Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 33.0s

Alternatives: 32

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -6.48950768720805e+121
  2. Ec = 3.3702324287677894e+129
  3. Vef = 3.4692113412811895e+161
  4. EDonor = -1.982476258713604e+133
  5. mu = -1.884236076755794e-243
  6. KbT = -4.090451282659618e+69
  7. NaChar = -2.21491159370977e+122
  8. Ev = 1.478215159775834e+290
  9. EAccept = 9.869527151382107e+273

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, 0.5× speedup

Math

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

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (pow(sqrt(exp(((Vef - ((Ec - mu) - EDonor)) / KbT))), 2.0) + 1.0)) + (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0));
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / ((sqrt(exp(((vef - ((ec - mu) - edonor)) / kbt))) ** 2.0d0) + 1.0d0)) + (nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0))
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (Math.pow(Math.sqrt(Math.exp(((Vef - ((Ec - mu) - EDonor)) / KbT))), 2.0) + 1.0)) + (NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. add-sqr-sqrt 100.0%

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

   2. pow2 100.0%

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

   3. div-inv 100.0%

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

   4. div-inv 100.0%

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

   5. associate-+l- 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 76.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_2 := t\_1 + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ t_3 := t\_1 + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;EDonor \leq -3.2 \cdot 10^{+48}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EDonor \leq -1.12 \cdot 10^{-162}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - t\_0\\ \mathbf{elif}\;EDonor \leq 9.2 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EDonor \leq 1.35 \cdot 10^{-107}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} - t\_0\\ \mathbf{elif}\;EDonor \leq 4.9 \cdot 10^{-57}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (- (+ Vef mu) Ec) KbT)))))
        (t_1 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_2 (+ t_1 (/ NdChar (+ (exp (/ mu KbT)) 1.0))))
        (t_3 (+ t_1 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)))))
   (if (<= EDonor -3.2e+48)
     t_3
     (if (<= EDonor -1.12e-162)
       (- (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) t_0)
       (if (<= EDonor 9.2e-203)
         t_2
         (if (<= EDonor 1.35e-107)
           (- (/ NaChar (+ (exp (/ Vef KbT)) 1.0)) t_0)
           (if (<= EDonor 4.9e-57) t_2 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 = NdChar / (-1.0 - exp((((Vef + mu) - Ec) / KbT)));
	double t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / (exp((mu / KbT)) + 1.0));
	double t_3 = t_1 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -3.2e+48) {
		tmp = t_3;
	} else if (EDonor <= -1.12e-162) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - t_0;
	} else if (EDonor <= 9.2e-203) {
		tmp = t_2;
	} else if (EDonor <= 1.35e-107) {
		tmp = (NaChar / (exp((Vef / KbT)) + 1.0)) - t_0;
	} else if (EDonor <= 4.9e-57) {
		tmp = t_2;
	} 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 = ndchar / ((-1.0d0) - exp((((vef + mu) - ec) / kbt)))
    t_1 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_2 = t_1 + (ndchar / (exp((mu / kbt)) + 1.0d0))
    t_3 = t_1 + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    if (edonor <= (-3.2d+48)) then
        tmp = t_3
    else if (edonor <= (-1.12d-162)) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) - t_0
    else if (edonor <= 9.2d-203) then
        tmp = t_2
    else if (edonor <= 1.35d-107) then
        tmp = (nachar / (exp((vef / kbt)) + 1.0d0)) - t_0
    else if (edonor <= 4.9d-57) then
        tmp = t_2
    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 = NdChar / (-1.0 - Math.exp((((Vef + mu) - Ec) / KbT)));
	double t_1 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / (Math.exp((mu / KbT)) + 1.0));
	double t_3 = t_1 + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -3.2e+48) {
		tmp = t_3;
	} else if (EDonor <= -1.12e-162) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) - t_0;
	} else if (EDonor <= 9.2e-203) {
		tmp = t_2;
	} else if (EDonor <= 1.35e-107) {
		tmp = (NaChar / (Math.exp((Vef / KbT)) + 1.0)) - t_0;
	} else if (EDonor <= 4.9e-57) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp((((Vef + mu) - Ec) / KbT)))
	t_1 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_2 = t_1 + (NdChar / (math.exp((mu / KbT)) + 1.0))
	t_3 = t_1 + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	tmp = 0
	if EDonor <= -3.2e+48:
		tmp = t_3
	elif EDonor <= -1.12e-162:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) - t_0
	elif EDonor <= 9.2e-203:
		tmp = t_2
	elif EDonor <= 1.35e-107:
		tmp = (NaChar / (math.exp((Vef / KbT)) + 1.0)) - t_0
	elif EDonor <= 4.9e-57:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT))))
	t_1 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)))
	t_3 = Float64(t_1 + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)))
	tmp = 0.0
	if (EDonor <= -3.2e+48)
		tmp = t_3;
	elseif (EDonor <= -1.12e-162)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) - t_0);
	elseif (EDonor <= 9.2e-203)
		tmp = t_2;
	elseif (EDonor <= 1.35e-107)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) - t_0);
	elseif (EDonor <= 4.9e-57)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp((((Vef + mu) - Ec) / KbT)));
	t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_2 = t_1 + (NdChar / (exp((mu / KbT)) + 1.0));
	t_3 = t_1 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	tmp = 0.0;
	if (EDonor <= -3.2e+48)
		tmp = t_3;
	elseif (EDonor <= -1.12e-162)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - t_0;
	elseif (EDonor <= 9.2e-203)
		tmp = t_2;
	elseif (EDonor <= 1.35e-107)
		tmp = (NaChar / (exp((Vef / KbT)) + 1.0)) - t_0;
	elseif (EDonor <= 4.9e-57)
		tmp = t_2;
	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[(NdChar / N[(-1.0 - N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -3.2e+48], t$95$3, If[LessEqual[EDonor, -1.12e-162], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[EDonor, 9.2e-203], t$95$2, If[LessEqual[EDonor, 1.35e-107], N[(N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[EDonor, 4.9e-57], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if EDonor < -3.2000000000000001e48 or 4.89999999999999988e-57 < 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%

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

   5. Taylor expanded in EDonor around inf 87.0%

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

   if -3.2000000000000001e48 < EDonor < -1.12e-162

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 81.9%

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

   6. Taylor expanded in EDonor around 0 81.9%

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

   if -1.12e-162 < EDonor < 9.19999999999999966e-203 or 1.35e-107 < EDonor < 4.89999999999999988e-57

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 83.7%

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

   if 9.19999999999999966e-203 < EDonor < 1.35e-107

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 96.3%

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

   6. Taylor expanded in EDonor around 0 96.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -3.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq -1.12 \cdot 10^{-162}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 9.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 1.35 \cdot 10^{-107}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 4.9 \cdot 10^{-57}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} - t\_0\\ \mathbf{if}\;Vef \leq -2.7 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq -3.9 \cdot 10^{-128}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + NdChar \cdot \frac{-1}{\left(\frac{Ec - EDonor}{KbT} - \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - 2}\\ \mathbf{elif}\;Vef \leq -6.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{NaChar}{\left(\left(\left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right) + 1\right) + \frac{EAccept - mu}{KbT}\right) + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq -7.5 \cdot 10^{-267}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{elif}\;Vef \leq 7.3 \cdot 10^{+189}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (- (+ Vef mu) Ec) KbT)))))
        (t_1 (- (/ NaChar (+ (exp (/ Vef KbT)) 1.0)) t_0)))
   (if (<= Vef -2.7e-13)
     t_1
     (if (<= Vef -3.9e-128)
       (+
        (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0))
        (*
         NdChar
         (/
          -1.0
          (- (- (/ (- Ec EDonor) KbT) (+ (/ mu KbT) (/ Vef KbT))) 2.0))))
       (if (<= Vef -6.8e-191)
         (-
          (/
           NaChar
           (+
            (+ (+ (+ (/ Ev KbT) (/ Vef KbT)) 1.0) (/ (- EAccept mu) KbT))
            1.0))
          (/ NdChar (- -1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)))))
         (if (<= Vef -7.5e-267)
           (+
            (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))
            (/ NaChar (+ (exp (/ mu (- KbT))) 1.0)))
           (if (<= Vef 7.3e+189)
             (- (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) t_0)
             t_1)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp((((Vef + mu) - Ec) / KbT)));
	double t_1 = (NaChar / (exp((Vef / KbT)) + 1.0)) - t_0;
	double tmp;
	if (Vef <= -2.7e-13) {
		tmp = t_1;
	} else if (Vef <= -3.9e-128) {
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	} else if (Vef <= -6.8e-191) {
		tmp = (NaChar / (((((Ev / KbT) + (Vef / KbT)) + 1.0) + ((EAccept - mu) / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	} else if (Vef <= -7.5e-267) {
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / (exp((mu / -KbT)) + 1.0));
	} else if (Vef <= 7.3e+189) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp((((vef + mu) - ec) / kbt)))
    t_1 = (nachar / (exp((vef / kbt)) + 1.0d0)) - t_0
    if (vef <= (-2.7d-13)) then
        tmp = t_1
    else if (vef <= (-3.9d-128)) then
        tmp = (nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)) + (ndchar * ((-1.0d0) / ((((ec - edonor) / kbt) - ((mu / kbt) + (vef / kbt))) - 2.0d0)))
    else if (vef <= (-6.8d-191)) then
        tmp = (nachar / (((((ev / kbt) + (vef / kbt)) + 1.0d0) + ((eaccept - mu) / kbt)) + 1.0d0)) - (ndchar / ((-1.0d0) - exp(((vef + (mu + (edonor - ec))) / kbt))))
    else if (vef <= (-7.5d-267)) then
        tmp = (ndchar / (exp((edonor / kbt)) + 1.0d0)) + (nachar / (exp((mu / -kbt)) + 1.0d0))
    else if (vef <= 7.3d+189) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) - t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp((((Vef + mu) - Ec) / KbT)));
	double t_1 = (NaChar / (Math.exp((Vef / KbT)) + 1.0)) - t_0;
	double tmp;
	if (Vef <= -2.7e-13) {
		tmp = t_1;
	} else if (Vef <= -3.9e-128) {
		tmp = (NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	} else if (Vef <= -6.8e-191) {
		tmp = (NaChar / (((((Ev / KbT) + (Vef / KbT)) + 1.0) + ((EAccept - mu) / KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	} else if (Vef <= -7.5e-267) {
		tmp = (NdChar / (Math.exp((EDonor / KbT)) + 1.0)) + (NaChar / (Math.exp((mu / -KbT)) + 1.0));
	} else if (Vef <= 7.3e+189) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) - t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp((((Vef + mu) - Ec) / KbT)))
	t_1 = (NaChar / (math.exp((Vef / KbT)) + 1.0)) - t_0
	tmp = 0
	if Vef <= -2.7e-13:
		tmp = t_1
	elif Vef <= -3.9e-128:
		tmp = (NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)))
	elif Vef <= -6.8e-191:
		tmp = (NaChar / (((((Ev / KbT) + (Vef / KbT)) + 1.0) + ((EAccept - mu) / KbT)) + 1.0)) - (NdChar / (-1.0 - math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))))
	elif Vef <= -7.5e-267:
		tmp = (NdChar / (math.exp((EDonor / KbT)) + 1.0)) + (NaChar / (math.exp((mu / -KbT)) + 1.0))
	elif Vef <= 7.3e+189:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) - t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) - t_0)
	tmp = 0.0
	if (Vef <= -2.7e-13)
		tmp = t_1;
	elseif (Vef <= -3.9e-128)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0)) + Float64(NdChar * Float64(-1.0 / Float64(Float64(Float64(Float64(Ec - EDonor) / KbT) - Float64(Float64(mu / KbT) + Float64(Vef / KbT))) - 2.0))));
	elseif (Vef <= -6.8e-191)
		tmp = Float64(Float64(NaChar / Float64(Float64(Float64(Float64(Float64(Ev / KbT) + Float64(Vef / KbT)) + 1.0) + Float64(Float64(EAccept - mu) / KbT)) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)))));
	elseif (Vef <= -7.5e-267)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0)));
	elseif (Vef <= 7.3e+189)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) - t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp((((Vef + mu) - Ec) / KbT)));
	t_1 = (NaChar / (exp((Vef / KbT)) + 1.0)) - t_0;
	tmp = 0.0;
	if (Vef <= -2.7e-13)
		tmp = t_1;
	elseif (Vef <= -3.9e-128)
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	elseif (Vef <= -6.8e-191)
		tmp = (NaChar / (((((Ev / KbT) + (Vef / KbT)) + 1.0) + ((EAccept - mu) / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	elseif (Vef <= -7.5e-267)
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / (exp((mu / -KbT)) + 1.0));
	elseif (Vef <= 7.3e+189)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[Vef, -2.7e-13], t$95$1, If[LessEqual[Vef, -3.9e-128], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar * N[(-1.0 / N[(N[(N[(N[(Ec - EDonor), $MachinePrecision] / KbT), $MachinePrecision] - N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -6.8e-191], N[(N[(NaChar / N[(N[(N[(N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(N[(EAccept - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -7.5e-267], N[(N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 7.3e+189], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if Vef < -2.70000000000000011e-13 or 7.3000000000000003e189 < 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%

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

   5. Taylor expanded in Vef around inf 87.4%

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

   6. Taylor expanded in EDonor around 0 81.5%

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

   if -2.70000000000000011e-13 < Vef < -3.89999999999999997e-128

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 86.7%

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

      1. associate--l+ 86.7%

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

      2. +-commutative 86.7%

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

      3. associate--l+ 86.7%

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

      4. sub-neg 86.7%

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

      5. +-commutative 86.7%

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

      6. neg-sub0 86.7%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 86.7%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 86.7%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 86.7%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 86.7%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 86.7%

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

      12. distribute-neg-frac 86.7%

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

      13. +-commutative 86.7%

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

      14. distribute-neg-in 86.7%

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

      15. mul-1-neg 86.7%

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

      16. remove-double-neg 86.7%

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

      17. sub-neg 86.7%

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

   7. Simplified 86.7%

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

      1. div-inv 86.7%

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

      2. associate-+r+ 86.7%

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

      3. metadata-eval 86.7%

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

   9. Applied egg-rr 86.7%

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

   if -3.89999999999999997e-128 < Vef < -6.79999999999999988e-191

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 87.7%

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

      1. +-commutative 26.7%

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

      2. associate-+r+ 26.7%

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

      3. associate--l+ 26.7%

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

      4. +-commutative 26.7%

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

      5. sub-neg 26.7%

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

      6. +-commutative 26.7%

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

      7. neg-sub0 26.7%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \left(\color{blue}{\left(0 - \frac{mu}{KbT}\right)} + \frac{EAccept}{KbT}\right)\right)} \]

      8. associate-+l- 26.7%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \color{blue}{\left(0 - \left(\frac{mu}{KbT} - \frac{EAccept}{KbT}\right)\right)}\right)} \]

      9. div-sub 26.7%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \left(0 - \color{blue}{\frac{mu - EAccept}{KbT}}\right)\right)} \]

