Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 38.1s

Alternatives: 29

Speedup: 1.0×

• could not determine a ground truth

  1. branch3900 = -3.2977906702144725e-32
  2. NdChar = 7.117733753730101e-189
  3. Ec = 5.517687558454947e-257
  4. Vef = -7.332148097473621e+215
  5. EDonor = -4.87852156085021e-254
  6. mu = 4.2454935651371106e-243
  7. KbT = 3.0008261610562795e-291
  8. NaChar = -2.6201750557064767e-31
  9. Ev = -0.02586550276019816
  10. EAccept = 1.9696388092746072e-8

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

\[\begin{array}{l} \\ \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\sqrt[3]{{\left(1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\right)}^{3}}} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
  (/
   NaChar
   (cbrt (pow (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))) 3.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / cbrt(pow((1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))), 3.0)));
}

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / Math.cbrt(Math.pow((1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))), 3.0)));
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / cbrt((Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))) ^ 3.0))))
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[Power[N[Power[N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

   1. add-cbrt-cube 100.0%

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

   2. pow3 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\sqrt[3]{\color{blue}{{\left(1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}\right)}^{3}}}} \]

   3. +-commutative 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\sqrt[3]{{\color{blue}{\left(e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}} + 1\right)}}^{3}}} \]

   4. *-un-lft-identity 100.0%

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

   5. *-un-lft-identity 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\sqrt[3]{{\left(e^{\frac{\color{blue}{Vef + \left(EAccept + \left(Ev - mu\right)\right)}}{KbT}} + 1\right)}^{3}}} \]

   6. +-commutative 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\sqrt[3]{{\left(e^{\frac{Vef + \color{blue}{\left(\left(Ev - mu\right) + EAccept\right)}}{KbT}} + 1\right)}^{3}}} \]

   7. associate-+l- 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\sqrt[3]{{\left(e^{\frac{Vef + \color{blue}{\left(Ev - \left(mu - EAccept\right)\right)}}{KbT}} + 1\right)}^{3}}} \]

6. Applied egg-rr 100.0%

   \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\sqrt[3]{{\left(e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1\right)}^{3}}}} \]

7. Final simplification 100.0%

   \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\sqrt[3]{{\left(1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\right)}^{3}}} \]
8. Add Preprocessing

Alternative 2: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ t_2 := t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_3 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;mu \leq -4.7 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -2.6 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq -2.15 \cdot 10^{-45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq -3.2 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 1.1 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT))))))
        (t_2 (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT))))))
        (t_3 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= mu -4.7e+179)
     t_1
     (if (<= mu -2.6e+57)
       t_2
       (if (<= mu -2.15e-45)
         t_3
         (if (<= mu -3.2e-241) t_2 (if (<= mu 1.1e-41) t_3 t_1)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	double t_3 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (mu <= -4.7e+179) {
		tmp = t_1;
	} else if (mu <= -2.6e+57) {
		tmp = t_2;
	} else if (mu <= -2.15e-45) {
		tmp = t_3;
	} else if (mu <= -3.2e-241) {
		tmp = t_2;
	} else if (mu <= 1.1e-41) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt))))
    t_2 = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    t_3 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (mu <= (-4.7d+179)) then
        tmp = t_1
    else if (mu <= (-2.6d+57)) then
        tmp = t_2
    else if (mu <= (-2.15d-45)) then
        tmp = t_3
    else if (mu <= (-3.2d-241)) then
        tmp = t_2
    else if (mu <= 1.1d-41) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	double t_3 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (mu <= -4.7e+179) {
		tmp = t_1;
	} else if (mu <= -2.6e+57) {
		tmp = t_2;
	} else if (mu <= -2.15e-45) {
		tmp = t_3;
	} else if (mu <= -3.2e-241) {
		tmp = t_2;
	} else if (mu <= 1.1e-41) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT))))
	t_2 = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	t_3 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if mu <= -4.7e+179:
		tmp = t_1
	elif mu <= -2.6e+57:
		tmp = t_2
	elif mu <= -2.15e-45:
		tmp = t_3
	elif mu <= -3.2e-241:
		tmp = t_2
	elif mu <= 1.1e-41:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT)))))
	t_2 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	t_3 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (mu <= -4.7e+179)
		tmp = t_1;
	elseif (mu <= -2.6e+57)
		tmp = t_2;
	elseif (mu <= -2.15e-45)
		tmp = t_3;
	elseif (mu <= -3.2e-241)
		tmp = t_2;
	elseif (mu <= 1.1e-41)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT))));
	t_2 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	t_3 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (mu <= -4.7e+179)
		tmp = t_1;
	elseif (mu <= -2.6e+57)
		tmp = t_2;
	elseif (mu <= -2.15e-45)
		tmp = t_3;
	elseif (mu <= -3.2e-241)
		tmp = t_2;
	elseif (mu <= 1.1e-41)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -4.7e+179], t$95$1, If[LessEqual[mu, -2.6e+57], t$95$2, If[LessEqual[mu, -2.15e-45], t$95$3, If[LessEqual[mu, -3.2e-241], t$95$2, If[LessEqual[mu, 1.1e-41], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -4.70000000000000007e179 or 1.1e-41 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 88.8%

