vef <= 4.3e+15:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(2.0 + Float64(EAccept / KbT))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_3 = Float64(Float64(NdChar / t_0) + Float64(NaChar / t_0))
	tmp = 0.0
	if (Vef <= -2.65e+184)
		tmp = t_3;
	elseif (Vef <= -6.4e+34)
		tmp = Float64(t_2 + Float64(NaChar / t_1));
	elseif (Vef <= -2.45e-207)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (Vef <= 8.2e-222)
		tmp = Float64(t_2 + Float64(NaChar / Float64(Float64(t_1 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	elseif (Vef <= 4.3e+15)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = 2.0 + (EAccept / KbT);
	t_2 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_3 = (NdChar / t_0) + (NaChar / t_0);
	tmp = 0.0;
	if (Vef <= -2.65e+184)
		tmp = t_3;
	elseif (Vef <= -6.4e+34)
		tmp = t_2 + (NaChar / t_1);
	elseif (Vef <= -2.45e-207)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (Vef <= 8.2e-222)
		tmp = t_2 + (NaChar / ((t_1 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	elseif (Vef <= 4.3e+15)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NdChar / t$95$0), $MachinePrecision] + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -2.65e+184], t$95$3, If[LessEqual[Vef, -6.4e+34], N[(t$95$2 + N[(NaChar / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -2.45e-207], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 8.2e-222], N[(t$95$2 + N[(NaChar / N[(N[(t$95$1 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 4.3e+15], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if Vef < -2.65000000000000011e184 or 4.3e15 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 89.7%

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

   6. Taylor expanded in EAccept around 0 85.5%

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

      1. +-commutative 32.3%

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

   8. Simplified 85.5%

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

   9. Taylor expanded in Vef around inf 80.7%

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

   if -2.65000000000000011e184 < Vef < -6.3999999999999997e34

   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%

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

   5. Taylor expanded in EAccept around inf 72.3%

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

   6. Taylor expanded in EAccept around 0 65.2%

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

   if -6.3999999999999997e34 < Vef < -2.45e-207

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 85.5%

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

   6. Taylor expanded in EAccept around inf 59.0%

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

   if -2.45e-207 < Vef < 8.2000000000000006e-222

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 72.1%

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

      1. associate-+r+ 30.4%

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

      2. +-commutative 30.4%

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

   7. Simplified 72.1%

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

   if 8.2000000000000006e-222 < Vef < 4.3e15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 82.4%

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

   6. Taylor expanded in Ev around inf 53.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.65 \cdot 10^{+184}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -6.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;Vef \leq -2.45 \cdot 10^{-207}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.2 \cdot 10^{-222}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Vef \leq 4.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_2 := t_1 + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{if}\;mu \leq -6.5 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 3 \cdot 10^{-50}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{NdChar}{t_0} + \frac{NaChar}{t_0}\\ \mathbf{elif}\;mu \leq 1.22 \cdot 10^{+148}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
        (t_2 (+ t_1 (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))))
   (if (<= mu -6.5e+143)
     t_2
     (if (<= mu 3e-50)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
        (/
         NaChar
         (-
          (+ (+ 2.0 (/ EAccept KbT)) (+ (/ Vef KbT) (/ Ev KbT)))
          (/ mu KbT))))
       (if (<= mu 6.2e+104)
         (+ (/ NdChar t_0) (/ NaChar t_0))
         (if (<= mu 1.22e+148)
           (+ t_1 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
           t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + exp((Vef / KbT));
	double t_1 = NdChar / (1.0 + exp((mu / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + exp((-mu / KbT))));
	double tmp;
	if (mu <= -6.5e+143) {
		tmp = t_2;
	} else if (mu <= 3e-50) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (mu <= 6.2e+104) {
		tmp = (NdChar / t_0) + (NaChar / t_0);
	} else if (mu <= 1.22e+148) {
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = ndchar / (1.0d0 + exp((mu / kbt)))
    t_2 = t_1 + (nachar / (1.0d0 + exp((-mu / kbt))))
    if (mu <= (-6.5d+143)) then
        tmp = t_2
    else if (mu <= 3d-50) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (((2.0d0 + (eaccept / kbt)) + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    else if (mu <= 6.2d+104) then
        tmp = (ndchar / t_0) + (nachar / t_0)
    else if (mu <= 1.22d+148) then
        tmp = t_1 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = NdChar / (1.0 + Math.exp((mu / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	double tmp;
	if (mu <= -6.5e+143) {
		tmp = t_2;
	} else if (mu <= 3e-50) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (mu <= 6.2e+104) {
		tmp = (NdChar / t_0) + (NaChar / t_0);
	} else if (mu <= 1.22e+148) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = NdChar / (1.0 + math.exp((mu / KbT)))
	t_2 = t_1 + (NaChar / (1.0 + math.exp((-mu / KbT))))
	tmp = 0
	if mu <= -6.5e+143:
		tmp = t_2
	elif mu <= 3e-50:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	elif mu <= 6.2e+104:
		tmp = (NdChar / t_0) + (NaChar / t_0)
	elif mu <= 1.22e+148:
		tmp = t_1 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))))
	tmp = 0.0
	if (mu <= -6.5e+143)
		tmp = t_2;
	elseif (mu <= 3e-50)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(Float64(2.0 + Float64(EAccept / KbT)) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	elseif (mu <= 6.2e+104)
		tmp = Float64(Float64(NdChar / t_0) + Float64(NaChar / t_0));
	elseif (mu <= 1.22e+148)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = NdChar / (1.0 + exp((mu / KbT)));
	t_2 = t_1 + (NaChar / (1.0 + exp((-mu / KbT))));
	tmp = 0.0;
	if (mu <= -6.5e+143)
		tmp = t_2;
	elseif (mu <= 3e-50)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	elseif (mu <= 6.2e+104)
		tmp = (NdChar / t_0) + (NaChar / t_0);
	elseif (mu <= 1.22e+148)
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -6.5e+143], t$95$2, If[LessEqual[mu, 3e-50], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 6.2e+104], N[(N[(NdChar / t$95$0), $MachinePrecision] + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.22e+148], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if mu < -6.4999999999999997e143 or 1.22000000000000007e148 < 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%