      10. unsub-neg 26.7%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \left(0 - \frac{\color{blue}{mu + \left(-EAccept\right)}}{KbT}\right)\right)} \]

      11. mul-1-neg 26.7%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \left(0 - \frac{mu + \color{blue}{-1 \cdot EAccept}}{KbT}\right)\right)} \]

      12. neg-sub0 26.7%

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

      13. distribute-neg-frac 26.7%

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

      14. distribute-neg-in 26.7%

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

      15. mul-1-neg 26.7%

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

      16. remove-double-neg 26.7%

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

      17. +-commutative 26.7%

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

      18. sub-neg 26.7%

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

   7. Simplified 87.7%

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

   if -6.79999999999999988e-191 < Vef < -7.4999999999999999e-267

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 77.0%

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

   6. Taylor expanded in mu around inf 77.0%

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

      1. associate-*r/ 56.9%

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

      2. mul-1-neg 56.9%

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

   8. Simplified 77.0%

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

   if -7.4999999999999999e-267 < Vef < 7.3000000000000003e189

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 77.6%

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

   6. Taylor expanded in EDonor around 0 71.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.7 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.9 \cdot 10^{-128}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + NdChar \cdot \frac{-1}{\left(\frac{Ec - EDonor}{KbT} - \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - 2}\\ \mathbf{elif}\;Vef \leq -6.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{NaChar}{\left(\left(\left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right) + 1\right) + \frac{EAccept - mu}{KbT}\right) + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq -7.5 \cdot 10^{-267}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{elif}\;Vef \leq 7.3 \cdot 10^{+189}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_1 := \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ t_2 := \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_3 := \frac{NaChar}{\left(\frac{Vef}{KbT} + 1\right) + 1} - t\_2\\ \mathbf{if}\;NaChar \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;t\_0 + NdChar \cdot \frac{-1}{\left(\frac{Ec - EDonor}{KbT} - \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - 2}\\ \mathbf{elif}\;NaChar \leq -1.55 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -2.5 \cdot 10^{-146}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-127}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - t\_2\\ \mathbf{elif}\;NaChar \leq 2.15 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 5.8 \cdot 10^{-54}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_1
         (-
          (/ NaChar (+ (exp (/ mu (- KbT))) 1.0))
          (/ NdChar (- -1.0 (exp (/ mu KbT))))))
        (t_2 (/ NdChar (- -1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)))))
        (t_3 (- (/ NaChar (+ (+ (/ Vef KbT) 1.0) 1.0)) t_2)))
   (if (<= NaChar -3.7e+37)
     (+
      t_0
      (*
       NdChar
       (/ -1.0 (- (- (/ (- Ec EDonor) KbT) (+ (/ mu KbT) (/ Vef KbT))) 2.0))))
     (if (<= NaChar -1.55e-17)
       t_1
       (if (<= NaChar -2.5e-146)
         t_3
         (if (<= NaChar 1.85e-127)
           (- (/ NaChar (+ 2.0 (/ Ev KbT))) t_2)
           (if (<= NaChar 2.15e-77)
             t_1
             (if (<= NaChar 5.8e-54)
               t_3
               (+
                t_0
                (/
                 NdChar
                 (+ 2.0 (+ (/ Vef KbT) (/ (- EDonor Ec) KbT)))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = (NaChar / (exp((mu / -KbT)) + 1.0)) - (NdChar / (-1.0 - exp((mu / KbT))));
	double t_2 = NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	double t_3 = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_2;
	double tmp;
	if (NaChar <= -3.7e+37) {
		tmp = t_0 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	} else if (NaChar <= -1.55e-17) {
		tmp = t_1;
	} else if (NaChar <= -2.5e-146) {
		tmp = t_3;
	} else if (NaChar <= 1.85e-127) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_2;
	} else if (NaChar <= 2.15e-77) {
		tmp = t_1;
	} else if (NaChar <= 5.8e-54) {
		tmp = t_3;
	} else {
		tmp = t_0 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_1 = (nachar / (exp((mu / -kbt)) + 1.0d0)) - (ndchar / ((-1.0d0) - exp((mu / kbt))))
    t_2 = ndchar / ((-1.0d0) - exp(((vef + (mu + (edonor - ec))) / kbt)))
    t_3 = (nachar / (((vef / kbt) + 1.0d0) + 1.0d0)) - t_2
    if (nachar <= (-3.7d+37)) then
        tmp = t_0 + (ndchar * ((-1.0d0) / ((((ec - edonor) / kbt) - ((mu / kbt) + (vef / kbt))) - 2.0d0)))
    else if (nachar <= (-1.55d-17)) then
        tmp = t_1
    else if (nachar <= (-2.5d-146)) then
        tmp = t_3
    else if (nachar <= 1.85d-127) then
        tmp = (nachar / (2.0d0 + (ev / kbt))) - t_2
    else if (nachar <= 2.15d-77) then
        tmp = t_1
    else if (nachar <= 5.8d-54) then
        tmp = t_3
    else
        tmp = t_0 + (ndchar / (2.0d0 + ((vef / kbt) + ((edonor - ec) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = (NaChar / (Math.exp((mu / -KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp((mu / KbT))));
	double t_2 = NdChar / (-1.0 - Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	double t_3 = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_2;
	double tmp;
	if (NaChar <= -3.7e+37) {
		tmp = t_0 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	} else if (NaChar <= -1.55e-17) {
		tmp = t_1;
	} else if (NaChar <= -2.5e-146) {
		tmp = t_3;
	} else if (NaChar <= 1.85e-127) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_2;
	} else if (NaChar <= 2.15e-77) {
		tmp = t_1;
	} else if (NaChar <= 5.8e-54) {
		tmp = t_3;
	} else {
		tmp = t_0 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_1 = (NaChar / (math.exp((mu / -KbT)) + 1.0)) - (NdChar / (-1.0 - math.exp((mu / KbT))))
	t_2 = NdChar / (-1.0 - math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)))
	t_3 = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_2
	tmp = 0
	if NaChar <= -3.7e+37:
		tmp = t_0 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)))
	elif NaChar <= -1.55e-17:
		tmp = t_1
	elif NaChar <= -2.5e-146:
		tmp = t_3
	elif NaChar <= 1.85e-127:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_2
	elif NaChar <= 2.15e-77:
		tmp = t_1
	elif NaChar <= 5.8e-54:
		tmp = t_3
	else:
		tmp = t_0 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_1 = Float64(Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(mu / KbT)))))
	t_2 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT))))
	t_3 = Float64(Float64(NaChar / Float64(Float64(Float64(Vef / KbT) + 1.0) + 1.0)) - t_2)
	tmp = 0.0
	if (NaChar <= -3.7e+37)
		tmp = Float64(t_0 + Float64(NdChar * Float64(-1.0 / Float64(Float64(Float64(Float64(Ec - EDonor) / KbT) - Float64(Float64(mu / KbT) + Float64(Vef / KbT))) - 2.0))));
	elseif (NaChar <= -1.55e-17)
		tmp = t_1;
	elseif (NaChar <= -2.5e-146)
		tmp = t_3;
	elseif (NaChar <= 1.85e-127)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - t_2);
	elseif (NaChar <= 2.15e-77)
		tmp = t_1;
	elseif (NaChar <= 5.8e-54)
		tmp = t_3;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Float64(EDonor - Ec) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_1 = (NaChar / (exp((mu / -KbT)) + 1.0)) - (NdChar / (-1.0 - exp((mu / KbT))));
	t_2 = NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	t_3 = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_2;
	tmp = 0.0;
	if (NaChar <= -3.7e+37)
		tmp = t_0 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	elseif (NaChar <= -1.55e-17)
		tmp = t_1;
	elseif (NaChar <= -2.5e-146)
		tmp = t_3;
	elseif (NaChar <= 1.85e-127)
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_2;
	elseif (NaChar <= 2.15e-77)
		tmp = t_1;
	elseif (NaChar <= 5.8e-54)
		tmp = t_3;
	else
		tmp = t_0 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NaChar / N[(N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[NaChar, -3.7e+37], N[(t$95$0 + N[(NdChar * N[(-1.0 / N[(N[(N[(N[(Ec - EDonor), $MachinePrecision] / KbT), $MachinePrecision] - N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.55e-17], t$95$1, If[LessEqual[NaChar, -2.5e-146], t$95$3, If[LessEqual[NaChar, 1.85e-127], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[NaChar, 2.15e-77], t$95$1, If[LessEqual[NaChar, 5.8e-54], t$95$3, N[(t$95$0 + N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(EDonor - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -3.6999999999999999e37

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. +-commutative 73.5%

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

      3. associate--l+ 73.5%

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

      4. sub-neg 73.5%

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

      5. +-commutative 73.5%

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

      6. neg-sub0 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 73.5%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 73.5%

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

      12. distribute-neg-frac 73.5%

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

      13. +-commutative 73.5%

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

      14. distribute-neg-in 73.5%

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

      15. mul-1-neg 73.5%

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

      16. remove-double-neg 73.5%

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

      17. sub-neg 73.5%

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

   7. Simplified 73.5%

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

      1. div-inv 73.5%

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

      2. associate-+r+ 73.5%

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

      3. metadata-eval 73.5%

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

   9. Applied egg-rr 73.5%

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

   if -3.6999999999999999e37 < NaChar < -1.5499999999999999e-17 or 1.8500000000000002e-127 < NaChar < 2.1500000000000001e-77

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 88.6%

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

   6. Taylor expanded in mu around inf 78.9%

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

      1. associate-*r/ 42.2%

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

      2. mul-1-neg 42.2%

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

   8. Simplified 78.9%

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

   if -1.5499999999999999e-17 < NaChar < -2.49999999999999979e-146 or 2.1500000000000001e-77 < NaChar < 5.80000000000000029e-54

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 87.9%

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

   6. Taylor expanded in Vef around 0 77.7%

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

   if -2.49999999999999979e-146 < NaChar < 1.8500000000000002e-127

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 87.5%

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

   6. Taylor expanded in Ev around 0 75.3%

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

   if 5.80000000000000029e-54 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 70.9%

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

      1. associate--l+ 70.9%

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

      2. +-commutative 70.9%

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

      3. associate--l+ 70.9%

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

      4. sub-neg 70.9%

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

      5. +-commutative 70.9%

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

      6. neg-sub0 70.9%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 70.9%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 73.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 73.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 73.4%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 73.4%

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

      12. distribute-neg-frac 73.4%

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

      13. +-commutative 73.4%

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

      14. distribute-neg-in 73.4%

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

      15. mul-1-neg 73.4%

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

      16. remove-double-neg 73.4%

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

      17. sub-neg 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in mu around 0 73.7%

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

      1. associate--l+ 73.7%

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

      2. +-commutative 73.7%

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

      3. associate--l+ 73.7%

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

      4. div-sub 76.1%

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

   10. Simplified 76.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + NdChar \cdot \frac{-1}{\left(\frac{Ec - EDonor}{KbT} - \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - 2}\\ \mathbf{elif}\;NaChar \leq -1.55 \cdot 10^{-17}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{NaChar}{\left(\frac{Vef}{KbT} + 1\right) + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-127}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 2.15 \cdot 10^{-77}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 5.8 \cdot 10^{-54}:\\ \;\;\;\;\frac{NaChar}{\left(\frac{Vef}{KbT} + 1\right) + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{+47}:\\ \;\;\;\;t\_1 + NdChar \cdot \frac{-1}{\left(\frac{Ec - EDonor}{KbT} - \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - 2}\\ \mathbf{elif}\;NaChar \leq -2.55 \cdot 10^{-11}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -7.4 \cdot 10^{-124}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;NaChar \leq 5.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 2.6 \cdot 10^{-75}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ (exp (/ mu (- KbT))) 1.0))
          (/ NdChar (- -1.0 (exp (/ mu KbT))))))
        (t_1 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0))))
   (if (<= NaChar -2.7e+47)
     (+
      t_1
      (*
       NdChar
       (/ -1.0 (- (- (/ (- Ec EDonor) KbT) (+ (/ mu KbT) (/ Vef KbT))) 2.0))))
     (if (<= NaChar -2.55e-11)
       t_0
       (if (<= NaChar -7.4e-124)
         (-
          (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
          (/ NdChar (- -1.0 (exp (/ Ec (- KbT))))))
         (if (<= NaChar 5.8e-129)
           (-
            (/ NaChar (+ 2.0 (/ Ev KbT)))
            (/ NdChar (- -1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)))))
           (if (<= NaChar 2.6e-75)
             t_0
             (+
              t_1
              (/ NdChar (+ 2.0 (+ (/ Vef KbT) (/ (- EDonor Ec) KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (exp((mu / -KbT)) + 1.0)) - (NdChar / (-1.0 - exp((mu / KbT))));
	double t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -2.7e+47) {
		tmp = t_1 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	} else if (NaChar <= -2.55e-11) {
		tmp = t_0;
	} else if (NaChar <= -7.4e-124) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - exp((Ec / -KbT))));
	} else if (NaChar <= 5.8e-129) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	} else if (NaChar <= 2.6e-75) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / (exp((mu / -kbt)) + 1.0d0)) - (ndchar / ((-1.0d0) - exp((mu / kbt))))
    t_1 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    if (nachar <= (-2.7d+47)) then
        tmp = t_1 + (ndchar * ((-1.0d0) / ((((ec - edonor) / kbt) - ((mu / kbt) + (vef / kbt))) - 2.0d0)))
    else if (nachar <= (-2.55d-11)) then
        tmp = t_0
    else if (nachar <= (-7.4d-124)) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) - (ndchar / ((-1.0d0) - exp((ec / -kbt))))
    else if (nachar <= 5.8d-129) then
        tmp = (nachar / (2.0d0 + (ev / kbt))) - (ndchar / ((-1.0d0) - exp(((vef + (mu + (edonor - ec))) / kbt))))
    else if (nachar <= 2.6d-75) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / (2.0d0 + ((vef / kbt) + ((edonor - ec) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (Math.exp((mu / -KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp((mu / KbT))));
	double t_1 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -2.7e+47) {
		tmp = t_1 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	} else if (NaChar <= -2.55e-11) {
		tmp = t_0;
	} else if (NaChar <= -7.4e-124) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp((Ec / -KbT))));
	} else if (NaChar <= 5.8e-129) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	} else if (NaChar <= 2.6e-75) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (math.exp((mu / -KbT)) + 1.0)) - (NdChar / (-1.0 - math.exp((mu / KbT))))
	t_1 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	tmp = 0
	if NaChar <= -2.7e+47:
		tmp = t_1 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)))
	elif NaChar <= -2.55e-11:
		tmp = t_0
	elif NaChar <= -7.4e-124:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - math.exp((Ec / -KbT))))
	elif NaChar <= 5.8e-129:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))))
	elif NaChar <= 2.6e-75:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(mu / KbT)))))
	t_1 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	tmp = 0.0
	if (NaChar <= -2.7e+47)
		tmp = Float64(t_1 + Float64(NdChar * Float64(-1.0 / Float64(Float64(Float64(Float64(Ec - EDonor) / KbT) - Float64(Float64(mu / KbT) + Float64(Vef / KbT))) - 2.0))));
	elseif (NaChar <= -2.55e-11)
		tmp = t_0;
	elseif (NaChar <= -7.4e-124)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Ec / Float64(-KbT))))));
	elseif (NaChar <= 5.8e-129)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)))));
	elseif (NaChar <= 2.6e-75)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Float64(EDonor - Ec) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (exp((mu / -KbT)) + 1.0)) - (NdChar / (-1.0 - exp((mu / KbT))));
	t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NaChar <= -2.7e+47)
		tmp = t_1 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	elseif (NaChar <= -2.55e-11)
		tmp = t_0;
	elseif (NaChar <= -7.4e-124)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - exp((Ec / -KbT))));
	elseif (NaChar <= 5.8e-129)
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	elseif (NaChar <= 2.6e-75)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.7e+47], N[(t$95$1 + N[(NdChar * N[(-1.0 / N[(N[(N[(N[(Ec - EDonor), $MachinePrecision] / KbT), $MachinePrecision] - N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2.55e-11], t$95$0, If[LessEqual[NaChar, -7.4e-124], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 5.8e-129], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.6e-75], t$95$0, N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(EDonor - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -2.69999999999999996e47