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

   6. Taylor expanded in Ev around 0 85.0%

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

      1. +-commutative 38.6%

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

      2. sub-neg 38.6%

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

      3. associate-+l+ 38.6%

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

      4. mul-1-neg 38.6%

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

      5. +-commutative 38.6%

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

      6. mul-1-neg 38.6%

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

      7. sub-neg 38.6%

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

      8. associate--r- 38.6%

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

   8. Simplified 85.0%

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

   if -4.70000000000000007e179 < mu < -2.6e57 or -2.1499999999999999e-45 < mu < -3.2e-241

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 82.4%

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

   if -2.6e57 < mu < -2.1499999999999999e-45 or -3.2e-241 < mu < 1.1e-41

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 85.4%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -4.7 \cdot 10^{+179}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq -2.6 \cdot 10^{+57}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;mu \leq -2.15 \cdot 10^{-45}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq -3.2 \cdot 10^{-241}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.7 \cdot 10^{+136}:\\ \;\;\;\;t_1 + t_0\\ \mathbf{elif}\;Vef \leq -2.7 \cdot 10^{-196}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_1\\ \mathbf{elif}\;Vef \leq -5.8 \cdot 10^{-265}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;Vef \leq 3.3 \cdot 10^{+120}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef - mu\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT))))))
   (if (<= Vef -1.7e+136)
     (+ t_1 t_0)
     (if (<= Vef -2.7e-196)
       (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) t_1)
       (if (<= Vef -5.8e-265)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ 1.0 (/ EDonor KbT))))
         (if (<= Vef 3.3e+120)
           (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_1)
           (+ t_0 (/ NaChar (+ 1.0 (exp (/ (+ Ev (- Vef mu)) KbT)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((Vef / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)));
	double tmp;
	if (Vef <= -1.7e+136) {
		tmp = t_1 + t_0;
	} else if (Vef <= -2.7e-196) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + t_1;
	} else if (Vef <= -5.8e-265) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (Vef <= 3.3e+120) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp(((Ev + (Vef - mu)) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((vef / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt)))
    if (vef <= (-1.7d+136)) then
        tmp = t_1 + t_0
    else if (vef <= (-2.7d-196)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + t_1
    else if (vef <= (-5.8d-265)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (vef <= 3.3d+120) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_1
    else
        tmp = t_0 + (nachar / (1.0d0 + exp(((ev + (vef - mu)) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((Vef / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT)));
	double tmp;
	if (Vef <= -1.7e+136) {
		tmp = t_1 + t_0;
	} else if (Vef <= -2.7e-196) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + t_1;
	} else if (Vef <= -5.8e-265) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (Vef <= 3.3e+120) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_1;
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp(((Ev + (Vef - mu)) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((Vef / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT)))
	tmp = 0
	if Vef <= -1.7e+136:
		tmp = t_1 + t_0
	elif Vef <= -2.7e-196:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + t_1
	elif Vef <= -5.8e-265:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)))
	elif Vef <= 3.3e+120:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_1
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp(((Ev + (Vef - mu)) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT))))
	tmp = 0.0
	if (Vef <= -1.7e+136)
		tmp = Float64(t_1 + t_0);
	elseif (Vef <= -2.7e-196)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + t_1);
	elseif (Vef <= -5.8e-265)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (Vef <= 3.3e+120)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_1);
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef - mu)) / 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 / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)));
	tmp = 0.0;
	if (Vef <= -1.7e+136)
		tmp = t_1 + t_0;
	elseif (Vef <= -2.7e-196)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + t_1;
	elseif (Vef <= -5.8e-265)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (Vef <= 3.3e+120)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	else
		tmp = t_0 + (NaChar / (1.0 + exp(((Ev + (Vef - mu)) / 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[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -1.7e+136], N[(t$95$1 + t$95$0), $MachinePrecision], If[LessEqual[Vef, -2.7e-196], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[Vef, -5.8e-265], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 3.3e+120], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if Vef < -1.69999999999999998e136