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

   5. Taylor expanded in mu around inf 88.2%

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

   6. Taylor expanded in mu around inf 77.9%

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

      1. associate-*r/ 52.7%

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

      2. mul-1-neg 52.7%

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

   8. Simplified 77.9%

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

   if -6.4999999999999997e143 < mu < 2.9999999999999999e-50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 62.8%

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

      1. associate-+r+ 34.9%

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

      2. +-commutative 34.9%

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

   7. Simplified 62.8%

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

   if 2.9999999999999999e-50 < mu < 6.20000000000000033e104

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 75.9%

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

   6. Taylor expanded in EAccept around 0 75.9%

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

      1. +-commutative 37.3%

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

   8. Simplified 75.9%

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

   9. Taylor expanded in Vef around inf 75.3%

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

   if 6.20000000000000033e104 < mu < 1.22000000000000007e148

   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%

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

   5. Taylor expanded in mu around inf 86.9%

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

   6. Taylor expanded in EAccept around inf 70.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -6.5 \cdot 10^{+143}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;mu \leq 3 \cdot 10^{-50}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.22 \cdot 10^{+148}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 + \frac{EAccept}{KbT}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NaChar}{\left(t_0 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_4 := t_3 + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+121}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;NaChar \leq -7.5 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq -1.46 \cdot 10^{-25}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;NaChar \leq -1.7 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq 0.0037:\\ \;\;\;\;t_1 + \frac{NaChar}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_3 + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 2.0 (/ EAccept KbT)))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_2
         (+ t_1 (/ NaChar (- (+ t_0 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT)))))
        (t_3 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_4 (+ t_3 (/ NdChar (+ 2.0 (/ EDonor KbT))))))
   (if (<= NaChar -1.9e+121)
     t_4
     (if (<= NaChar -7.5e+105)
       t_2
       (if (<= NaChar -1.46e-25)
         t_4
         (if (<= NaChar -1.7e-194)
           t_2
           (if (<= NaChar 0.0037)
             (+ t_1 (/ NaChar t_0))
             (+ t_3 (/ NdChar (+ (/ mu KbT) 2.0))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 2.0 + (EAccept / KbT);
	double t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (NaChar / ((t_0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	double t_3 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_4 = t_3 + (NdChar / (2.0 + (EDonor / KbT)));
	double tmp;
	if (NaChar <= -1.9e+121) {
		tmp = t_4;
	} else if (NaChar <= -7.5e+105) {
		tmp = t_2;
	} else if (NaChar <= -1.46e-25) {
		tmp = t_4;
	} else if (NaChar <= -1.7e-194) {
		tmp = t_2;
	} else if (NaChar <= 0.0037) {
		tmp = t_1 + (NaChar / t_0);
	} else {
		tmp = t_3 + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = 2.0d0 + (eaccept / kbt)
    t_1 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_2 = t_1 + (nachar / ((t_0 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    t_3 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_4 = t_3 + (ndchar / (2.0d0 + (edonor / kbt)))
    if (nachar <= (-1.9d+121)) then
        tmp = t_4
    else if (nachar <= (-7.5d+105)) then
        tmp = t_2
    else if (nachar <= (-1.46d-25)) then
        tmp = t_4
    else if (nachar <= (-1.7d-194)) then
        tmp = t_2
    else if (nachar <= 0.0037d0) then
        tmp = t_1 + (nachar / t_0)
    else
        tmp = t_3 + (ndchar / ((mu / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 2.0 + (EAccept / KbT);
	double t_1 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (NaChar / ((t_0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	double t_3 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_4 = t_3 + (NdChar / (2.0 + (EDonor / KbT)));
	double tmp;
	if (NaChar <= -1.9e+121) {
		tmp = t_4;
	} else if (NaChar <= -7.5e+105) {
		tmp = t_2;
	} else if (NaChar <= -1.46e-25) {
		tmp = t_4;
	} else if (NaChar <= -1.7e-194) {
		tmp = t_2;
	} else if (NaChar <= 0.0037) {
		tmp = t_1 + (NaChar / t_0);
	} else {
		tmp = t_3 + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 2.0 + (EAccept / KbT)
	t_1 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_2 = t_1 + (NaChar / ((t_0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	t_3 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_4 = t_3 + (NdChar / (2.0 + (EDonor / KbT)))
	tmp = 0
	if NaChar <= -1.9e+121:
		tmp = t_4
	elif NaChar <= -7.5e+105:
		tmp = t_2
	elif NaChar <= -1.46e-25:
		tmp = t_4
	elif NaChar <= -1.7e-194:
		tmp = t_2
	elif NaChar <= 0.0037:
		tmp = t_1 + (NaChar / t_0)
	else:
		tmp = t_3 + (NdChar / ((mu / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(2.0 + Float64(EAccept / KbT))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(Float64(t_0 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))))
	t_3 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_4 = Float64(t_3 + Float64(NdChar / Float64(2.0 + Float64(EDonor / KbT))))
	tmp = 0.0
	if (NaChar <= -1.9e+121)
		tmp = t_4;
	elseif (NaChar <= -7.5e+105)
		tmp = t_2;
	elseif (NaChar <= -1.46e-25)
		tmp = t_4;
	elseif (NaChar <= -1.7e-194)
		tmp = t_2;
	elseif (NaChar <= 0.0037)
		tmp = Float64(t_1 + Float64(NaChar / t_0));
	else
		tmp = Float64(t_3 + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 2.0 + (EAccept / KbT);
	t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_2 = t_1 + (NaChar / ((t_0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	t_3 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_4 = t_3 + (NdChar / (2.0 + (EDonor / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.9e+121)
		tmp = t_4;
	elseif (NaChar <= -7.5e+105)
		tmp = t_2;
	elseif (NaChar <= -1.46e-25)
		tmp = t_4;
	elseif (NaChar <= -1.7e-194)
		tmp = t_2;
	elseif (NaChar <= 0.0037)
		tmp = t_1 + (NaChar / t_0);
	else
		tmp = t_3 + (NdChar / ((mu / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / N[(N[(t$95$0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(NdChar / N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.9e+121], t$95$4, If[LessEqual[NaChar, -7.5e+105], t$95$2, If[LessEqual[NaChar, -1.46e-25], t$95$4, If[LessEqual[NaChar, -1.7e-194], t$95$2, If[LessEqual[NaChar, 0.0037], N[(t$95$1 + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision], N[(t$95$3 + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.9e121 or -7.5000000000000002e105 < NaChar < -1.46e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 68.9%