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. +-commutative 73.5%

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

      3. associate--l+ 73.5%

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

      4. sub-neg 73.5%

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

      5. +-commutative 73.5%

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

      6. neg-sub0 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 73.5%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 73.5%

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

      12. distribute-neg-frac 73.5%

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

      13. +-commutative 73.5%

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

      14. distribute-neg-in 73.5%

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

      15. mul-1-neg 73.5%

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

      16. remove-double-neg 73.5%

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

      17. sub-neg 73.5%

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

   7. Simplified 73.5%

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

      1. div-inv 73.5%

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

      2. associate-+r+ 73.5%

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

      3. metadata-eval 73.5%

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

   9. Applied egg-rr 73.5%

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

   if -2.69999999999999996e47 < NaChar < -2.54999999999999992e-11 or 5.80000000000000034e-129 < NaChar < 2.6e-75

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 91.0%

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

   6. Taylor expanded in mu around inf 83.2%

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

      1. associate-*r/ 41.0%

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

      2. mul-1-neg 41.0%

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

   8. Simplified 83.2%

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

   if -2.54999999999999992e-11 < NaChar < -7.3999999999999998e-124

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 75.1%

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

   6. Taylor expanded in Ec around inf 62.7%

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

      1. associate-*r/ 56.7%

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

      2. mul-1-neg 56.7%

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

   8. Simplified 62.7%

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

   if -7.3999999999999998e-124 < NaChar < 5.80000000000000034e-129

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 87.2%

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

   6. Taylor expanded in Ev around 0 76.0%

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

   if 2.6e-75 < 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%

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

   5. Taylor expanded in KbT around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. +-commutative 67.6%

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

      3. associate--l+ 67.6%

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

      4. sub-neg 67.6%

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

      5. +-commutative 67.6%

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

      6. neg-sub0 67.6%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 67.6%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 71.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 71.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 71.0%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 71.0%

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

      12. distribute-neg-frac 71.0%

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

      13. +-commutative 71.0%

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

      14. distribute-neg-in 71.0%

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

      15. mul-1-neg 71.0%

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

      16. remove-double-neg 71.0%

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

      17. sub-neg 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in mu around 0 70.1%

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

      1. associate--l+ 70.1%

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

      2. +-commutative 70.1%

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

      3. associate--l+ 70.1%

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

      4. div-sub 73.5%

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

   10. Simplified 73.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{+47}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + NdChar \cdot \frac{-1}{\left(\frac{Ec - EDonor}{KbT} - \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - 2}\\ \mathbf{elif}\;NaChar \leq -2.55 \cdot 10^{-11}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -7.4 \cdot 10^{-124}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;NaChar \leq 5.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 2.6 \cdot 10^{-75}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_2 := t\_1 + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;EDonor \leq -3 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EDonor \leq -3.2 \cdot 10^{-189}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - t\_0\\ \mathbf{elif}\;EDonor \leq -1.8 \cdot 10^{-251}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \mathbf{elif}\;EDonor \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (- (+ Vef mu) Ec) KbT)))))
        (t_1 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_2 (+ t_1 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)))))
   (if (<= EDonor -3e+48)
     t_2
     (if (<= EDonor -3.2e-189)
       (- (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) t_0)
       (if (<= EDonor -1.8e-251)
         (+ t_1 (/ NdChar (+ 2.0 (+ (/ Vef KbT) (/ (- EDonor Ec) KbT)))))
         (if (<= EDonor 6.2e-55)
           (- (/ NaChar (+ (exp (/ Vef KbT)) 1.0)) t_0)
           t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp((((Vef + mu) - Ec) / KbT)));
	double t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -3e+48) {
		tmp = t_2;
	} else if (EDonor <= -3.2e-189) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - t_0;
	} else if (EDonor <= -1.8e-251) {
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	} else if (EDonor <= 6.2e-55) {
		tmp = (NaChar / (exp((Vef / KbT)) + 1.0)) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp((((vef + mu) - ec) / kbt)))
    t_1 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_2 = t_1 + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    if (edonor <= (-3d+48)) then
        tmp = t_2
    else if (edonor <= (-3.2d-189)) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) - t_0
    else if (edonor <= (-1.8d-251)) then
        tmp = t_1 + (ndchar / (2.0d0 + ((vef / kbt) + ((edonor - ec) / kbt))))
    else if (edonor <= 6.2d-55) then
        tmp = (nachar / (exp((vef / kbt)) + 1.0d0)) - t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp((((Vef + mu) - Ec) / KbT)));
	double t_1 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -3e+48) {
		tmp = t_2;
	} else if (EDonor <= -3.2e-189) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) - t_0;
	} else if (EDonor <= -1.8e-251) {
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	} else if (EDonor <= 6.2e-55) {
		tmp = (NaChar / (Math.exp((Vef / KbT)) + 1.0)) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp((((Vef + mu) - Ec) / KbT)))
	t_1 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_2 = t_1 + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	tmp = 0
	if EDonor <= -3e+48:
		tmp = t_2
	elif EDonor <= -3.2e-189:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) - t_0
	elif EDonor <= -1.8e-251:
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))))
	elif EDonor <= 6.2e-55:
		tmp = (NaChar / (math.exp((Vef / KbT)) + 1.0)) - t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT))))
	t_1 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)))
	tmp = 0.0
	if (EDonor <= -3e+48)
		tmp = t_2;
	elseif (EDonor <= -3.2e-189)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) - t_0);
	elseif (EDonor <= -1.8e-251)
		tmp = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Float64(EDonor - Ec) / KbT)))));
	elseif (EDonor <= 6.2e-55)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) - t_0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp((((Vef + mu) - Ec) / KbT)));
	t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_2 = t_1 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	tmp = 0.0;
	if (EDonor <= -3e+48)
		tmp = t_2;
	elseif (EDonor <= -3.2e-189)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - t_0;
	elseif (EDonor <= -1.8e-251)
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	elseif (EDonor <= 6.2e-55)
		tmp = (NaChar / (exp((Vef / KbT)) + 1.0)) - t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -3e+48], t$95$2, If[LessEqual[EDonor, -3.2e-189], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[EDonor, -1.8e-251], N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(EDonor - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 6.2e-55], N[(N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if EDonor < -3e48 or 6.19999999999999993e-55 < 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%

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

   5. Taylor expanded in EDonor around inf 87.0%

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

   if -3e48 < EDonor < -3.2000000000000001e-189

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 78.1%

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

   6. Taylor expanded in EDonor around 0 78.1%

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

   if -3.2000000000000001e-189 < EDonor < -1.8000000000000001e-251

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 78.6%

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

      1. associate--l+ 78.6%

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

      2. +-commutative 78.6%

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

      3. associate--l+ 78.6%

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

      4. sub-neg 78.6%

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

      5. +-commutative 78.6%

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

      6. neg-sub0 78.6%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 78.6%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 78.6%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 78.6%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 78.6%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 78.6%

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

      12. distribute-neg-frac 78.6%

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

      13. +-commutative 78.6%

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

      14. distribute-neg-in 78.6%

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

      15. mul-1-neg 78.6%

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

      16. remove-double-neg 78.6%

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

      17. sub-neg 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in mu around 0 84.5%

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

      1. associate--l+ 84.5%

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

      2. +-commutative 84.5%

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

      3. associate--l+ 84.5%

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

      4. div-sub 84.5%

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

   10. Simplified 84.5%

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

   if -1.8000000000000001e-251 < EDonor < 6.19999999999999993e-55

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 79.5%

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

   6. Taylor expanded in EDonor around 0 79.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -3 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq -3.2 \cdot 10^{-189}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -1.8 \cdot 10^{-251}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \mathbf{elif}\;EDonor \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -2.7 \cdot 10^{-61} \lor \neg \left(NdChar \leq 1.25 \cdot 10^{-164} \lor \neg \left(NdChar \leq 3.5 \cdot 10^{-78}\right) \land NdChar \leq 2.5 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -2.7e-61)
         (not
          (or (<= NdChar 1.25e-164)
              (and (not (<= NdChar 3.5e-78)) (<= NdChar 2.5e+21)))))
   (-
    (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
    (/ NdChar (- -1.0 (exp (/ (- (+ Vef mu) Ec) KbT)))))
   (+
    (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0))
    (/ NdChar (+ 2.0 (+ (/ Vef KbT) (/ (- EDonor Ec) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -2.7e-61) || !((NdChar <= 1.25e-164) || (!(NdChar <= 3.5e-78) && (NdChar <= 2.5e+21)))) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - exp((((Vef + mu) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-2.7d-61)) .or. (.not. (ndchar <= 1.25d-164) .or. (.not. (ndchar <= 3.5d-78)) .and. (ndchar <= 2.5d+21))) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) - (ndchar / ((-1.0d0) - exp((((vef + mu) - ec) / kbt))))
    else
        tmp = (nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)) + (ndchar / (2.0d0 + ((vef / kbt) + ((edonor - ec) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -2.7e-61) || !((NdChar <= 1.25e-164) || (!(NdChar <= 3.5e-78) && (NdChar <= 2.5e+21)))) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp((((Vef + mu) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -2.7e-61) or not ((NdChar <= 1.25e-164) or (not (NdChar <= 3.5e-78) and (NdChar <= 2.5e+21))):
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - math.exp((((Vef + mu) - Ec) / KbT))))
	else:
		tmp = (NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -2.7e-61) || !((NdChar <= 1.25e-164) || (!(NdChar <= 3.5e-78) && (NdChar <= 2.5e+21))))
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0)) + Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Float64(EDonor - Ec) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -2.7e-61) || ~(((NdChar <= 1.25e-164) || (~((NdChar <= 3.5e-78)) && (NdChar <= 2.5e+21)))))
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - exp((((Vef + mu) - Ec) / KbT))));
	else
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -2.7e-61], N[Not[Or[LessEqual[NdChar, 1.25e-164], And[N[Not[LessEqual[NdChar, 3.5e-78]], $MachinePrecision], LessEqual[NdChar, 2.5e+21]]]], $MachinePrecision]], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(EDonor - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -2.69999999999999993e-61 or 1.2499999999999999e-164 < NdChar < 3.4999999999999999e-78 or 2.5e21 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 74.5%

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

   6. Taylor expanded in EDonor around 0 68.4%

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

   if -2.69999999999999993e-61 < NdChar < 1.2499999999999999e-164 or 3.4999999999999999e-78 < NdChar < 2.5e21

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 78.0%

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

      1. associate--l+ 78.0%

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

      2. +-commutative 78.0%

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

      3. associate--l+ 78.0%

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

      4. sub-neg 78.0%

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

      5. +-commutative 78.0%

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

      6. neg-sub0 78.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 78.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 79.1%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 79.1%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 79.1%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 79.1%

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

      12. distribute-neg-frac 79.1%

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

      13. +-commutative 79.1%

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

      14. distribute-neg-in 79.1%

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

      15. mul-1-neg 79.1%

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

      16. remove-double-neg 79.1%

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

      17. sub-neg 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in mu around 0 80.4%

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

      1. associate--l+ 80.4%

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

      2. +-commutative 80.4%

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

      3. associate--l+ 80.4%

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

      4. div-sub 81.5%

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

   10. Simplified 81.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.7 \cdot 10^{-61} \lor \neg \left(NdChar \leq 1.25 \cdot 10^{-164} \lor \neg \left(NdChar \leq 3.5 \cdot 10^{-78}\right) \land NdChar \leq 2.5 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_1 := t\_0 + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{if}\;NaChar \leq -2.05 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 6.9 \cdot 10^{-133}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_1 (+ t_0 (/ NdChar (+ (exp (/ mu KbT)) 1.0)))))
   (if (<= NaChar -2.05e-79)
     t_1
     (if (<= NaChar 6.9e-133)
       (-
        (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))
        (/ NdChar (- -1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)))))
       (if (<= NaChar 3.8e-77)
         t_1
         (+ t_0 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))))))))

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 / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (exp((mu / KbT)) + 1.0));
	double tmp;
	if (NaChar <= -2.05e-79) {
		tmp = t_1;
	} else if (NaChar <= 6.9e-133) {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	} else if (NaChar <= 3.8e-77) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_1 = t_0 + (ndchar / (exp((mu / kbt)) + 1.0d0))
    if (nachar <= (-2.05d-79)) then
        tmp = t_1
    else if (nachar <= 6.9d-133) then
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) - (ndchar / ((-1.0d0) - exp(((vef + (mu + (edonor - ec))) / kbt))))
    else if (nachar <= 3.8d-77) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    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 / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (Math.exp((mu / KbT)) + 1.0));
	double tmp;
	if (NaChar <= -2.05e-79) {
		tmp = t_1;
	} else if (NaChar <= 6.9e-133) {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	} else if (NaChar <= 3.8e-77) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_1 = t_0 + (NdChar / (math.exp((mu / KbT)) + 1.0))
	tmp = 0
	if NaChar <= -2.05e-79:
		tmp = t_1
	elif NaChar <= 6.9e-133:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) - (NdChar / (-1.0 - math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))))
	elif NaChar <= 3.8e-77:
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)))
	tmp = 0.0
	if (NaChar <= -2.05e-79)
		tmp = t_1;
	elseif (NaChar <= 6.9e-133)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)))));
	elseif (NaChar <= 3.8e-77)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_1 = t_0 + (NdChar / (exp((mu / KbT)) + 1.0));
	tmp = 0.0;
	if (NaChar <= -2.05e-79)
		tmp = t_1;
	elseif (NaChar <= 6.9e-133)
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	elseif (NaChar <= 3.8e-77)
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.05e-79], t$95$1, If[LessEqual[NaChar, 6.9e-133], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.8e-77], t$95$1, N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2.04999999999999997e-79 or 6.9000000000000001e-133 < NaChar < 3.7999999999999999e-77