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 89.4%

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

   6. Taylor expanded in Ev around 0 79.0%

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

      1. +-commutative 31.6%

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

      2. sub-neg 31.6%

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

      3. associate-+l+ 31.6%

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

      4. mul-1-neg 31.6%

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

      5. +-commutative 31.6%

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

      6. mul-1-neg 31.6%

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

      7. sub-neg 31.6%

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

      8. associate--r- 31.6%

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

   8. Simplified 79.0%

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

   if -1.69999999999999998e136 < Vef < -2.69999999999999982e-196

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EDonor around inf 73.9%

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

   6. Taylor expanded in Ev around 0 69.5%

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

      1. +-commutative 24.0%

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

      2. sub-neg 24.0%

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

      3. associate-+l+ 24.0%

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

      4. mul-1-neg 24.0%

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

      5. +-commutative 24.0%

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

      6. mul-1-neg 24.0%

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

      7. sub-neg 24.0%

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

      8. associate--r- 24.0%

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

   8. Simplified 69.5%

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

   if -2.69999999999999982e-196 < Vef < -5.7999999999999995e-265

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.5%

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

      1. associate-+r+ 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in EDonor around inf 83.8%

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

   if -5.7999999999999995e-265 < Vef < 3.29999999999999991e120

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 77.0%

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

   6. Taylor expanded in Ev around 0 72.7%

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

      1. +-commutative 32.6%

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

      2. sub-neg 32.6%

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

      3. associate-+l+ 32.6%

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

      4. mul-1-neg 32.6%

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

      5. +-commutative 32.6%

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

      6. mul-1-neg 32.6%

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

      7. sub-neg 32.6%

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

      8. associate--r- 32.6%

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

   8. Simplified 72.7%

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

   if 3.29999999999999991e120 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 91.9%

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

   6. Taylor expanded in EAccept around 0 91.6%

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

      1. +-commutative 40.2%

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

      2. associate--l+ 40.2%

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

   8. Simplified 91.6%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1.7 \cdot 10^{+136}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -2.7 \cdot 10^{-196}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq -5.8 \cdot 10^{-265}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;Vef \leq 3.3 \cdot 10^{+120}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef - mu\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 5: 64.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.15 \cdot 10^{-141}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.3 \cdot 10^{+62}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT)))))))
   (if (<= NaChar -1.15e-141)
     t_0
     (if (<= NaChar 1.95e-218)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
        (/
         NaChar
         (-
          (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
          (/ mu KbT))))
       (if (<= NaChar 2.3e+62)
         t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (- (+ 2.0 (+ (/ mu KbT) (/ Vef KbT))) (/ Ec KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT))));
	double tmp;
	if (NaChar <= -1.15e-141) {
		tmp = t_0;
	} else if (NaChar <= 1.95e-218) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NaChar <= 2.3e+62) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt))))
    if (nachar <= (-1.15d-141)) then
        tmp = t_0
    else if (nachar <= 1.95d-218) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (nachar <= 2.3d+62) then
        tmp = t_0
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((2.0d0 + ((mu / kbt) + (vef / kbt))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT))));
	double tmp;
	if (NaChar <= -1.15e-141) {
		tmp = t_0;
	} else if (NaChar <= 1.95e-218) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NaChar <= 2.3e+62) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT))))
	tmp = 0
	if NaChar <= -1.15e-141:
		tmp = t_0
	elif NaChar <= 1.95e-218:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NaChar <= 2.3e+62:
		tmp = t_0
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT)))))
	tmp = 0.0
	if (NaChar <= -1.15e-141)
		tmp = t_0;
	elseif (NaChar <= 1.95e-218)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NaChar <= 2.3e+62)
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(mu / KbT) + Float64(Vef / KbT))) - Float64(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((EDonor / KbT)))) + (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT))));
	tmp = 0.0;
	if (NaChar <= -1.15e-141)
		tmp = t_0;
	elseif (NaChar <= 1.95e-218)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NaChar <= 2.3e+62)
		tmp = t_0;
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.15e-141], t$95$0, If[LessEqual[NaChar, 1.95e-218], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.3e+62], t$95$0, N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(2.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.14999999999999997e-141 or 1.95e-218 < NaChar < 2.29999999999999984e62