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

   6. Taylor expanded in EDonor around 0 58.0%

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

   if -1.9e121 < NaChar < -7.5000000000000002e105 or -1.46e-25 < NaChar < -1.70000000000000005e-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%

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

   5. Taylor expanded in KbT around inf 78.5%

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

      1. associate-+r+ 27.3%

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

      2. +-commutative 27.3%

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

   7. Simplified 78.5%

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

   if -1.70000000000000005e-194 < NaChar < 0.0037000000000000002

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 78.9%

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

   6. Taylor expanded in EAccept around 0 70.8%

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

   if 0.0037000000000000002 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 82.9%

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

   6. Taylor expanded in mu around 0 69.6%

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

      1. +-commutative 69.6%

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

   8. Simplified 69.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+121}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq -7.5 \cdot 10^{+105}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.46 \cdot 10^{-25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.7 \cdot 10^{-194}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 0.0037:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 + \frac{EAccept}{KbT}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{if}\;NaChar \leq -4.8 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq -4.8 \cdot 10^{+104}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(t_0 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.85 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq 0.0095:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 2.0 (/ EAccept KbT)))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_2 (+ t_1 (/ NdChar (+ 2.0 (/ EDonor KbT))))))
   (if (<= NaChar -4.8e+121)
     t_2
     (if (<= NaChar -4.8e+104)
       (+
        (/ NdChar (+ 1.0 (exp (/ mu KbT))))
        (/ NaChar (- (+ t_0 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT))))
       (if (<= NaChar -1.85e-25)
         t_2
         (if (<= NaChar 0.0095)
           (+
            (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
            (/ NaChar t_0))
           (+ t_1 (/ NdChar (+ (/ mu KbT) 2.0)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 2.0 + (EAccept / KbT);
	double t_1 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_2 = t_1 + (NdChar / (2.0 + (EDonor / KbT)));
	double tmp;
	if (NaChar <= -4.8e+121) {
		tmp = t_2;
	} else if (NaChar <= -4.8e+104) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((t_0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (NaChar <= -1.85e-25) {
		tmp = t_2;
	} else if (NaChar <= 0.0095) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / t_0);
	} else {
		tmp = t_1 + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 2.0d0 + (eaccept / kbt)
    t_1 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_2 = t_1 + (ndchar / (2.0d0 + (edonor / kbt)))
    if (nachar <= (-4.8d+121)) then
        tmp = t_2
    else if (nachar <= (-4.8d+104)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / ((t_0 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    else if (nachar <= (-1.85d-25)) then
        tmp = t_2
    else if (nachar <= 0.0095d0) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / t_0)
    else
        tmp = t_1 + (ndchar / ((mu / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 2.0 + (EAccept / KbT);
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_2 = t_1 + (NdChar / (2.0 + (EDonor / KbT)));
	double tmp;
	if (NaChar <= -4.8e+121) {
		tmp = t_2;
	} else if (NaChar <= -4.8e+104) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / ((t_0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	} else if (NaChar <= -1.85e-25) {
		tmp = t_2;
	} else if (NaChar <= 0.0095) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / t_0);
	} else {
		tmp = t_1 + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 2.0 + (EAccept / KbT)
	t_1 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_2 = t_1 + (NdChar / (2.0 + (EDonor / KbT)))
	tmp = 0
	if NaChar <= -4.8e+121:
		tmp = t_2
	elif NaChar <= -4.8e+104:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / ((t_0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	elif NaChar <= -1.85e-25:
		tmp = t_2
	elif NaChar <= 0.0095:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / t_0)
	else:
		tmp = t_1 + (NdChar / ((mu / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(2.0 + Float64(EAccept / KbT))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(EDonor / KbT))))
	tmp = 0.0
	if (NaChar <= -4.8e+121)
		tmp = t_2;
	elseif (NaChar <= -4.8e+104)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(Float64(t_0 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	elseif (NaChar <= -1.85e-25)
		tmp = t_2;
	elseif (NaChar <= 0.0095)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / t_0));
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 2.0 + (EAccept / KbT);