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 83.7%

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

   if -2.04999999999999997e-79 < NaChar < 6.9000000000000001e-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%

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

   5. Taylor expanded in EAccept around inf 86.7%

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

   if 3.7999999999999999e-77 < 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%

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

   5. Taylor expanded in EDonor around inf 83.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.05 \cdot 10^{-79}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq 6.9 \cdot 10^{-133}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_1 := t\_0 + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{if}\;NaChar \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.06 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_1 (+ t_0 (/ NdChar (+ (exp (/ mu KbT)) 1.0)))))
   (if (<= NaChar -7.2e+19)
     t_1
     (if (<= NaChar 1.75e-127)
       (-
        (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
        (/ NdChar (- -1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)))))
       (if (<= NaChar 1.06e-76)
         t_1
         (+ t_0 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))))))))

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 / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (exp((mu / KbT)) + 1.0));
	double tmp;
	if (NaChar <= -7.2e+19) {
		tmp = t_1;
	} else if (NaChar <= 1.75e-127) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	} else if (NaChar <= 1.06e-76) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_1 = t_0 + (ndchar / (exp((mu / kbt)) + 1.0d0))
    if (nachar <= (-7.2d+19)) then
        tmp = t_1
    else if (nachar <= 1.75d-127) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) - (ndchar / ((-1.0d0) - exp(((vef + (mu + (edonor - ec))) / kbt))))
    else if (nachar <= 1.06d-76) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    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 / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (Math.exp((mu / KbT)) + 1.0));
	double tmp;
	if (NaChar <= -7.2e+19) {
		tmp = t_1;
	} else if (NaChar <= 1.75e-127) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	} else if (NaChar <= 1.06e-76) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_1 = t_0 + (NdChar / (math.exp((mu / KbT)) + 1.0))
	tmp = 0
	if NaChar <= -7.2e+19:
		tmp = t_1
	elif NaChar <= 1.75e-127:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))))
	elif NaChar <= 1.06e-76:
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)))
	tmp = 0.0
	if (NaChar <= -7.2e+19)
		tmp = t_1;
	elseif (NaChar <= 1.75e-127)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)))));
	elseif (NaChar <= 1.06e-76)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_1 = t_0 + (NdChar / (exp((mu / KbT)) + 1.0));
	tmp = 0.0;
	if (NaChar <= -7.2e+19)
		tmp = t_1;
	elseif (NaChar <= 1.75e-127)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	elseif (NaChar <= 1.06e-76)
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -7.2e+19], t$95$1, If[LessEqual[NaChar, 1.75e-127], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.06e-76], t$95$1, N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -7.2e19 or 1.74999999999999995e-127 < NaChar < 1.06000000000000003e-76

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 87.1%

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

   if -7.2e19 < NaChar < 1.74999999999999995e-127

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 84.0%

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

   if 1.06000000000000003e-76 < 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%

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

   5. Taylor expanded in EDonor around inf 83.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.06 \cdot 10^{-76}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

5. Final simplification 100.0%

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

Alternative 11: 64.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_2 := t\_1 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \mathbf{if}\;NaChar \leq -3.6 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -9.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - t\_0\\ \mathbf{elif}\;NaChar \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;t\_1 - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{elif}\;NaChar \leq 6 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{\left(\frac{Vef}{KbT} + 1\right) + 1} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)))))
        (t_1 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_2 (+ t_1 (/ NdChar (+ 2.0 (+ (/ Vef KbT) (/ (- EDonor Ec) KbT)))))))
   (if (<= NaChar -3.6e+41)
     t_2
     (if (<= NaChar -9.8e-14)
       (- (/ NaChar (+ 2.0 (/ Ev KbT))) t_0)
       (if (<= NaChar -2.05e-17)
         (- t_1 (* KbT (/ NdChar Ec)))
         (if (<= NaChar 6e-52)
           (- (/ NaChar (+ (+ (/ Vef KbT) 1.0) 1.0)) t_0)
           t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	double t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	double tmp;
	if (NaChar <= -3.6e+41) {
		tmp = t_2;
	} else if (NaChar <= -9.8e-14) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	} else if (NaChar <= -2.05e-17) {
		tmp = t_1 - (KbT * (NdChar / Ec));
	} else if (NaChar <= 6e-52) {
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((vef + (mu + (edonor - ec))) / kbt)))
    t_1 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_2 = t_1 + (ndchar / (2.0d0 + ((vef / kbt) + ((edonor - ec) / kbt))))
    if (nachar <= (-3.6d+41)) then
        tmp = t_2
    else if (nachar <= (-9.8d-14)) then
        tmp = (nachar / (2.0d0 + (ev / kbt))) - t_0
    else if (nachar <= (-2.05d-17)) then
        tmp = t_1 - (kbt * (ndchar / ec))
    else if (nachar <= 6d-52) then
        tmp = (nachar / (((vef / kbt) + 1.0d0) + 1.0d0)) - t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	double t_1 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	double tmp;
	if (NaChar <= -3.6e+41) {
		tmp = t_2;
	} else if (NaChar <= -9.8e-14) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	} else if (NaChar <= -2.05e-17) {
		tmp = t_1 - (KbT * (NdChar / Ec));
	} else if (NaChar <= 6e-52) {
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)))
	t_1 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_2 = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))))
	tmp = 0
	if NaChar <= -3.6e+41:
		tmp = t_2
	elif NaChar <= -9.8e-14:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0
	elif NaChar <= -2.05e-17:
		tmp = t_1 - (KbT * (NdChar / Ec))
	elif NaChar <= 6e-52:
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Float64(EDonor - Ec) / KbT)))))
	tmp = 0.0
	if (NaChar <= -3.6e+41)
		tmp = t_2;
	elseif (NaChar <= -9.8e-14)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - t_0);
	elseif (NaChar <= -2.05e-17)
		tmp = Float64(t_1 - Float64(KbT * Float64(NdChar / Ec)));
	elseif (NaChar <= 6e-52)
		tmp = Float64(Float64(NaChar / Float64(Float64(Float64(Vef / KbT) + 1.0) + 1.0)) - t_0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_2 = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	tmp = 0.0;
	if (NaChar <= -3.6e+41)
		tmp = t_2;
	elseif (NaChar <= -9.8e-14)
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	elseif (NaChar <= -2.05e-17)
		tmp = t_1 - (KbT * (NdChar / Ec));
	elseif (NaChar <= 6e-52)
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(EDonor - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -3.6e+41], t$95$2, If[LessEqual[NaChar, -9.8e-14], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, -2.05e-17], N[(t$95$1 - N[(KbT * N[(NdChar / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 6e-52], N[(N[(NaChar / N[(N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -3.60000000000000025e41 or 6e-52 < 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%

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

   5. Taylor expanded in KbT around inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. +-commutative 71.8%

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

      3. associate--l+ 71.8%

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

      4. sub-neg 71.8%

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

      5. +-commutative 71.8%

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

      6. neg-sub0 71.8%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 71.8%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 73.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 73.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 73.4%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 73.4%

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

      12. distribute-neg-frac 73.4%

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

      13. +-commutative 73.4%

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

      14. distribute-neg-in 73.4%

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

      15. mul-1-neg 73.4%

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

      16. remove-double-neg 73.4%

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

      17. sub-neg 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in mu around 0 72.3%

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

      1. associate--l+ 72.3%

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

      2. +-commutative 72.3%

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

      3. associate--l+ 72.3%

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

      4. div-sub 73.9%

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

   10. Simplified 73.9%

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

   if -3.60000000000000025e41 < NaChar < -9.79999999999999989e-14

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 68.3%

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

   6. Taylor expanded in Ev around 0 68.3%

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

   if -9.79999999999999989e-14 < NaChar < -2.05e-17

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. neg-sub0 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 100.0%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 100.0%

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

      12. distribute-neg-frac 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-neg-in 100.0%

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

      15. mul-1-neg 100.0%

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

      16. remove-double-neg 100.0%

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

      17. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in Ec around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -2.05e-17 < NaChar < 6e-52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 81.4%

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

   6. Taylor expanded in Vef around 0 73.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -9.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{elif}\;NaChar \leq 6 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{\left(\frac{Vef}{KbT} + 1\right) + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NaChar \leq -4 \cdot 10^{+34}:\\ \;\;\;\;t\_1 + NdChar \cdot \frac{-1}{\left(\frac{Ec - EDonor}{KbT} - \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - 2}\\ \mathbf{elif}\;NaChar \leq -2.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - t\_0\\ \mathbf{elif}\;NaChar \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;t\_1 - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{NaChar}{\left(\frac{Vef}{KbT} + 1\right) + 1} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)))))
        (t_1 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0))))
   (if (<= NaChar -4e+34)
     (+
      t_1
      (*
       NdChar
       (/ -1.0 (- (- (/ (- Ec EDonor) KbT) (+ (/ mu KbT) (/ Vef KbT))) 2.0))))
     (if (<= NaChar -2.5e-13)
       (- (/ NaChar (+ 2.0 (/ Ev KbT))) t_0)
       (if (<= NaChar -2.05e-17)
         (- t_1 (* KbT (/ NdChar Ec)))
         (if (<= NaChar 8.5e-55)
           (- (/ NaChar (+ (+ (/ Vef KbT) 1.0) 1.0)) t_0)
           (+
            t_1
            (/ NdChar (+ 2.0 (+ (/ Vef KbT) (/ (- EDonor Ec) KbT)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	double t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -4e+34) {
		tmp = t_1 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	} else if (NaChar <= -2.5e-13) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	} else if (NaChar <= -2.05e-17) {
		tmp = t_1 - (KbT * (NdChar / Ec));
	} else if (NaChar <= 8.5e-55) {
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0;
	} else {
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((vef + (mu + (edonor - ec))) / kbt)))
    t_1 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    if (nachar <= (-4d+34)) then
        tmp = t_1 + (ndchar * ((-1.0d0) / ((((ec - edonor) / kbt) - ((mu / kbt) + (vef / kbt))) - 2.0d0)))
    else if (nachar <= (-2.5d-13)) then
        tmp = (nachar / (2.0d0 + (ev / kbt))) - t_0
    else if (nachar <= (-2.05d-17)) then
        tmp = t_1 - (kbt * (ndchar / ec))
    else if (nachar <= 8.5d-55) then
        tmp = (nachar / (((vef / kbt) + 1.0d0) + 1.0d0)) - t_0
    else
        tmp = t_1 + (ndchar / (2.0d0 + ((vef / kbt) + ((edonor - ec) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	double t_1 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -4e+34) {
		tmp = t_1 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	} else if (NaChar <= -2.5e-13) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	} else if (NaChar <= -2.05e-17) {
		tmp = t_1 - (KbT * (NdChar / Ec));
	} else if (NaChar <= 8.5e-55) {
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0;
	} else {
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)))
	t_1 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	tmp = 0
	if NaChar <= -4e+34:
		tmp = t_1 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)))
	elif NaChar <= -2.5e-13:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0
	elif NaChar <= -2.05e-17:
		tmp = t_1 - (KbT * (NdChar / Ec))
	elif NaChar <= 8.5e-55:
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0
	else:
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	tmp = 0.0
	if (NaChar <= -4e+34)
		tmp = Float64(t_1 + Float64(NdChar * Float64(-1.0 / Float64(Float64(Float64(Float64(Ec - EDonor) / KbT) - Float64(Float64(mu / KbT) + Float64(Vef / KbT))) - 2.0))));
	elseif (NaChar <= -2.5e-13)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - t_0);
	elseif (NaChar <= -2.05e-17)
		tmp = Float64(t_1 - Float64(KbT * Float64(NdChar / Ec)));
	elseif (NaChar <= 8.5e-55)
		tmp = Float64(Float64(NaChar / Float64(Float64(Float64(Vef / KbT) + 1.0) + 1.0)) - t_0);
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Float64(EDonor - Ec) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NaChar <= -4e+34)
		tmp = t_1 + (NdChar * (-1.0 / ((((Ec - EDonor) / KbT) - ((mu / KbT) + (Vef / KbT))) - 2.0)));
	elseif (NaChar <= -2.5e-13)
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	elseif (NaChar <= -2.05e-17)
		tmp = t_1 - (KbT * (NdChar / Ec));
	elseif (NaChar <= 8.5e-55)
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0;
	else
		tmp = t_1 + (NdChar / (2.0 + ((Vef / KbT) + ((EDonor - Ec) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4e+34], N[(t$95$1 + N[(NdChar * N[(-1.0 / N[(N[(N[(N[(Ec - EDonor), $MachinePrecision] / KbT), $MachinePrecision] - N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2.5e-13], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, -2.05e-17], N[(t$95$1 - N[(KbT * N[(NdChar / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8.5e-55], N[(N[(NaChar / N[(N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(EDonor - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -3.99999999999999978e34

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. +-commutative 73.5%

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

      3. associate--l+ 73.5%

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

      4. sub-neg 73.5%

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

      5. +-commutative 73.5%

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

      6. neg-sub0 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 73.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 73.5%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 73.5%

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

      12. distribute-neg-frac 73.5%

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

      13. +-commutative 73.5%

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

      14. distribute-neg-in 73.5%

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

      15. mul-1-neg 73.5%

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

      16. remove-double-neg 73.5%

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

      17. sub-neg 73.5%

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

   7. Simplified 73.5%

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

      1. div-inv 73.5%

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

      2. associate-+r+ 73.5%

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

      3. metadata-eval 73.5%

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

   9. Applied egg-rr 73.5%

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

   if -3.99999999999999978e34 < NaChar < -2.49999999999999995e-13

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 68.3%

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

   6. Taylor expanded in Ev around 0 68.3%

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

   if -2.49999999999999995e-13 < NaChar < -2.05e-17

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. neg-sub0 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 100.0%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 100.0%

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

      12. distribute-neg-frac 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-neg-in 100.0%

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

      15. mul-1-neg 100.0%

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

      16. remove-double-neg 100.0%

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

      17. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in Ec around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -2.05e-17 < NaChar < 8.49999999999999968e-55

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 81.4%

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

   6. Taylor expanded in Vef around 0 73.2%

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

   if 8.49999999999999968e-55 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 70.9%

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

      1. associate--l+ 70.9%

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

      2. +-commutative 70.9%

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

      3. associate--l+ 70.9%

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

      4. sub-neg 70.9%

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

      5. +-commutative 70.9%

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

      6. neg-sub0 70.9%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 70.9%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 73.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 73.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 73.4%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 73.4%

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

      12. distribute-neg-frac 73.4%

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

      13. +-commutative 73.4%

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

      14. distribute-neg-in 73.4%

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

      15. mul-1-neg 73.4%

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

      16. remove-double-neg 73.4%

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

      17. sub-neg 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in mu around 0 73.7%