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EDonor around inf 75.1%

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

   6. Taylor expanded in Ev around 0 70.0%

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

      1. +-commutative 31.2%

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

      2. sub-neg 31.2%

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

      3. associate-+l+ 31.2%

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

      4. mul-1-neg 31.2%

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

      5. +-commutative 31.2%

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

      6. mul-1-neg 31.2%

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

      7. sub-neg 31.2%

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

      8. associate--r- 31.2%

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

   8. Simplified 70.0%

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

   if -1.14999999999999997e-141 < NaChar < 1.95e-218

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.9%

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

   if 2.29999999999999984e62 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 75.8%

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

      1. associate-+r+ 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in EDonor around 0 75.9%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.15 \cdot 10^{-141}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.3 \cdot 10^{+62}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.15 \cdot 10^{-153}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{-219}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -2.15e-153)
   (+
    (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
    (/ NaChar (+ 1.0 (exp (/ (+ Ev (- Vef mu)) KbT)))))
   (if (<= NaChar 8e-219)
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
      (/
       NaChar
       (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT))))
     (if (<= NaChar 8e+63)
       (+
        (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
        (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT)))))
       (+
        (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
        (/ NdChar (- (+ 2.0 (+ (/ mu KbT) (/ Vef KbT))) (/ Ec KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -2.15e-153) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp(((Ev + (Vef - mu)) / KbT))));
	} else if (NaChar <= 8e-219) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NaChar <= 8e+63) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-2.15d-153)) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / (1.0d0 + exp(((ev + (vef - mu)) / kbt))))
    else if (nachar <= 8d-219) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (nachar <= 8d+63) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((2.0d0 + ((mu / kbt) + (vef / kbt))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -2.15e-153) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / (1.0 + Math.exp(((Ev + (Vef - mu)) / KbT))));
	} else if (NaChar <= 8e-219) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NaChar <= 8e+63) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -2.15e-153:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / (1.0 + math.exp(((Ev + (Vef - mu)) / KbT))))
	elif NaChar <= 8e-219:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NaChar <= 8e+63:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -2.15e-153)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef - mu)) / KbT)))));
	elseif (NaChar <= 8e-219)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NaChar <= 8e+63)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(mu / KbT) + Float64(Vef / KbT))) - Float64(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 <= -2.15e-153)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp(((Ev + (Vef - mu)) / KbT))));
	elseif (NaChar <= 8e-219)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NaChar <= 8e+63)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -2.15e-153], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8e-219], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8e+63], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(2.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.15e-153

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 73.9%

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

   6. Taylor expanded in EAccept around 0 66.2%

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

      1. +-commutative 33.7%

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

      2. associate--l+ 33.7%

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

   8. Simplified 66.2%

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

   if -2.15e-153 < NaChar < 8.0000000000000003e-219

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 77.7%

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

   if 8.0000000000000003e-219 < NaChar < 8.00000000000000046e63

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 74.5%

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

   6. Taylor expanded in Ev around 0 67.8%

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

      1. +-commutative 26.1%

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

      2. sub-neg 26.1%

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

      3. associate-+l+ 26.1%

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

      4. mul-1-neg 26.1%

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

      5. +-commutative 26.1%

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

      6. mul-1-neg 26.1%

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

      7. sub-neg 26.1%

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

      8. associate--r- 26.1%

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

   8. Simplified 67.8%

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

   if 8.00000000000000046e63 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 75.8%

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

      1. associate-+r+ 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in EDonor around 0 75.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.15 \cdot 10^{-153}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{-219}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -1.12 \cdot 10^{+136} \lor \neg \left(mu \leq 9.2 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= mu -1.12e+136) (not (<= mu 9.2e-42)))
   (+
    (/ NdChar (+ 1.0 (exp (/ mu KbT))))
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -1.12e+136) || !(mu <= 9.2e-42)) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((mu <= (-1.12d+136)) .or. (.not. (mu <= 9.2d-42))) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -1.12e+136) || !(mu <= 9.2e-42)) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (mu <= -1.12e+136) or not (mu <= 9.2e-42):
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((mu <= -1.12e+136) || !(mu <= 9.2e-42))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((mu <= -1.12e+136) || ~((mu <= 9.2e-42)))
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[mu, -1.12e+136], N[Not[LessEqual[mu, 9.2e-42]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if mu < -1.12000000000000001e136 or 9.20000000000000015e-42 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 89.1%