	t_1 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_2 = t_1 + (NdChar / (2.0 + (EDonor / KbT)));
	tmp = 0.0;
	if (NaChar <= -4.8e+121)
		tmp = t_2;
	elseif (NaChar <= -4.8e+104)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((t_0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	elseif (NaChar <= -1.85e-25)
		tmp = t_2;
	elseif (NaChar <= 0.0095)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / t_0);
	else
		tmp = t_1 + (NdChar / ((mu / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.8e+121], t$95$2, If[LessEqual[NaChar, -4.8e+104], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(t$95$0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.85e-25], t$95$2, If[LessEqual[NaChar, 0.0095], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / t$95$0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -4.8e121 or -4.8e104 < NaChar < -1.85000000000000004e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 68.9%

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

   6. Taylor expanded in EDonor around 0 58.0%

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

   if -4.8e121 < NaChar < -4.8e104

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 88.4%

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

   6. Taylor expanded in KbT around inf 88.4%

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

      1. associate-+r+ 23.7%

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

      2. +-commutative 23.7%

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

   8. Simplified 88.4%

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

   if -1.85000000000000004e-25 < NaChar < 0.00949999999999999976

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 78.4%

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

   6. Taylor expanded in EAccept around 0 67.9%

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

   if 0.00949999999999999976 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 82.9%

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

   6. Taylor expanded in mu around 0 69.6%

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

      1. +-commutative 69.6%

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

   8. Simplified 69.6%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.8 \cdot 10^{+121}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq -4.8 \cdot 10^{+104}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.85 \cdot 10^{-25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 0.0095:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{+56} \lor \neg \left(NaChar \leq 0.00192\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -4.5e+56) (not (<= NaChar 0.00192)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (* NdChar 0.5))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ NaChar (+ 2.0 (/ EAccept KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -4.5e+56) || !(NaChar <= 0.00192)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-4.5d+56)) .or. (.not. (nachar <= 0.00192d0))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (2.0d0 + (eaccept / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -4.5e+56) || !(NaChar <= 0.00192)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -4.5e+56) or not (NaChar <= 0.00192):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -4.5e+56) || !(NaChar <= 0.00192))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -4.5e+56) || ~((NaChar <= 0.00192)))
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -4.5e+56], N[Not[LessEqual[NaChar, 0.00192]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.5000000000000003e56 or 0.00192000000000000005 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   if -4.5000000000000003e56 < NaChar < 0.00192000000000000005

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 77.6%

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

   6. Taylor expanded in EAccept around 0 66.3%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{+56} \lor \neg \left(NaChar \leq 0.00192\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -9.5 \cdot 10^{-26} \lor \neg \left(NaChar \leq 0.0042\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -9.5e-26) (not (<= NaChar 0.0042)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar (+ 2.0 (/ EDonor KbT))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ NaChar (+ 2.0 (/ EAccept KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -9.5e-26) || !(NaChar <= 0.0042)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-9.5d-26)) .or. (.not. (nachar <= 0.0042d0))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (2.0d0 + (edonor / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (2.0d0 + (eaccept / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -9.5e-26) || !(NaChar <= 0.0042)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -9.5e-26) or not (NaChar <= 0.0042):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -9.5e-26) || !(NaChar <= 0.0042))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(2.0 + Float64(EDonor / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -9.5e-26) || ~((NaChar <= 0.0042)))
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (2.0 + (EDonor / KbT)));
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -9.5e-26], N[Not[LessEqual[NaChar, 0.0042]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -9.4999999999999995e-26 or 0.00419999999999999974 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 70.8%