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

      1. associate--l+ 73.7%

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

      2. +-commutative 73.7%

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

      3. associate--l+ 73.7%

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

      4. div-sub 76.1%

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

   10. Simplified 76.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4 \cdot 10^{+34}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + NdChar \cdot \frac{-1}{\left(\frac{Ec - EDonor}{KbT} - \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - 2}\\ \mathbf{elif}\;NaChar \leq -2.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{NaChar}{\left(\frac{Vef}{KbT} + 1\right) + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{EDonor - Ec}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_2 := t\_1 + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{if}\;NaChar \leq -7.8 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -9.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - t\_0\\ \mathbf{elif}\;NaChar \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;t\_1 - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{elif}\;NaChar \leq 2.9 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{\left(\frac{Vef}{KbT} + 1\right) + 1} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)))))
        (t_1 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_2 (+ t_1 (/ NdChar (+ 2.0 (/ mu KbT))))))
   (if (<= NaChar -7.8e+55)
     t_2
     (if (<= NaChar -9.8e-14)
       (- (/ NaChar (+ 2.0 (/ Ev KbT))) t_0)
       (if (<= NaChar -2.05e-17)
         (- t_1 (* KbT (/ NdChar Ec)))
         (if (<= NaChar 2.9e-52)
           (- (/ NaChar (+ (+ (/ Vef KbT) 1.0) 1.0)) t_0)
           t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	double t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / (2.0 + (mu / KbT)));
	double tmp;
	if (NaChar <= -7.8e+55) {
		tmp = t_2;
	} else if (NaChar <= -9.8e-14) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	} else if (NaChar <= -2.05e-17) {
		tmp = t_1 - (KbT * (NdChar / Ec));
	} else if (NaChar <= 2.9e-52) {
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((vef + (mu + (edonor - ec))) / kbt)))
    t_1 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_2 = t_1 + (ndchar / (2.0d0 + (mu / kbt)))
    if (nachar <= (-7.8d+55)) then
        tmp = t_2
    else if (nachar <= (-9.8d-14)) then
        tmp = (nachar / (2.0d0 + (ev / kbt))) - t_0
    else if (nachar <= (-2.05d-17)) then
        tmp = t_1 - (kbt * (ndchar / ec))
    else if (nachar <= 2.9d-52) then
        tmp = (nachar / (((vef / kbt) + 1.0d0) + 1.0d0)) - t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	double t_1 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / (2.0 + (mu / KbT)));
	double tmp;
	if (NaChar <= -7.8e+55) {
		tmp = t_2;
	} else if (NaChar <= -9.8e-14) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	} else if (NaChar <= -2.05e-17) {
		tmp = t_1 - (KbT * (NdChar / Ec));
	} else if (NaChar <= 2.9e-52) {
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)))
	t_1 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_2 = t_1 + (NdChar / (2.0 + (mu / KbT)))
	tmp = 0
	if NaChar <= -7.8e+55:
		tmp = t_2
	elif NaChar <= -9.8e-14:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0
	elif NaChar <= -2.05e-17:
		tmp = t_1 - (KbT * (NdChar / Ec))
	elif NaChar <= 2.9e-52:
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(mu / KbT))))
	tmp = 0.0
	if (NaChar <= -7.8e+55)
		tmp = t_2;
	elseif (NaChar <= -9.8e-14)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - t_0);
	elseif (NaChar <= -2.05e-17)
		tmp = Float64(t_1 - Float64(KbT * Float64(NdChar / Ec)));
	elseif (NaChar <= 2.9e-52)
		tmp = Float64(Float64(NaChar / Float64(Float64(Float64(Vef / KbT) + 1.0) + 1.0)) - t_0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT)));
	t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_2 = t_1 + (NdChar / (2.0 + (mu / KbT)));
	tmp = 0.0;
	if (NaChar <= -7.8e+55)
		tmp = t_2;
	elseif (NaChar <= -9.8e-14)
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	elseif (NaChar <= -2.05e-17)
		tmp = t_1 - (KbT * (NdChar / Ec));
	elseif (NaChar <= 2.9e-52)
		tmp = (NaChar / (((Vef / KbT) + 1.0) + 1.0)) - t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -7.8e+55], t$95$2, If[LessEqual[NaChar, -9.8e-14], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, -2.05e-17], N[(t$95$1 - N[(KbT * N[(NdChar / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.9e-52], N[(N[(NaChar / N[(N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -7.80000000000000054e55 or 2.9000000000000002e-52 < 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%

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

   5. Taylor expanded in mu around inf 76.1%

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

   6. Taylor expanded in mu around 0 70.6%

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

   if -7.80000000000000054e55 < NaChar < -9.79999999999999989e-14

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 68.9%

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

   6. Taylor expanded in Ev around 0 68.9%

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

   if -9.79999999999999989e-14 < NaChar < -2.05e-17

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. neg-sub0 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 100.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 100.0%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 100.0%

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

      12. distribute-neg-frac 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-neg-in 100.0%

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

      15. mul-1-neg 100.0%

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

      16. remove-double-neg 100.0%

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

      17. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in Ec around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -2.05e-17 < NaChar < 2.9000000000000002e-52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 81.4%

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

   6. Taylor expanded in Vef around 0 73.2%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq -9.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{elif}\;NaChar \leq 2.9 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{\left(\frac{Vef}{KbT} + 1\right) + 1} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ t_1 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_2 := t\_1 + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -2 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 0.00033:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 3.9 \cdot 10^{+23}:\\ \;\;\;\;t\_1 + KbT \cdot \frac{NdChar}{mu}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{+52}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)) 1.0))
          (* NaChar 0.5)))
        (t_1 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_2 (+ t_1 (/ NdChar 2.0))))
   (if (<= NaChar -2e+56)
     t_2
     (if (<= NaChar 0.00033)
       t_0
       (if (<= NaChar 3.9e+23)
         (+ t_1 (* KbT (/ NdChar mu)))
         (if (<= NaChar 4.1e+52) t_0 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	double t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -2e+56) {
		tmp = t_2;
	} else if (NaChar <= 0.00033) {
		tmp = t_0;
	} else if (NaChar <= 3.9e+23) {
		tmp = t_1 + (KbT * (NdChar / mu));
	} else if (NaChar <= 4.1e+52) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (ndchar / (exp(((vef + (mu + (edonor - ec))) / kbt)) + 1.0d0)) + (nachar * 0.5d0)
    t_1 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_2 = t_1 + (ndchar / 2.0d0)
    if (nachar <= (-2d+56)) then
        tmp = t_2
    else if (nachar <= 0.00033d0) then
        tmp = t_0
    else if (nachar <= 3.9d+23) then
        tmp = t_1 + (kbt * (ndchar / mu))
    else if (nachar <= 4.1d+52) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	double t_1 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -2e+56) {
		tmp = t_2;
	} else if (NaChar <= 0.00033) {
		tmp = t_0;
	} else if (NaChar <= 3.9e+23) {
		tmp = t_1 + (KbT * (NdChar / mu));
	} else if (NaChar <= 4.1e+52) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5)
	t_1 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_2 = t_1 + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -2e+56:
		tmp = t_2
	elif NaChar <= 0.00033:
		tmp = t_0
	elif NaChar <= 3.9e+23:
		tmp = t_1 + (KbT * (NdChar / mu))
	elif NaChar <= 4.1e+52:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)) + 1.0)) + Float64(NaChar * 0.5))
	t_1 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_2 = Float64(t_1 + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -2e+56)
		tmp = t_2;
	elseif (NaChar <= 0.00033)
		tmp = t_0;
	elseif (NaChar <= 3.9e+23)
		tmp = Float64(t_1 + Float64(KbT * Float64(NdChar / mu)));
	elseif (NaChar <= 4.1e+52)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_2 = t_1 + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -2e+56)
		tmp = t_2;
	elseif (NaChar <= 0.00033)
		tmp = t_0;
	elseif (NaChar <= 3.9e+23)
		tmp = t_1 + (KbT * (NdChar / mu));
	elseif (NaChar <= 4.1e+52)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2e+56], t$95$2, If[LessEqual[NaChar, 0.00033], t$95$0, If[LessEqual[NaChar, 3.9e+23], N[(t$95$1 + N[(KbT * N[(NdChar / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.1e+52], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2.00000000000000018e56 or 4.1e52 < 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%

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

   5. Taylor expanded in KbT around inf 66.3%

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

   if -2.00000000000000018e56 < NaChar < 3.3e-4 or 3.9e23 < NaChar < 4.1e52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 76.6%

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

   6. Taylor expanded in Ev around 0 64.3%

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

   if 3.3e-4 < NaChar < 3.9e23

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. +-commutative 71.4%

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

      3. associate--l+ 71.4%

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

      4. sub-neg 71.4%

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

      5. +-commutative 71.4%

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

      6. neg-sub0 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 71.4%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 71.4%

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

      12. distribute-neg-frac 71.4%

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

      13. +-commutative 71.4%

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

      14. distribute-neg-in 71.4%

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

      15. mul-1-neg 71.4%

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

      16. remove-double-neg 71.4%

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

      17. sub-neg 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in mu around inf 86.4%

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

      1. associate-/l* 86.4%

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

   10. Simplified 86.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2 \cdot 10^{+56}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 0.00033:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 3.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + KbT \cdot \frac{NdChar}{mu}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{+52}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ t_1 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_2 := t\_1 + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 0.00033:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.15 \cdot 10^{+24}:\\ \;\;\;\;t\_1 + \frac{NdChar \cdot KbT}{EDonor}\\ \mathbf{elif}\;NaChar \leq 6 \cdot 10^{+52}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)) 1.0))
          (* NaChar 0.5)))
        (t_1 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_2 (+ t_1 (/ NdChar 2.0))))
   (if (<= NaChar -1.5e+58)
     t_2
     (if (<= NaChar 0.00033)
       t_0
       (if (<= NaChar 1.15e+24)
         (+ t_1 (/ (* NdChar KbT) EDonor))
         (if (<= NaChar 6e+52) t_0 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	double t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -1.5e+58) {
		tmp = t_2;
	} else if (NaChar <= 0.00033) {
		tmp = t_0;
	} else if (NaChar <= 1.15e+24) {
		tmp = t_1 + ((NdChar * KbT) / EDonor);
	} else if (NaChar <= 6e+52) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (ndchar / (exp(((vef + (mu + (edonor - ec))) / kbt)) + 1.0d0)) + (nachar * 0.5d0)
    t_1 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_2 = t_1 + (ndchar / 2.0d0)
    if (nachar <= (-1.5d+58)) then
        tmp = t_2
    else if (nachar <= 0.00033d0) then
        tmp = t_0
    else if (nachar <= 1.15d+24) then
        tmp = t_1 + ((ndchar * kbt) / edonor)
    else if (nachar <= 6d+52) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	double t_1 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -1.5e+58) {
		tmp = t_2;
	} else if (NaChar <= 0.00033) {
		tmp = t_0;
	} else if (NaChar <= 1.15e+24) {
		tmp = t_1 + ((NdChar * KbT) / EDonor);
	} else if (NaChar <= 6e+52) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5)
	t_1 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_2 = t_1 + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -1.5e+58:
		tmp = t_2
	elif NaChar <= 0.00033:
		tmp = t_0
	elif NaChar <= 1.15e+24:
		tmp = t_1 + ((NdChar * KbT) / EDonor)
	elif NaChar <= 6e+52:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)) + 1.0)) + Float64(NaChar * 0.5))
	t_1 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_2 = Float64(t_1 + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -1.5e+58)
		tmp = t_2;
	elseif (NaChar <= 0.00033)
		tmp = t_0;
	elseif (NaChar <= 1.15e+24)
		tmp = Float64(t_1 + Float64(Float64(NdChar * KbT) / EDonor));
	elseif (NaChar <= 6e+52)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_2 = t_1 + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -1.5e+58)
		tmp = t_2;
	elseif (NaChar <= 0.00033)
		tmp = t_0;
	elseif (NaChar <= 1.15e+24)
		tmp = t_1 + ((NdChar * KbT) / EDonor);
	elseif (NaChar <= 6e+52)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.5e+58], t$95$2, If[LessEqual[NaChar, 0.00033], t$95$0, If[LessEqual[NaChar, 1.15e+24], N[(t$95$1 + N[(N[(NdChar * KbT), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 6e+52], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.5000000000000001e58 or 6e52 < 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%

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

   5. Taylor expanded in KbT around inf 66.3%

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

   if -1.5000000000000001e58 < NaChar < 3.3e-4 or 1.15e24 < NaChar < 6e52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 76.6%

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

   6. Taylor expanded in Ev around 0 64.3%

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

   if 3.3e-4 < NaChar < 1.15e24

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. +-commutative 71.4%

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

      3. associate--l+ 71.4%

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

      4. sub-neg 71.4%

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

      5. +-commutative 71.4%

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

      6. neg-sub0 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 71.4%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 71.4%

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

      12. distribute-neg-frac 71.4%

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

      13. +-commutative 71.4%

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

      14. distribute-neg-in 71.4%

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

      15. mul-1-neg 71.4%

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

      16. remove-double-neg 71.4%

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

      17. sub-neg 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in EDonor around inf 100.0%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 0.00033:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 1.15 \cdot 10^{+24}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar \cdot KbT}{EDonor}\\ \mathbf{elif}\;NaChar \leq 6 \cdot 10^{+52}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_2 := t\_1 + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -5 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 0.00033:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - t\_0}\\ \mathbf{elif}\;NaChar \leq 7.6 \cdot 10^{+23}:\\ \;\;\;\;t\_1 + \frac{NdChar \cdot KbT}{EDonor}\\ \mathbf{elif}\;NaChar \leq 2.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{NdChar}{t\_0 + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)))
        (t_1 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_2 (+ t_1 (/ NdChar 2.0))))
   (if (<= NaChar -5e+54)
     t_2
     (if (<= NaChar 0.00033)
       (- (/ NaChar (+ 2.0 (/ Ev KbT))) (/ NdChar (- -1.0 t_0)))
       (if (<= NaChar 7.6e+23)
         (+ t_1 (/ (* NdChar KbT) EDonor))
         (if (<= NaChar 2.5e+52)
           (+ (/ NdChar (+ t_0 1.0)) (* NaChar 0.5))
           t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((Vef + (mu + (EDonor - Ec))) / KbT));
	double t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -5e+54) {
		tmp = t_2;
	} else if (NaChar <= 0.00033) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - t_0));
	} else if (NaChar <= 7.6e+23) {
		tmp = t_1 + ((NdChar * KbT) / EDonor);
	} else if (NaChar <= 2.5e+52) {
		tmp = (NdChar / (t_0 + 1.0)) + (NaChar * 0.5);
	} 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 = exp(((vef + (mu + (edonor - ec))) / kbt))
    t_1 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_2 = t_1 + (ndchar / 2.0d0)
    if (nachar <= (-5d+54)) then
        tmp = t_2
    else if (nachar <= 0.00033d0) then
        tmp = (nachar / (2.0d0 + (ev / kbt))) - (ndchar / ((-1.0d0) - t_0))
    else if (nachar <= 7.6d+23) then
        tmp = t_1 + ((ndchar * kbt) / edonor)
    else if (nachar <= 2.5d+52) then
        tmp = (ndchar / (t_0 + 1.0d0)) + (nachar * 0.5d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT));
	double t_1 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_2 = t_1 + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -5e+54) {
		tmp = t_2;
	} else if (NaChar <= 0.00033) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - t_0));
	} else if (NaChar <= 7.6e+23) {
		tmp = t_1 + ((NdChar * KbT) / EDonor);
	} else if (NaChar <= 2.5e+52) {
		tmp = (NdChar / (t_0 + 1.0)) + (NaChar * 0.5);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))
	t_1 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_2 = t_1 + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -5e+54:
		tmp = t_2
	elif NaChar <= 0.00033:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - t_0))
	elif NaChar <= 7.6e+23:
		tmp = t_1 + ((NdChar * KbT) / EDonor)
	elif NaChar <= 2.5e+52:
		tmp = (NdChar / (t_0 + 1.0)) + (NaChar * 0.5)
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT))
	t_1 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_2 = Float64(t_1 + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -5e+54)
		tmp = t_2;
	elseif (NaChar <= 0.00033)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - Float64(NdChar / Float64(-1.0 - t_0)));
	elseif (NaChar <= 7.6e+23)
		tmp = Float64(t_1 + Float64(Float64(NdChar * KbT) / EDonor));
	elseif (NaChar <= 2.5e+52)
		tmp = Float64(Float64(NdChar / Float64(t_0 + 1.0)) + Float64(NaChar * 0.5));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((Vef + (mu + (EDonor - Ec))) / KbT));
	t_1 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_2 = t_1 + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -5e+54)
		tmp = t_2;
	elseif (NaChar <= 0.00033)
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - t_0));
	elseif (NaChar <= 7.6e+23)
		tmp = t_1 + ((NdChar * KbT) / EDonor);
	elseif (NaChar <= 2.5e+52)
		tmp = (NdChar / (t_0 + 1.0)) + (NaChar * 0.5);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -5e+54], t$95$2, If[LessEqual[NaChar, 0.00033], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 7.6e+23], N[(t$95$1 + N[(N[(NdChar * KbT), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.5e+52], N[(N[(NdChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -5.00000000000000005e54 or 2.5e52 < 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%