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

   6. Taylor expanded in Ev around 0 85.7%

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

      1. +-commutative 42.6%

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

      2. sub-neg 42.6%

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

      3. associate-+l+ 42.6%

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

      4. mul-1-neg 42.6%

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

      5. +-commutative 42.6%

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

      6. mul-1-neg 42.6%

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

      7. sub-neg 42.6%

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

      8. associate--r- 42.6%

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

   8. Simplified 85.7%

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

   if -1.12000000000000001e136 < mu < 9.20000000000000015e-42

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EDonor around inf 76.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -1.12 \cdot 10^{+136} \lor \neg \left(mu \leq 9.2 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -1.9 \cdot 10^{+63} \lor \neg \left(mu \leq 5.2 \cdot 10^{-42}\right):\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (or (<= mu -1.9e+63) (not (<= mu 5.2e-42)))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if ((mu <= -1.9e+63) || !(mu <= 5.2e-42)) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    if ((mu <= (-1.9d+63)) .or. (.not. (mu <= 5.2d-42))) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if ((mu <= -1.9e+63) || !(mu <= 5.2e-42)) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	tmp = 0
	if (mu <= -1.9e+63) or not (mu <= 5.2e-42):
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	tmp = 0.0
	if ((mu <= -1.9e+63) || !(mu <= 5.2e-42))
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if ((mu <= -1.9e+63) || ~((mu <= 5.2e-42)))
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	else
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[mu, -1.9e+63], N[Not[LessEqual[mu, 5.2e-42]], $MachinePrecision]], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if mu < -1.9000000000000001e63 or 5.2e-42 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 87.2%

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

   if -1.9000000000000001e63 < mu < 5.2e-42

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EDonor around inf 78.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -1.9 \cdot 10^{+63} \lor \neg \left(mu \leq 5.2 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -4.7 \cdot 10^{+170}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + t_0\\ \mathbf{elif}\;Vef \leq 2.6 \cdot 10^{+124}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef - mu\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT))))))
   (if (<= Vef -4.7e+170)
     (+ (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT)))) t_0)
     (if (<= Vef 2.6e+124)
       (+
        (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT))))
        (/ NaChar (+ 1.0 (exp (/ (+ EAccept (- Ev mu)) KbT)))))
       (+ t_0 (/ NaChar (+ 1.0 (exp (/ (+ Ev (- Vef mu)) KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((Vef / KbT)));
	double tmp;
	if (Vef <= -4.7e+170) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + t_0;
	} else if (Vef <= 2.6e+124) {
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (1.0 + exp(((EAccept + (Ev - mu)) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp(((Ev + (Vef - mu)) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((vef / kbt)))
    if (vef <= (-4.7d+170)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt)))) + t_0
    else if (vef <= 2.6d+124) then
        tmp = (ndchar / (1.0d0 + exp((-ec / kbt)))) + (nachar / (1.0d0 + exp(((eaccept + (ev - mu)) / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp(((ev + (vef - mu)) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((Vef / KbT)));
	double tmp;
	if (Vef <= -4.7e+170) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT)))) + t_0;
	} else if (Vef <= 2.6e+124) {
		tmp = (NdChar / (1.0 + Math.exp((-Ec / KbT)))) + (NaChar / (1.0 + Math.exp(((EAccept + (Ev - mu)) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp(((Ev + (Vef - mu)) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((Vef / KbT)))
	tmp = 0
	if Vef <= -4.7e+170:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT)))) + t_0
	elif Vef <= 2.6e+124:
		tmp = (NdChar / (1.0 + math.exp((-Ec / KbT)))) + (NaChar / (1.0 + math.exp(((EAccept + (Ev - mu)) / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp(((Ev + (Vef - mu)) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	tmp = 0.0
	if (Vef <= -4.7e+170)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT)))) + t_0);
	elseif (Vef <= 2.6e+124)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(EAccept + Float64(Ev - mu)) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef - mu)) / 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 / KbT)));
	tmp = 0.0;
	if (Vef <= -4.7e+170)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + t_0;
	elseif (Vef <= 2.6e+124)
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (1.0 + exp(((EAccept + (Ev - mu)) / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp(((Ev + (Vef - mu)) / 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[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -4.7e+170], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[Vef, 2.6e+124], N[(N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -4.70000000000000004e170