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

   6. Taylor expanded in EDonor around 0 60.8%

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

   if -9.4999999999999995e-26 < NaChar < 0.00419999999999999974

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 78.4%

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

   6. Taylor expanded in EAccept around 0 67.9%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -9.5 \cdot 10^{-26} \lor \neg \left(NaChar \leq 0.0042\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.1 \cdot 10^{-25}:\\ \;\;\;\;t_0 + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 0.0028:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (<= NaChar -1.1e-25)
     (+ t_0 (/ NdChar (+ 2.0 (/ EDonor KbT))))
     (if (<= NaChar 0.0028)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
        (/ NaChar (+ 2.0 (/ EAccept KbT))))
       (+ t_0 (/ NdChar (+ (/ mu KbT) 2.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (NaChar <= -1.1e-25) {
		tmp = t_0 + (NdChar / (2.0 + (EDonor / KbT)));
	} else if (NaChar <= 0.0028) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)));
	} else {
		tmp = t_0 + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    if (nachar <= (-1.1d-25)) then
        tmp = t_0 + (ndchar / (2.0d0 + (edonor / kbt)))
    else if (nachar <= 0.0028d0) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (2.0d0 + (eaccept / kbt)))
    else
        tmp = t_0 + (ndchar / ((mu / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (NaChar <= -1.1e-25) {
		tmp = t_0 + (NdChar / (2.0 + (EDonor / KbT)));
	} else if (NaChar <= 0.0028) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)));
	} else {
		tmp = t_0 + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	tmp = 0
	if NaChar <= -1.1e-25:
		tmp = t_0 + (NdChar / (2.0 + (EDonor / KbT)))
	elif NaChar <= 0.0028:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)))
	else:
		tmp = t_0 + (NdChar / ((mu / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.1e-25)
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 + Float64(EDonor / KbT))));
	elseif (NaChar <= 0.0028)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.1e-25)
		tmp = t_0 + (NdChar / (2.0 + (EDonor / KbT)));
	elseif (NaChar <= 0.0028)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (2.0 + (EAccept / KbT)));
	else
		tmp = t_0 + (NdChar / ((mu / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.1e-25], N[(t$95$0 + N[(NdChar / N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 0.0028], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.1000000000000001e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 67.2%

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

   6. Taylor expanded in EDonor around 0 54.5%

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

   if -1.1000000000000001e-25 < NaChar < 0.00279999999999999997

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 78.4%

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

   6. Taylor expanded in EAccept around 0 67.9%

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

   if 0.00279999999999999997 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 82.9%

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

   6. Taylor expanded in mu around 0 69.6%

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

      1. +-commutative 69.6%

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

   8. Simplified 69.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.1 \cdot 10^{-25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 0.0028:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.02 \cdot 10^{-25} \lor \neg \left(NaChar \leq 5.3 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.02e-25) (not (<= NaChar 5.3e-11)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (* NdChar 0.5))
   (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.02e-25) || !(NaChar <= 5.3e-11)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-1.02d-25)) .or. (.not. (nachar <= 5.3d-11))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = ndchar / (1.0d0 + exp((edonor / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.02e-25) || !(NaChar <= 5.3e-11)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.02e-25) or not (NaChar <= 5.3e-11):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = NdChar / (1.0 + math.exp((EDonor / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.02e-25) || !(NaChar <= 5.3e-11))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1.02e-25) || ~((NaChar <= 5.3e-11)))
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	else
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.02e-25], N[Not[LessEqual[NaChar, 5.3e-11]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.01999999999999998e-25 or 5.2999999999999998e-11 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.9%

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

      1. *-commutative 55.9%

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

   7. Simplified 55.9%

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

   if -1.01999999999999998e-25 < NaChar < 5.2999999999999998e-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%

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

   5. Taylor expanded in EDonor around inf 65.0%

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

   6. Taylor expanded in Ev around inf 49.2%

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

   7. Taylor expanded in NdChar around inf 54.4%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.02 \cdot 10^{-25} \lor \neg \left(NaChar \leq 5.3 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.3 \cdot 10^{+53} \lor \neg \left(NaChar \leq 3.6 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.3e+53) (not (<= NaChar 3.6e-11)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (* NdChar 0.5))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) 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 ((NaChar <= -1.3e+53) || !(NaChar <= 3.6e-11)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / 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 ((nachar <= (-1.3d+53)) .or. (.not. (nachar <= 3.6d-11))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / 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 ((NaChar <= -1.3e+53) || !(NaChar <= 3.6e-11)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.3e+53) or not (NaChar <= 3.6e-11):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.3e+53) || !(NaChar <= 3.6e-11))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / 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 ((NaChar <= -1.3e+53) || ~((NaChar <= 3.6e-11)))
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.3e+53], N[Not[LessEqual[NaChar, 3.6e-11]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.29999999999999999e53 or 3.59999999999999985e-11 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.2%