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

   5. Taylor expanded in KbT around inf 66.3%

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

   if -5.00000000000000005e54 < NaChar < 3.3e-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%

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

   5. Taylor expanded in Ev around inf 77.6%

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

   6. Taylor expanded in Ev around 0 68.4%

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

   if 3.3e-4 < NaChar < 7.5999999999999995e23

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. +-commutative 71.4%

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

      3. associate--l+ 71.4%

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

      4. sub-neg 71.4%

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

      5. +-commutative 71.4%

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

      6. neg-sub0 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 71.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 71.4%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 71.4%

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

      12. distribute-neg-frac 71.4%

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

      13. +-commutative 71.4%

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

      14. distribute-neg-in 71.4%

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

      15. mul-1-neg 71.4%

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

      16. remove-double-neg 71.4%

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

      17. sub-neg 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in EDonor around inf 100.0%

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

   if 7.5999999999999995e23 < NaChar < 2.5e52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 60.3%

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

   6. Taylor expanded in Ev around 0 62.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{Vef + \left(\left(EDonor - Ec\right) + mu\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5 \cdot 10^{+54}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 0.00033:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 7.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar \cdot KbT}{EDonor}\\ \mathbf{elif}\;NaChar \leq 2.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{if}\;NaChar \leq -1.95 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + t\_0\\ \mathbf{elif}\;NaChar \leq 9.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 6.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} + t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + KbT \cdot \frac{NdChar}{mu}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 2.0 (/ mu KbT)))))
   (if (<= NaChar -1.95e+87)
     (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) t_0)
     (if (<= NaChar 9.5e-52)
       (+
        (/ NdChar (+ (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)) 1.0))
        (* NaChar 0.5))
       (if (<= NaChar 6.5e+144)
         (+ (/ NaChar (+ (exp (/ mu (- KbT))) 1.0)) t_0)
         (+
          (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0))
          (* KbT (/ NdChar mu))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (2.0 + (mu / KbT));
	double tmp;
	if (NaChar <= -1.95e+87) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + t_0;
	} else if (NaChar <= 9.5e-52) {
		tmp = (NdChar / (exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	} else if (NaChar <= 6.5e+144) {
		tmp = (NaChar / (exp((mu / -KbT)) + 1.0)) + t_0;
	} else {
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (KbT * (NdChar / mu));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (2.0d0 + (mu / kbt))
    if (nachar <= (-1.95d+87)) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + t_0
    else if (nachar <= 9.5d-52) then
        tmp = (ndchar / (exp(((vef + (mu + (edonor - ec))) / kbt)) + 1.0d0)) + (nachar * 0.5d0)
    else if (nachar <= 6.5d+144) then
        tmp = (nachar / (exp((mu / -kbt)) + 1.0d0)) + t_0
    else
        tmp = (nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)) + (kbt * (ndchar / mu))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (2.0 + (mu / KbT));
	double tmp;
	if (NaChar <= -1.95e+87) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + t_0;
	} else if (NaChar <= 9.5e-52) {
		tmp = (NdChar / (Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	} else if (NaChar <= 6.5e+144) {
		tmp = (NaChar / (Math.exp((mu / -KbT)) + 1.0)) + t_0;
	} else {
		tmp = (NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (KbT * (NdChar / mu));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (2.0 + (mu / KbT))
	tmp = 0
	if NaChar <= -1.95e+87:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + t_0
	elif NaChar <= 9.5e-52:
		tmp = (NdChar / (math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5)
	elif NaChar <= 6.5e+144:
		tmp = (NaChar / (math.exp((mu / -KbT)) + 1.0)) + t_0
	else:
		tmp = (NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (KbT * (NdChar / mu))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(2.0 + Float64(mu / KbT)))
	tmp = 0.0
	if (NaChar <= -1.95e+87)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + t_0);
	elseif (NaChar <= 9.5e-52)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)) + 1.0)) + Float64(NaChar * 0.5));
	elseif (NaChar <= 6.5e+144)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0)) + t_0);
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0)) + Float64(KbT * Float64(NdChar / mu)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (2.0 + (mu / KbT));
	tmp = 0.0;
	if (NaChar <= -1.95e+87)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + t_0;
	elseif (NaChar <= 9.5e-52)
		tmp = (NdChar / (exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	elseif (NaChar <= 6.5e+144)
		tmp = (NaChar / (exp((mu / -KbT)) + 1.0)) + t_0;
	else
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (KbT * (NdChar / mu));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.95e+87], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[NaChar, 9.5e-52], N[(N[(NdChar / N[(N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 6.5e+144], N[(N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NdChar / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.9500000000000001e87

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 86.2%

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

   6. Taylor expanded in mu around 0 65.0%

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

   7. Taylor expanded in Ev around inf 52.4%

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

   if -1.9500000000000001e87 < NaChar < 9.50000000000000007e-52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 77.2%

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

   6. Taylor expanded in Ev around 0 64.1%

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

   if 9.50000000000000007e-52 < NaChar < 6.50000000000000007e144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 62.9%

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

   6. Taylor expanded in mu around 0 71.4%

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

   7. Taylor expanded in mu around inf 64.5%

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

      1. associate-*r/ 64.5%

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

      2. mul-1-neg 64.5%

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

   9. Simplified 64.5%

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

   if 6.50000000000000007e144 < 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%

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

   5. Taylor expanded in KbT around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. +-commutative 72.6%

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

      3. associate--l+ 72.6%

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

      4. sub-neg 72.6%

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

      5. +-commutative 72.6%

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

      6. neg-sub0 72.6%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 72.6%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 75.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 75.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 75.4%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 75.4%

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

      12. distribute-neg-frac 75.4%

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

      13. +-commutative 75.4%

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

      14. distribute-neg-in 75.4%

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

      15. mul-1-neg 75.4%

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

      16. remove-double-neg 75.4%

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

      17. sub-neg 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in mu around inf 59.4%

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

      1. associate-/l* 59.4%

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

   10. Simplified 59.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.95 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 9.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 6.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + KbT \cdot \frac{NdChar}{mu}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{2 + \frac{mu}{KbT}}\\ t_1 := \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + t\_0\\ \mathbf{if}\;NaChar \leq -4 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 6.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 2.0 (/ mu KbT))))
        (t_1 (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) t_0)))
   (if (<= NaChar -4e+89)
     t_1
     (if (<= NaChar 6.2e-54)
       (+
        (/ NdChar (+ (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT)) 1.0))
        (* NaChar 0.5))
       (if (<= NaChar 1.8e+93)
         (+ (/ NaChar (+ (exp (/ mu (- KbT))) 1.0)) t_0)
         t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (2.0 + (mu / KbT));
	double t_1 = (NaChar / (exp((Ev / KbT)) + 1.0)) + t_0;
	double tmp;
	if (NaChar <= -4e+89) {
		tmp = t_1;
	} else if (NaChar <= 6.2e-54) {
		tmp = (NdChar / (exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	} else if (NaChar <= 1.8e+93) {
		tmp = (NaChar / (exp((mu / -KbT)) + 1.0)) + t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (2.0d0 + (mu / kbt))
    t_1 = (nachar / (exp((ev / kbt)) + 1.0d0)) + t_0
    if (nachar <= (-4d+89)) then
        tmp = t_1
    else if (nachar <= 6.2d-54) then
        tmp = (ndchar / (exp(((vef + (mu + (edonor - ec))) / kbt)) + 1.0d0)) + (nachar * 0.5d0)
    else if (nachar <= 1.8d+93) then
        tmp = (nachar / (exp((mu / -kbt)) + 1.0d0)) + t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (2.0 + (mu / KbT));
	double t_1 = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + t_0;
	double tmp;
	if (NaChar <= -4e+89) {
		tmp = t_1;
	} else if (NaChar <= 6.2e-54) {
		tmp = (NdChar / (Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	} else if (NaChar <= 1.8e+93) {
		tmp = (NaChar / (Math.exp((mu / -KbT)) + 1.0)) + t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (2.0 + (mu / KbT))
	t_1 = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + t_0
	tmp = 0
	if NaChar <= -4e+89:
		tmp = t_1
	elif NaChar <= 6.2e-54:
		tmp = (NdChar / (math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5)
	elif NaChar <= 1.8e+93:
		tmp = (NaChar / (math.exp((mu / -KbT)) + 1.0)) + t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(2.0 + Float64(mu / KbT)))
	t_1 = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + t_0)
	tmp = 0.0
	if (NaChar <= -4e+89)
		tmp = t_1;
	elseif (NaChar <= 6.2e-54)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)) + 1.0)) + Float64(NaChar * 0.5));
	elseif (NaChar <= 1.8e+93)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0)) + t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (2.0 + (mu / KbT));
	t_1 = (NaChar / (exp((Ev / KbT)) + 1.0)) + t_0;
	tmp = 0.0;
	if (NaChar <= -4e+89)
		tmp = t_1;
	elseif (NaChar <= 6.2e-54)
		tmp = (NdChar / (exp(((Vef + (mu + (EDonor - Ec))) / KbT)) + 1.0)) + (NaChar * 0.5);
	elseif (NaChar <= 1.8e+93)
		tmp = (NaChar / (exp((mu / -KbT)) + 1.0)) + t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]}, If[LessEqual[NaChar, -4e+89], t$95$1, If[LessEqual[NaChar, 6.2e-54], N[(N[(NdChar / N[(N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.8e+93], N[(N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -3.99999999999999998e89 or 1.8e93 < 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%

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

   5. Taylor expanded in mu around inf 82.2%

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

   6. Taylor expanded in mu around 0 70.2%

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

   7. Taylor expanded in Ev around inf 52.2%

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

   if -3.99999999999999998e89 < NaChar < 6.20000000000000008e-54

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 77.2%

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

   6. Taylor expanded in Ev around 0 64.1%

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

   if 6.20000000000000008e-54 < NaChar < 1.8e93

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 58.1%

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

   6. Taylor expanded in mu around 0 69.7%

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

   7. Taylor expanded in mu around inf 63.5%

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

      1. associate-*r/ 63.5%

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

      2. mul-1-neg 63.5%

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

   9. Simplified 63.5%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4 \cdot 10^{+89}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 6.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{mu}{-KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 61.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.3 \cdot 10^{+57} \lor \neg \left(NaChar \leq 9 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.3e+57) (not (<= NaChar 9e-52)))
   (+
    (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0))
    (/ NdChar (+ 2.0 (/ mu KbT))))
   (-
    (/ NaChar (+ 2.0 (/ Ev KbT)))
    (/ NdChar (- -1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) 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 <= -2.3e+57) || !(NaChar <= 9e-52)) {
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)));
	} else {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-2.3d+57)) .or. (.not. (nachar <= 9d-52))) then
        tmp = (nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)) + (ndchar / (2.0d0 + (mu / kbt)))
    else
        tmp = (nachar / (2.0d0 + (ev / kbt))) - (ndchar / ((-1.0d0) - exp(((vef + (mu + (edonor - ec))) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.3e+57) || !(NaChar <= 9e-52)) {
		tmp = (NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)));
	} else {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2.3e+57) or not (NaChar <= 9e-52):
		tmp = (NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)))
	else:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - math.exp(((Vef + (mu + (EDonor - Ec))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -2.3e+57) || !(NaChar <= 9e-52))
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0)) + Float64(NdChar / Float64(2.0 + Float64(mu / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -2.3e+57) || ~((NaChar <= 9e-52)))
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)));
	else
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - exp(((Vef + (mu + (EDonor - Ec))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -2.3e+57], N[Not[LessEqual[NaChar, 9e-52]], $MachinePrecision]], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.2999999999999999e57 or 9.0000000000000001e-52 < 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%

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

   5. Taylor expanded in mu around inf 76.1%

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

   6. Taylor expanded in mu around 0 70.6%

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

   if -2.2999999999999999e57 < NaChar < 9.0000000000000001e-52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 76.9%