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

      1. *-commutative 57.2%

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

   7. Simplified 57.2%

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

   if -1.29999999999999999e53 < NaChar < 3.59999999999999985e-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%

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

   5. Taylor expanded in KbT around inf 55.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.3 \cdot 10^{+53} \lor \neg \left(NaChar \leq 3.6 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 46.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.8 \cdot 10^{-25} \lor \neg \left(NaChar \leq 2.9 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.8e-25) (not (<= NaChar 2.9e-15)))
   (+ (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))) (* NdChar 0.5))
   (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.8e-25) || !(NaChar <= 2.9e-15)) {
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-1.8d-25)) .or. (.not. (nachar <= 2.9d-15))) then
        tmp = (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = ndchar / (1.0d0 + exp((edonor / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.8e-25) || !(NaChar <= 2.9e-15)) {
		tmp = (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.8e-25) or not (NaChar <= 2.9e-15):
		tmp = (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = NdChar / (1.0 + math.exp((EDonor / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.8e-25) || !(NaChar <= 2.9e-15))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1.8e-25) || ~((NaChar <= 2.9e-15)))
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar * 0.5);
	else
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.8e-25], N[Not[LessEqual[NaChar, 2.9e-15]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.8e-25 or 2.90000000000000019e-15 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.9%

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

      1. *-commutative 55.9%

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

   7. Simplified 55.9%

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

   8. Taylor expanded in EAccept around 0 52.3%

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

      1. +-commutative 52.3%

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

   10. Simplified 52.3%

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

   if -1.8e-25 < NaChar < 2.90000000000000019e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 65.0%

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

   6. Taylor expanded in Ev around inf 49.2%

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

   7. Taylor expanded in NdChar around inf 54.4%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.8 \cdot 10^{-25} \lor \neg \left(NaChar \leq 2.9 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.25 \cdot 10^{+64}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00034:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -2.25e+64)
   (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
   (if (<= NaChar 0.00034)
     (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* NdChar 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 (NaChar <= -2.25e+64) {
		tmp = NaChar / (1.0 + exp((Ev / KbT)));
	} else if (NaChar <= 0.00034) {
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 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 (nachar <= (-2.25d+64)) then
        tmp = nachar / (1.0d0 + exp((ev / kbt)))
    else if (nachar <= 0.00034d0) then
        tmp = ndchar / (1.0d0 + exp((edonor / kbt)))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar * 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 (NaChar <= -2.25e+64) {
		tmp = NaChar / (1.0 + Math.exp((Ev / KbT)));
	} else if (NaChar <= 0.00034) {
		tmp = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -2.25e+64:
		tmp = NaChar / (1.0 + math.exp((Ev / KbT)))
	elif NaChar <= 0.00034:
		tmp = NdChar / (1.0 + math.exp((EDonor / KbT)))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -2.25e+64)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT))));
	elseif (NaChar <= 0.00034)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -2.25e+64)
		tmp = NaChar / (1.0 + exp((Ev / KbT)));
	elseif (NaChar <= 0.00034)
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -2.25e+64], N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 0.00034], N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2.24999999999999987e64