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

   6. Taylor expanded in Ev around 0 68.6%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.3 \cdot 10^{+57} \lor \neg \left(NaChar \leq 9 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ t_1 := \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;NdChar \leq -1.7 \cdot 10^{+77}:\\ \;\;\;\;t\_1 + t\_0\\ \mathbf{elif}\;NdChar \leq 940000000:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 1.4 \cdot 10^{+146}:\\ \;\;\;\;t\_0 - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 2.0 (/ Ev KbT))))
        (t_1 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))))
   (if (<= NdChar -1.7e+77)
     (+ t_1 t_0)
     (if (<= NdChar 940000000.0)
       (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (/ NdChar 2.0))
       (if (<= NdChar 1.4e+146)
         (- t_0 (/ NdChar (- -1.0 (exp (/ mu KbT)))))
         (+ t_1 (/ 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 t_0 = NaChar / (2.0 + (Ev / KbT));
	double t_1 = NdChar / (exp((EDonor / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -1.7e+77) {
		tmp = t_1 + t_0;
	} else if (NdChar <= 940000000.0) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (NdChar <= 1.4e+146) {
		tmp = t_0 - (NdChar / (-1.0 - exp((mu / KbT))));
	} else {
		tmp = t_1 + (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (2.0d0 + (ev / kbt))
    t_1 = ndchar / (exp((edonor / kbt)) + 1.0d0)
    if (ndchar <= (-1.7d+77)) then
        tmp = t_1 + t_0
    else if (ndchar <= 940000000.0d0) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else if (ndchar <= 1.4d+146) then
        tmp = t_0 - (ndchar / ((-1.0d0) - exp((mu / kbt))))
    else
        tmp = t_1 + (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 t_0 = NaChar / (2.0 + (Ev / KbT));
	double t_1 = NdChar / (Math.exp((EDonor / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -1.7e+77) {
		tmp = t_1 + t_0;
	} else if (NdChar <= 940000000.0) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (NdChar <= 1.4e+146) {
		tmp = t_0 - (NdChar / (-1.0 - Math.exp((mu / KbT))));
	} else {
		tmp = t_1 + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (2.0 + (Ev / KbT))
	t_1 = NdChar / (math.exp((EDonor / KbT)) + 1.0)
	tmp = 0
	if NdChar <= -1.7e+77:
		tmp = t_1 + t_0
	elif NdChar <= 940000000.0:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0)
	elif NdChar <= 1.4e+146:
		tmp = t_0 - (NdChar / (-1.0 - math.exp((mu / KbT))))
	else:
		tmp = t_1 + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(2.0 + Float64(Ev / KbT)))
	t_1 = Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0))
	tmp = 0.0
	if (NdChar <= -1.7e+77)
		tmp = Float64(t_1 + t_0);
	elseif (NdChar <= 940000000.0)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	elseif (NdChar <= 1.4e+146)
		tmp = Float64(t_0 - Float64(NdChar / Float64(-1.0 - exp(Float64(mu / KbT)))));
	else
		tmp = Float64(t_1 + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (2.0 + (Ev / KbT));
	t_1 = NdChar / (exp((EDonor / KbT)) + 1.0);
	tmp = 0.0;
	if (NdChar <= -1.7e+77)
		tmp = t_1 + t_0;
	elseif (NdChar <= 940000000.0)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	elseif (NdChar <= 1.4e+146)
		tmp = t_0 - (NdChar / (-1.0 - exp((mu / KbT))));
	else
		tmp = t_1 + (NaChar / 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[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.7e+77], N[(t$95$1 + t$95$0), $MachinePrecision], If[LessEqual[NdChar, 940000000.0], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.4e+146], N[(t$95$0 - N[(NdChar / N[(-1.0 - N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -1.69999999999999998e77

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 79.9%

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

   6. Taylor expanded in Ev around 0 73.4%

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

   7. Taylor expanded in EDonor around inf 51.2%

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

   if -1.69999999999999998e77 < NdChar < 9.4e8

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.2%

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

   6. Taylor expanded in Ev around inf 48.9%

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

   if 9.4e8 < NdChar < 1.4e146

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 61.1%

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

   6. Taylor expanded in Ev around 0 49.2%

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

   7. Taylor expanded in mu around inf 42.3%

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

   if 1.4e146 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 67.0%

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

   6. Taylor expanded in KbT around inf 50.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NdChar \leq 940000000:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 1.4 \cdot 10^{+146}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 40.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ t_1 := \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;NdChar \leq -1.1 \cdot 10^{+72}:\\ \;\;\;\;t\_1 + t\_0\\ \mathbf{elif}\;NdChar \leq 6.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.8 \cdot 10^{+148}:\\ \;\;\;\;t\_0 - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 2.0 (/ Ev KbT))))
        (t_1 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))))
   (if (<= NdChar -1.1e+72)
     (+ t_1 t_0)
     (if (<= NdChar 6.5e+15)
       (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (/ NdChar (+ 2.0 (/ mu KbT))))
       (if (<= NdChar 3.8e+148)
         (- t_0 (/ NdChar (- -1.0 (exp (/ mu KbT)))))
         (+ t_1 (/ 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 t_0 = NaChar / (2.0 + (Ev / KbT));
	double t_1 = NdChar / (exp((EDonor / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -1.1e+72) {
		tmp = t_1 + t_0;
	} else if (NdChar <= 6.5e+15) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)));
	} else if (NdChar <= 3.8e+148) {
		tmp = t_0 - (NdChar / (-1.0 - exp((mu / KbT))));
	} else {
		tmp = t_1 + (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (2.0d0 + (ev / kbt))
    t_1 = ndchar / (exp((edonor / kbt)) + 1.0d0)
    if (ndchar <= (-1.1d+72)) then
        tmp = t_1 + t_0
    else if (ndchar <= 6.5d+15) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / (2.0d0 + (mu / kbt)))
    else if (ndchar <= 3.8d+148) then
        tmp = t_0 - (ndchar / ((-1.0d0) - exp((mu / kbt))))
    else
        tmp = t_1 + (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 t_0 = NaChar / (2.0 + (Ev / KbT));
	double t_1 = NdChar / (Math.exp((EDonor / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -1.1e+72) {
		tmp = t_1 + t_0;
	} else if (NdChar <= 6.5e+15) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)));
	} else if (NdChar <= 3.8e+148) {
		tmp = t_0 - (NdChar / (-1.0 - Math.exp((mu / KbT))));
	} else {
		tmp = t_1 + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (2.0 + (Ev / KbT))
	t_1 = NdChar / (math.exp((EDonor / KbT)) + 1.0)
	tmp = 0
	if NdChar <= -1.1e+72:
		tmp = t_1 + t_0
	elif NdChar <= 6.5e+15:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)))
	elif NdChar <= 3.8e+148:
		tmp = t_0 - (NdChar / (-1.0 - math.exp((mu / KbT))))
	else:
		tmp = t_1 + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(2.0 + Float64(Ev / KbT)))
	t_1 = Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0))
	tmp = 0.0
	if (NdChar <= -1.1e+72)
		tmp = Float64(t_1 + t_0);
	elseif (NdChar <= 6.5e+15)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / Float64(2.0 + Float64(mu / KbT))));
	elseif (NdChar <= 3.8e+148)
		tmp = Float64(t_0 - Float64(NdChar / Float64(-1.0 - exp(Float64(mu / KbT)))));
	else
		tmp = Float64(t_1 + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (2.0 + (Ev / KbT));
	t_1 = NdChar / (exp((EDonor / KbT)) + 1.0);
	tmp = 0.0;
	if (NdChar <= -1.1e+72)
		tmp = t_1 + t_0;
	elseif (NdChar <= 6.5e+15)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)));
	elseif (NdChar <= 3.8e+148)
		tmp = t_0 - (NdChar / (-1.0 - exp((mu / KbT))));
	else
		tmp = t_1 + (NaChar / 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[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.1e+72], N[(t$95$1 + t$95$0), $MachinePrecision], If[LessEqual[NdChar, 6.5e+15], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.8e+148], N[(t$95$0 - N[(NdChar / N[(-1.0 - N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -1.1e72

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 80.8%

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

   6. Taylor expanded in Ev around 0 72.5%

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

   7. Taylor expanded in EDonor around inf 49.5%

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

   if -1.1e72 < NdChar < 6.5e15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 76.9%

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

   6. Taylor expanded in mu around 0 67.9%

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

   7. Taylor expanded in Ev around inf 51.6%

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

   if 6.5e15 < NdChar < 3.7999999999999998e148

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 61.1%

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

   6. Taylor expanded in Ev around 0 49.2%

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

   7. Taylor expanded in mu around inf 42.3%

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

   if 3.7999999999999998e148 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 67.0%

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

   6. Taylor expanded in KbT around inf 50.7%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.1 \cdot 10^{+72}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NdChar \leq 6.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -1.6 \cdot 10^{+53}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -1.55 \cdot 10^{-85}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 3.5 \cdot 10^{+51}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 2.0))))
   (if (<= NaChar -1.6e+53)
     t_0
     (if (<= NaChar -1.55e-85)
       (+ (/ NdChar (+ (exp (/ mu KbT)) 1.0)) (/ NaChar 2.0))
       (if (<= NaChar 3.5e+51)
         (+ (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)) (/ NaChar 2.0))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -1.6e+53) {
		tmp = t_0;
	} else if (NaChar <= -1.55e-85) {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	} else if (NaChar <= 3.5e+51) {
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    if (nachar <= (-1.6d+53)) then
        tmp = t_0
    else if (nachar <= (-1.55d-85)) then
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else if (nachar <= 3.5d+51) then
        tmp = (ndchar / (exp((edonor / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -1.6e+53) {
		tmp = t_0;
	} else if (NaChar <= -1.55e-85) {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	} else if (NaChar <= 3.5e+51) {
		tmp = (NdChar / (Math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -1.6e+53:
		tmp = t_0
	elif NaChar <= -1.55e-85:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar / 2.0)
	elif NaChar <= 3.5e+51:
		tmp = (NdChar / (math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -1.6e+53)
		tmp = t_0;
	elseif (NaChar <= -1.55e-85)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	elseif (NaChar <= 3.5e+51)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -1.6e+53)
		tmp = t_0;
	elseif (NaChar <= -1.55e-85)
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	elseif (NaChar <= 3.5e+51)
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.6e+53], t$95$0, If[LessEqual[NaChar, -1.55e-85], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.5e+51], N[(N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.6e53 or 3.5e51 < 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%

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

   5. Taylor expanded in EDonor around inf 81.2%

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

   6. Taylor expanded in EAccept around inf 53.5%

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

   7. Taylor expanded in EDonor around 0 45.8%

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

   if -1.6e53 < NaChar < -1.5500000000000001e-85

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 77.3%

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

   6. Taylor expanded in KbT around inf 51.8%

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

   if -1.5500000000000001e-85 < NaChar < 3.5e51

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 66.9%

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

   6. Taylor expanded in KbT around inf 47.3%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq -1.55 \cdot 10^{-85}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 3.5 \cdot 10^{+51}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 39.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+79}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 3.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 1.9 \cdot 10^{+146}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)) (/ NaChar 2.0))))
   (if (<= NdChar -1.4e+79)
     t_0
     (if (<= NdChar 3.5e+16)
       (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (/ NdChar 2.0))
       (if (<= NdChar 1.9e+146)
         (+ (/ NdChar (+ (exp (/ mu KbT)) 1.0)) (/ NaChar 2.0))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -1.4e+79) {
		tmp = t_0;
	} else if (NdChar <= 3.5e+16) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (NdChar <= 1.9e+146) {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (exp((edonor / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    if (ndchar <= (-1.4d+79)) then
        tmp = t_0
    else if (ndchar <= 3.5d+16) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else if (ndchar <= 1.9d+146) then
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (Math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -1.4e+79) {
		tmp = t_0;
	} else if (NdChar <= 3.5e+16) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (NdChar <= 1.9e+146) {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -1.4e+79:
		tmp = t_0
	elif NdChar <= 3.5e+16:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0)
	elif NdChar <= 1.9e+146:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar / 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -1.4e+79)
		tmp = t_0;
	elseif (NdChar <= 3.5e+16)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	elseif (NdChar <= 1.9e+146)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -1.4e+79)
		tmp = t_0;
	elseif (NdChar <= 3.5e+16)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	elseif (NdChar <= 1.9e+146)
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.4e+79], t$95$0, If[LessEqual[NdChar, 3.5e+16], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.9e+146], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -1.4000000000000001e79 or 1.8999999999999999e146 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 65.2%

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

   6. Taylor expanded in KbT around inf 48.0%

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

   if -1.4000000000000001e79 < NdChar < 3.5e16

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.2%

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

   6. Taylor expanded in Ev around inf 48.9%

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

   if 3.5e16 < NdChar < 1.8999999999999999e146

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 70.2%

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

   6. Taylor expanded in KbT around inf 42.3%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.4 \cdot 10^{+79}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 3.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 1.9 \cdot 10^{+146}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 39.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;NdChar \leq -4.9 \cdot 10^{+76}:\\ \;\;\;\;t\_0 + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NdChar \leq 350000000000:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 2.25 \cdot 10^{+145}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))))
   (if (<= NdChar -4.9e+76)
     (+ t_0 (/ NaChar (+ 2.0 (/ Ev KbT))))
     (if (<= NdChar 350000000000.0)
       (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (/ NdChar 2.0))
       (if (<= NdChar 2.25e+145)
         (+ (/ NdChar (+ (exp (/ mu KbT)) 1.0)) (/ NaChar 2.0))
         (+ t_0 (/ NaChar 2.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp((EDonor / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -4.9e+76) {
		tmp = t_0 + (NaChar / (2.0 + (Ev / KbT)));
	} else if (NdChar <= 350000000000.0) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (NdChar <= 2.25e+145) {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = t_0 + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp((edonor / kbt)) + 1.0d0)
    if (ndchar <= (-4.9d+76)) then
        tmp = t_0 + (nachar / (2.0d0 + (ev / kbt)))
    else if (ndchar <= 350000000000.0d0) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else if (ndchar <= 2.25d+145) then
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else
        tmp = t_0 + (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 t_0 = NdChar / (Math.exp((EDonor / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -4.9e+76) {
		tmp = t_0 + (NaChar / (2.0 + (Ev / KbT)));
	} else if (NdChar <= 350000000000.0) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (NdChar <= 2.25e+145) {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = t_0 + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp((EDonor / KbT)) + 1.0)
	tmp = 0
	if NdChar <= -4.9e+76:
		tmp = t_0 + (NaChar / (2.0 + (Ev / KbT)))
	elif NdChar <= 350000000000.0:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0)
	elif NdChar <= 2.25e+145:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar / 2.0)
	else:
		tmp = t_0 + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0))
	tmp = 0.0
	if (NdChar <= -4.9e+76)
		tmp = Float64(t_0 + Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))));
	elseif (NdChar <= 350000000000.0)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	elseif (NdChar <= 2.25e+145)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	else
		tmp = Float64(t_0 + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp((EDonor / KbT)) + 1.0);
	tmp = 0.0;
	if (NdChar <= -4.9e+76)
		tmp = t_0 + (NaChar / (2.0 + (Ev / KbT)));
	elseif (NdChar <= 350000000000.0)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / 2.0);
	elseif (NdChar <= 2.25e+145)
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	else
		tmp = t_0 + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -4.9e+76], N[(t$95$0 + N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 350000000000.0], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.25e+145], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -4.90000000000000026e76

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 79.9%

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

   6. Taylor expanded in Ev around 0 73.4%

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

   7. Taylor expanded in EDonor around inf 51.2%

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

   if -4.90000000000000026e76 < NdChar < 3.5e11

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.2%

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

   6. Taylor expanded in Ev around inf 48.9%

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

   if 3.5e11 < NdChar < 2.2499999999999999e145

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 70.2%

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

   6. Taylor expanded in KbT around inf 42.3%

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

   if 2.2499999999999999e145 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 67.0%