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 67.1%

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

   6. Taylor expanded in Ev around inf 44.3%

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

   7. Taylor expanded in NdChar around 0 39.5%

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

   if -2.24999999999999987e64 < NaChar < 3.4e-4

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 64.9%

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

   6. Taylor expanded in Ev around inf 46.7%

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

   7. Taylor expanded in NdChar around inf 50.8%

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

   if 3.4e-4 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.4%

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

      1. *-commutative 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in EAccept around inf 42.3%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.25 \cdot 10^{+64}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00034:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 40.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -3.15 \cdot 10^{+122}:\\ \;\;\;\;\frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 3.35 \cdot 10^{+162}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \left(NdChar \cdot 0.5 + -0.25 \cdot \frac{NdChar}{\frac{KbT}{mu}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -3.15e+122)
   (+
    (/
     NaChar
     (- (+ (+ 2.0 (/ EAccept KbT)) (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT)))
    (* NdChar 0.5))
   (if (<= KbT 3.35e+162)
     (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
     (+ (/ NaChar 2.0) (+ (* NdChar 0.5) (* -0.25 (/ NdChar (/ KbT mu))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -3.15e+122) {
		tmp = (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar * 0.5);
	} else if (KbT <= 3.35e+162) {
		tmp = NaChar / (1.0 + exp((Ev / KbT)));
	} else {
		tmp = (NaChar / 2.0) + ((NdChar * 0.5) + (-0.25 * (NdChar / (KbT / mu))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-3.15d+122)) then
        tmp = (nachar / (((2.0d0 + (eaccept / kbt)) + ((vef / kbt) + (ev / kbt))) - (mu / kbt))) + (ndchar * 0.5d0)
    else if (kbt <= 3.35d+162) then
        tmp = nachar / (1.0d0 + exp((ev / kbt)))
    else
        tmp = (nachar / 2.0d0) + ((ndchar * 0.5d0) + ((-0.25d0) * (ndchar / (kbt / mu))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -3.15e+122) {
		tmp = (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar * 0.5);
	} else if (KbT <= 3.35e+162) {
		tmp = NaChar / (1.0 + Math.exp((Ev / KbT)));
	} else {
		tmp = (NaChar / 2.0) + ((NdChar * 0.5) + (-0.25 * (NdChar / (KbT / mu))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -3.15e+122:
		tmp = (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar * 0.5)
	elif KbT <= 3.35e+162:
		tmp = NaChar / (1.0 + math.exp((Ev / KbT)))
	else:
		tmp = (NaChar / 2.0) + ((NdChar * 0.5) + (-0.25 * (NdChar / (KbT / mu))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -3.15e+122)
		tmp = Float64(Float64(NaChar / Float64(Float64(Float64(2.0 + Float64(EAccept / KbT)) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))) + Float64(NdChar * 0.5));
	elseif (KbT <= 3.35e+162)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT))));
	else
		tmp = Float64(Float64(NaChar / 2.0) + Float64(Float64(NdChar * 0.5) + Float64(-0.25 * Float64(NdChar / Float64(KbT / mu)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -3.15e+122)
		tmp = (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar * 0.5);
	elseif (KbT <= 3.35e+162)
		tmp = NaChar / (1.0 + exp((Ev / KbT)));
	else
		tmp = (NaChar / 2.0) + ((NdChar * 0.5) + (-0.25 * (NdChar / (KbT / mu))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -3.15e+122], N[(N[(NaChar / N[(N[(N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 3.35e+162], N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(N[(NdChar * 0.5), $MachinePrecision] + N[(-0.25 * N[(NdChar / N[(KbT / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -3.1500000000000001e122

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 69.6%

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

      1. *-commutative 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in KbT around inf 61.6%

      \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]
   9. Step-by-step derivation

      1. associate-+r+ 61.3%

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

      2. +-commutative 61.3%

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

   10. Simplified 61.6%

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

   if -3.1500000000000001e122 < KbT < 3.34999999999999995e162

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 64.2%

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

   6. Taylor expanded in Ev around inf 41.0%

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

   7. Taylor expanded in NdChar around 0 29.2%

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

   if 3.34999999999999995e162 < 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%

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

   5. Taylor expanded in KbT around inf 70.5%

      \[\leadsto \color{blue}{\left(-0.25 \cdot \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT} + 0.5 \cdot NdChar\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in mu around inf 73.2%

      \[\leadsto \left(-0.25 \cdot \color{blue}{\frac{NdChar \cdot mu}{KbT}} + 0.5 \cdot NdChar\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 77.4%

         \[\leadsto \left(-0.25 \cdot \color{blue}{\frac{NdChar}{\frac{KbT}{mu}}} + 0.5 \cdot NdChar\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   8. Simplified 77.4%

      \[\leadsto \left(-0.25 \cdot \color{blue}{\frac{NdChar}{\frac{KbT}{mu}}} + 0.5 \cdot NdChar\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in KbT around inf 69.5%

      \[\leadsto \left(-0.25 \cdot \frac{NdChar}{\frac{KbT}{mu}} + 0.5 \cdot NdChar\right) + \frac{NaChar}{\color{blue}{2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.15 \cdot 10^{+122}:\\ \;\;\;\;\frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 3.35 \cdot 10^{+162}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \left(NdChar \cdot 0.5 + -0.25 \cdot \frac{NdChar}{\frac{KbT}{mu}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 40.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.2 \cdot 10^{+82}:\\ \;\;\;\;\frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.04 \cdot 10^{+155}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \left(NdChar \cdot 0.5 + -0.25 \cdot \frac{NdChar}{\frac{KbT}{mu}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2.2e+82)
   (+
    (/
     NaChar
     (- (+ (+ 2.0 (/ EAccept KbT)) (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT)))
    (* NdChar 0.5))
   (if (<= KbT 1.04e+155)
     (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
     (+ (/ NaChar 2.0) (+ (* NdChar 0.5) (* -0.25 (/ NdChar (/ KbT mu))))))))