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

   6. Taylor expanded in KbT around inf 50.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.9 \cdot 10^{+76}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NdChar \leq 350000000000:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 2.25 \cdot 10^{+145}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 40.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq -2 \cdot 10^{+164} \lor \neg \left(Ec \leq 1.1 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Ec}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Ec -2e+164) (not (<= Ec 1.1e+135)))
   (- (/ NaChar (+ 2.0 (/ Ev KbT))) (/ NdChar (- -1.0 (exp (/ Ec (- KbT))))))
   (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (/ NdChar (+ 2.0 (/ mu KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Ec <= -2e+164) || !(Ec <= 1.1e+135)) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - exp((Ec / -KbT))));
	} else {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ec <= (-2d+164)) .or. (.not. (ec <= 1.1d+135))) then
        tmp = (nachar / (2.0d0 + (ev / kbt))) - (ndchar / ((-1.0d0) - exp((ec / -kbt))))
    else
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / (2.0d0 + (mu / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Ec <= -2e+164) || !(Ec <= 1.1e+135)) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - Math.exp((Ec / -KbT))));
	} else {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Ec <= -2e+164) or not (Ec <= 1.1e+135):
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - math.exp((Ec / -KbT))))
	else:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Ec <= -2e+164) || !(Ec <= 1.1e+135))
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Ec / Float64(-KbT))))));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / Float64(2.0 + Float64(mu / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Ec <= -2e+164) || ~((Ec <= 1.1e+135)))
		tmp = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - exp((Ec / -KbT))));
	else
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (2.0 + (mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Ec, -2e+164], N[Not[LessEqual[Ec, 1.1e+135]], $MachinePrecision]], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < -2e164 or 1.1e135 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 79.0%

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

   6. Taylor expanded in Ev around 0 65.1%

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

   7. Taylor expanded in Ec around inf 62.2%

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

      1. associate-*r/ 62.2%

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

      2. mul-1-neg 62.2%

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

   9. Simplified 62.2%

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

   if -2e164 < Ec < 1.1e135

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 74.1%

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

   6. Taylor expanded in mu around 0 57.7%

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

   7. Taylor expanded in Ev around inf 43.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -2 \cdot 10^{+164} \lor \neg \left(Ec \leq 1.1 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{Ec}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 36.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 3.4 \cdot 10^{+131}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 3.4e+131)
   (+ (/ NaChar (+ (exp (/ Vef KbT)) 1.0)) (/ NdChar 2.0))
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 3.4e+131) {
		tmp = (NaChar / (exp((Vef / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= 3.4d+131) then
        tmp = (nachar / (exp((vef / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 3.4e+131) {
		tmp = (NaChar / (Math.exp((Vef / KbT)) + 1.0)) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 3.4e+131:
		tmp = (NaChar / (math.exp((Vef / KbT)) + 1.0)) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 3.4e+131)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 3.4e+131)
		tmp = (NaChar / (exp((Vef / KbT)) + 1.0)) + (NdChar / 2.0);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 3.4e+131], N[(N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 3.39999999999999986e131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.0%

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

   6. Taylor expanded in KbT around inf 38.8%

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

   if 3.39999999999999986e131 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 69.7%

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

   6. Taylor expanded in EAccept around inf 59.5%

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

   7. Taylor expanded in EDonor around 0 42.8%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 3.4 \cdot 10^{+131}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 37.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar 5.4e+51)
   (+ (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)) (/ NaChar 2.0))
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= 5.4e+51) {
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= 5.4d+51) then
        tmp = (ndchar / (exp((edonor / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= 5.4e+51) {
		tmp = (NdChar / (Math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= 5.4e+51:
		tmp = (NdChar / (math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= 5.4e+51)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= 5.4e+51)
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, 5.4e+51], N[(N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < 5.39999999999999983e51

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 69.6%

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

   6. Taylor expanded in KbT around inf 42.4%

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

   if 5.39999999999999983e51 < 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%

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

   5. Taylor expanded in EDonor around inf 81.7%

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

   6. Taylor expanded in EAccept around inf 58.4%

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

   7. Taylor expanded in EDonor around 0 50.5%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 35.5% accurate, 2.1× speedup

Math

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

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in EDonor around inf 72.3%

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

6. Taylor expanded in EAccept around inf 53.9%

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

7. Taylor expanded in EDonor around 0 40.5%

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

8. Final simplification 40.5%

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

Alternative 29: 28.0% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -1.9 \cdot 10^{+103}:\\ \;\;\;\;\frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq 2.3 \cdot 10^{-128}:\\ \;\;\;\;\frac{NaChar}{\left(\left(\left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right) + 1\right) + \frac{EAccept - mu}{KbT}\right) + 1} + \frac{NdChar}{\left(\left(\frac{EDonor - Ec}{KbT} + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= mu -1.9e+103)
   (/ NdChar (+ 2.0 (/ mu KbT)))
   (if (<= mu 2.3e-128)
     (+
      (/
       NaChar
       (+ (+ (+ (+ (/ Ev KbT) (/ Vef KbT)) 1.0) (/ (- EAccept mu) KbT)) 1.0))
      (/
       NdChar
       (+ (+ (+ (/ (- EDonor Ec) KbT) (+ (/ mu KbT) (/ Vef KbT))) 1.0) 1.0)))
     (* 0.5 (+ NdChar NaChar)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (mu <= -1.9e+103) {
		tmp = NdChar / (2.0 + (mu / KbT));
	} else if (mu <= 2.3e-128) {
		tmp = (NaChar / (((((Ev / KbT) + (Vef / KbT)) + 1.0) + ((EAccept - mu) / KbT)) + 1.0)) + (NdChar / (((((EDonor - Ec) / KbT) + ((mu / KbT) + (Vef / KbT))) + 1.0) + 1.0));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (mu <= (-1.9d+103)) then
        tmp = ndchar / (2.0d0 + (mu / kbt))
    else if (mu <= 2.3d-128) then
        tmp = (nachar / (((((ev / kbt) + (vef / kbt)) + 1.0d0) + ((eaccept - mu) / kbt)) + 1.0d0)) + (ndchar / (((((edonor - ec) / kbt) + ((mu / kbt) + (vef / kbt))) + 1.0d0) + 1.0d0))
    else
        tmp = 0.5d0 * (ndchar + nachar)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (mu <= -1.9e+103) {
		tmp = NdChar / (2.0 + (mu / KbT));
	} else if (mu <= 2.3e-128) {
		tmp = (NaChar / (((((Ev / KbT) + (Vef / KbT)) + 1.0) + ((EAccept - mu) / KbT)) + 1.0)) + (NdChar / (((((EDonor - Ec) / KbT) + ((mu / KbT) + (Vef / KbT))) + 1.0) + 1.0));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if mu <= -1.9e+103:
		tmp = NdChar / (2.0 + (mu / KbT))
	elif mu <= 2.3e-128:
		tmp = (NaChar / (((((Ev / KbT) + (Vef / KbT)) + 1.0) + ((EAccept - mu) / KbT)) + 1.0)) + (NdChar / (((((EDonor - Ec) / KbT) + ((mu / KbT) + (Vef / KbT))) + 1.0) + 1.0))
	else:
		tmp = 0.5 * (NdChar + NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (mu <= -1.9e+103)
		tmp = Float64(NdChar / Float64(2.0 + Float64(mu / KbT)));
	elseif (mu <= 2.3e-128)
		tmp = Float64(Float64(NaChar / Float64(Float64(Float64(Float64(Float64(Ev / KbT) + Float64(Vef / KbT)) + 1.0) + Float64(Float64(EAccept - mu) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Float64(Float64(Float64(EDonor - Ec) / KbT) + Float64(Float64(mu / KbT) + Float64(Vef / KbT))) + 1.0) + 1.0)));
	else
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (mu <= -1.9e+103)
		tmp = NdChar / (2.0 + (mu / KbT));
	elseif (mu <= 2.3e-128)
		tmp = (NaChar / (((((Ev / KbT) + (Vef / KbT)) + 1.0) + ((EAccept - mu) / KbT)) + 1.0)) + (NdChar / (((((EDonor - Ec) / KbT) + ((mu / KbT) + (Vef / KbT))) + 1.0) + 1.0));
	else
		tmp = 0.5 * (NdChar + NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[mu, -1.9e+103], N[(NdChar / N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 2.3e-128], N[(N[(NaChar / N[(N[(N[(N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(N[(EAccept - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(N[(EDonor - Ec), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if mu < -1.8999999999999998e103

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 80.1%

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

   6. Taylor expanded in mu around 0 46.7%

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

   7. Taylor expanded in KbT around inf 17.0%

      \[\leadsto \frac{NdChar}{2 + \frac{mu}{KbT}} + \frac{NaChar}{\color{blue}{2}} \]

   8. Taylor expanded in NdChar around inf 26.7%

      \[\leadsto \color{blue}{\frac{NdChar}{2 + \frac{mu}{KbT}}} \]

   if -1.8999999999999998e103 < mu < 2.3000000000000001e-128

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.0%

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

      1. associate--l+ 60.0%

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

      2. +-commutative 60.0%

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

      3. associate--l+ 60.0%

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

      4. sub-neg 60.0%

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

      5. +-commutative 60.0%

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

      6. neg-sub0 60.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      7. associate-+l- 60.0%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      8. div-sub 62.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      9. unsub-neg 62.4%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{\color{blue}{Ec + \left(-EDonor\right)}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      10. mul-1-neg 62.4%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \left(0 - \frac{Ec + \color{blue}{-1 \cdot EDonor}}{KbT}\right)\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      11. neg-sub0 62.4%

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

      12. distribute-neg-frac 62.4%

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

      13. +-commutative 62.4%

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

      14. distribute-neg-in 62.4%

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

      15. mul-1-neg 62.4%

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

      16. remove-double-neg 62.4%

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

      17. sub-neg 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in KbT around inf 40.5%

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

      1. +-commutative 40.5%

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

      2. associate-+r+ 40.5%

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

      3. associate--l+ 40.5%

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

      4. +-commutative 40.5%

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

      5. sub-neg 40.5%

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

      6. +-commutative 40.5%

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

      7. neg-sub0 40.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \left(\color{blue}{\left(0 - \frac{mu}{KbT}\right)} + \frac{EAccept}{KbT}\right)\right)} \]

      8. associate-+l- 40.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \color{blue}{\left(0 - \left(\frac{mu}{KbT} - \frac{EAccept}{KbT}\right)\right)}\right)} \]

      9. div-sub 40.5%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \left(0 - \color{blue}{\frac{mu - EAccept}{KbT}}\right)\right)} \]

      10. unsub-neg 40.5%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \left(0 - \frac{\color{blue}{mu + \left(-EAccept\right)}}{KbT}\right)\right)} \]

      11. mul-1-neg 40.5%

          \[\leadsto \frac{NdChar}{1 + \left(1 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor - Ec}{KbT}\right)\right)} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) + \left(0 - \frac{mu + \color{blue}{-1 \cdot EAccept}}{KbT}\right)\right)} \]

      12. neg-sub0 40.5%

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

      13. distribute-neg-frac 40.5%

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

      14. distribute-neg-in 40.5%

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

      15. mul-1-neg 40.5%

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

      16. remove-double-neg 40.5%

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

      17. +-commutative 40.5%

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

      18. sub-neg 40.5%

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

   10. Simplified 40.5%

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

   if 2.3000000000000001e-128 < 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%

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

   5. Taylor expanded in mu around inf 83.1%

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

   6. Taylor expanded in mu around 0 64.0%

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

   7. Taylor expanded in KbT around inf 30.5%

      \[\leadsto \frac{NdChar}{2 + \frac{mu}{KbT}} + \frac{NaChar}{\color{blue}{2}} \]

   8. Taylor expanded in mu around 0 31.9%

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

      1. distribute-lft-out 31.9%

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

   10. Simplified 31.9%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -1.9 \cdot 10^{+103}:\\ \;\;\;\;\frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq 2.3 \cdot 10^{-128}:\\ \;\;\;\;\frac{NaChar}{\left(\left(\left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right) + 1\right) + \frac{EAccept - mu}{KbT}\right) + 1} + \frac{NdChar}{\left(\left(\frac{EDonor - Ec}{KbT} + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 27.9% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -8.8 \cdot 10^{+238}:\\ \;\;\;\;\frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -8.8e+238)
   (/ NdChar (+ 2.0 (/ mu KbT)))
   (* 0.5 (+ NdChar NaChar))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -8.8e+238) {
		tmp = NdChar / (2.0 + (mu / KbT));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-8.8d+238)) then
        tmp = ndchar / (2.0d0 + (mu / kbt))
    else
        tmp = 0.5d0 * (ndchar + nachar)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -8.8e+238) {
		tmp = NdChar / (2.0 + (mu / KbT));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -8.8e+238:
		tmp = NdChar / (2.0 + (mu / KbT))
	else:
		tmp = 0.5 * (NdChar + NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -8.8e+238)
		tmp = Float64(NdChar / Float64(2.0 + Float64(mu / KbT)));
	else
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -8.8e+238)
		tmp = NdChar / (2.0 + (mu / KbT));
	else
		tmp = 0.5 * (NdChar + NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -8.8e+238], N[(NdChar / N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -8.8000000000000002e238

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 78.6%

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

   6. Taylor expanded in mu around 0 60.8%

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

   7. Taylor expanded in KbT around inf 16.7%

      \[\leadsto \frac{NdChar}{2 + \frac{mu}{KbT}} + \frac{NaChar}{\color{blue}{2}} \]

   8. Taylor expanded in NdChar around inf 30.2%

      \[\leadsto \color{blue}{\frac{NdChar}{2 + \frac{mu}{KbT}}} \]

   if -8.8000000000000002e238 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 69.9%

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

   6. Taylor expanded in mu around 0 54.9%

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

   7. Taylor expanded in KbT around inf 31.1%

      \[\leadsto \frac{NdChar}{2 + \frac{mu}{KbT}} + \frac{NaChar}{\color{blue}{2}} \]

   8. Taylor expanded in mu around 0 32.4%

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

      1. distribute-lft-out 32.4%

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

   10. Simplified 32.4%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -8.8 \cdot 10^{+238}:\\ \;\;\;\;\frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 27.9% 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%

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

5. Taylor expanded in mu around inf 70.4%

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

6. Taylor expanded in mu around 0 55.3%

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

7. Taylor expanded in KbT around inf 30.2%

   \[\leadsto \frac{NdChar}{2 + \frac{mu}{KbT}} + \frac{NaChar}{\color{blue}{2}} \]

8. Taylor expanded in mu around 0 31.5%

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

   1. distribute-lft-out 31.5%

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

10. Simplified 31.5%

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

11. Final simplification 31.5%

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

Alternative 32: 18.2% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in mu around inf 70.4%

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

6. Taylor expanded in mu around 0 55.3%

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

7. Taylor expanded in KbT around inf 30.2%

   \[\leadsto \frac{NdChar}{2 + \frac{mu}{KbT}} + \frac{NaChar}{\color{blue}{2}} \]

8. Taylor expanded in NdChar around 0 21.6%

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

9. Final simplification 21.6%

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

Reproduce

herbie shell --seed 2024048 
(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))))))