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 <= -2.2e+82) {
		tmp = (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar * 0.5);
	} else if (KbT <= 1.04e+155) {
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	} else {
		tmp = (NaChar / 2.0) + ((NdChar * 0.5) + (-0.25 * (NdChar / (KbT / mu))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-2.2d+82)) then
        tmp = (nachar / (((2.0d0 + (eaccept / kbt)) + ((vef / kbt) + (ev / kbt))) - (mu / kbt))) + (ndchar * 0.5d0)
    else if (kbt <= 1.04d+155) then
        tmp = ndchar / (1.0d0 + exp((edonor / kbt)))
    else
        tmp = (nachar / 2.0d0) + ((ndchar * 0.5d0) + ((-0.25d0) * (ndchar / (kbt / mu))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -2.2e+82) {
		tmp = (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar * 0.5);
	} else if (KbT <= 1.04e+155) {
		tmp = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	} else {
		tmp = (NaChar / 2.0) + ((NdChar * 0.5) + (-0.25 * (NdChar / (KbT / mu))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -2.2e+82:
		tmp = (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar * 0.5)
	elif KbT <= 1.04e+155:
		tmp = NdChar / (1.0 + math.exp((EDonor / KbT)))
	else:
		tmp = (NaChar / 2.0) + ((NdChar * 0.5) + (-0.25 * (NdChar / (KbT / mu))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -2.2e+82)
		tmp = Float64(Float64(NaChar / Float64(Float64(Float64(2.0 + Float64(EAccept / KbT)) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))) + Float64(NdChar * 0.5));
	elseif (KbT <= 1.04e+155)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))));
	else
		tmp = Float64(Float64(NaChar / 2.0) + Float64(Float64(NdChar * 0.5) + Float64(-0.25 * Float64(NdChar / Float64(KbT / mu)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -2.2e+82)
		tmp = (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar * 0.5);
	elseif (KbT <= 1.04e+155)
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	else
		tmp = (NaChar / 2.0) + ((NdChar * 0.5) + (-0.25 * (NdChar / (KbT / mu))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -2.2e+82], N[(N[(NaChar / N[(N[(N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.04e+155], N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(N[(NdChar * 0.5), $MachinePrecision] + N[(-0.25 * N[(NdChar / N[(KbT / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -2.2000000000000001e82

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.0%

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

      1. *-commutative 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in KbT around inf 55.8%

      \[\leadsto NdChar \cdot 0.5 + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]
   9. Step-by-step derivation

      1. associate-+r+ 55.5%

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

      2. +-commutative 55.5%

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

   10. Simplified 55.8%

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

   if -2.2000000000000001e82 < KbT < 1.03999999999999996e155

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 64.2%

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

   6. Taylor expanded in Ev around inf 41.1%

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

   7. Taylor expanded in NdChar around inf 41.6%

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

   if 1.03999999999999996e155 < 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%

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

   5. Taylor expanded in KbT around inf 68.5%

      \[\leadsto \color{blue}{\left(-0.25 \cdot \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT} + 0.5 \cdot NdChar\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in mu around inf 74.0%

      \[\leadsto \left(-0.25 \cdot \color{blue}{\frac{NdChar \cdot mu}{KbT}} + 0.5 \cdot NdChar\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 78.0%

         \[\leadsto \left(-0.25 \cdot \color{blue}{\frac{NdChar}{\frac{KbT}{mu}}} + 0.5 \cdot NdChar\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   8. Simplified 78.0%

      \[\leadsto \left(-0.25 \cdot \color{blue}{\frac{NdChar}{\frac{KbT}{mu}}} + 0.5 \cdot NdChar\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in KbT around inf 68.0%

      \[\leadsto \left(-0.25 \cdot \frac{NdChar}{\frac{KbT}{mu}} + 0.5 \cdot NdChar\right) + \frac{NaChar}{\color{blue}{2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.2 \cdot 10^{+82}:\\ \;\;\;\;\frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.04 \cdot 10^{+155}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \left(NdChar \cdot 0.5 + -0.25 \cdot \frac{NdChar}{\frac{KbT}{mu}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 26.4% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{1 + \left(1 + \frac{EDonor}{KbT}\right)} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/
   NaChar
   (- (+ (+ 2.0 (/ EAccept KbT)) (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT)))
  (/ NdChar (+ 1.0 (+ 1.0 (/ EDonor KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar / (1.0 + (1.0 + (EDonor / 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 = (nachar / (((2.0d0 + (eaccept / kbt)) + ((vef / kbt) + (ev / kbt))) - (mu / kbt))) + (ndchar / (1.0d0 + (1.0d0 + (edonor / 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 (NaChar / (((2.0 + (EAccept / KbT)) + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT))) + (NdChar / (1.0 + (1.0 + (EDonor / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NaChar / N[(N[(N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(1.0 + N[(EDonor / 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%

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

5. Taylor expanded in EDonor around inf 67.7%

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

6. Taylor expanded in EDonor around 0 49.5%

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

7. Taylor expanded in KbT around inf 29.1%

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

   1. associate-+r+ 29.1%

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

   2. +-commutative 29.1%

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

9. Simplified 29.1%

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

10. Final simplification 29.1%

    \[\leadsto \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{1 + \left(1 + \frac{EDonor}{KbT}\right)} \]
11. Add Preprocessing

Alternative 24: 27.8% 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%

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

5. Taylor expanded in EDonor around inf 67.7%

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

6. Taylor expanded in Ev around inf 48.9%

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

7. Taylor expanded in KbT around inf 28.5%

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

   1. +-commutative 28.5%

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

   2. distribute-lft-out 28.5%

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

9. Simplified 28.5%

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

10. Final simplification 28.5%

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

Reproduce

herbie shell --seed 2024017 
(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))))))