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 96.7%

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

   6. Taylor expanded in Ev around 0 86.8%

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

      1. +-commutative 36.4%

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

      2. sub-neg 36.4%

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

      3. associate-+l+ 36.4%

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

      4. mul-1-neg 36.4%

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

      5. +-commutative 36.4%

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

      6. mul-1-neg 36.4%

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

      7. sub-neg 36.4%

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

      8. associate--r- 36.4%

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

   8. Simplified 86.8%

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

   if -4.70000000000000004e170 < Vef < 2.6e124

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 72.9%

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

      1. associate-*r/ 39.0%

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

      2. mul-1-neg 39.0%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in Vef around 0 72.0%

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

      1. +-commutative 72.0%

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

      2. associate--l+ 72.0%

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

   10. Simplified 72.0%

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

   if 2.6e124 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 91.9%

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

   6. Taylor expanded in EAccept around 0 91.6%

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

      1. +-commutative 40.2%

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

      2. associate--l+ 40.2%

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

   8. Simplified 91.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4.7 \cdot 10^{+170}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.6 \cdot 10^{+124}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef - mu\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{mu}{KbT} + \frac{Vef}{KbT}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{\left(2 + t_0\right) - \frac{Ec}{KbT}}\\ \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{-33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NaChar \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;t_1 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 9.2 \cdot 10^{+21}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + t_0\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.25 \cdot 10^{+32}:\\ \;\;\;\;t_1 + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ mu KbT) (/ Vef KbT)))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_3 (+ t_2 (/ NdChar (- (+ 2.0 t_0) (/ Ec KbT))))))
   (if (<= NaChar -8.5e-33)
     t_3
     (if (<= NaChar 1.95e-218)
       (+
        t_1
        (/
         NaChar
         (-
          (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
          (/ mu KbT))))
       (if (<= NaChar 9.2e+21)
         (+
          t_2
          (/ NdChar (+ 1.0 (- (+ (+ 1.0 (/ EDonor KbT)) t_0) (/ Ec KbT)))))
         (if (<= NaChar 1.25e+32) (+ t_1 (/ NaChar 2.0)) 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 = (mu / KbT) + (Vef / KbT);
	double t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_3 = t_2 + (NdChar / ((2.0 + t_0) - (Ec / KbT)));
	double tmp;
	if (NaChar <= -8.5e-33) {
		tmp = t_3;
	} else if (NaChar <= 1.95e-218) {
		tmp = t_1 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NaChar <= 9.2e+21) {
		tmp = t_2 + (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + t_0) - (Ec / KbT))));
	} else if (NaChar <= 1.25e+32) {
		tmp = t_1 + (NaChar / 2.0);
	} 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 = (mu / kbt) + (vef / kbt)
    t_1 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_2 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_3 = t_2 + (ndchar / ((2.0d0 + t_0) - (ec / kbt)))
    if (nachar <= (-8.5d-33)) then
        tmp = t_3
    else if (nachar <= 1.95d-218) then
        tmp = t_1 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (nachar <= 9.2d+21) then
        tmp = t_2 + (ndchar / (1.0d0 + (((1.0d0 + (edonor / kbt)) + t_0) - (ec / kbt))))
    else if (nachar <= 1.25d+32) then
        tmp = t_1 + (nachar / 2.0d0)
    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 = (mu / KbT) + (Vef / KbT);
	double t_1 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_3 = t_2 + (NdChar / ((2.0 + t_0) - (Ec / KbT)));
	double tmp;
	if (NaChar <= -8.5e-33) {
		tmp = t_3;
	} else if (NaChar <= 1.95e-218) {
		tmp = t_1 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NaChar <= 9.2e+21) {
		tmp = t_2 + (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + t_0) - (Ec / KbT))));
	} else if (NaChar <= 1.25e+32) {
		tmp = t_1 + (NaChar / 2.0);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (mu / KbT) + (Vef / KbT)
	t_1 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_2 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_3 = t_2 + (NdChar / ((2.0 + t_0) - (Ec / KbT)))
	tmp = 0
	if NaChar <= -8.5e-33:
		tmp = t_3
	elif NaChar <= 1.95e-218:
		tmp = t_1 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NaChar <= 9.2e+21:
		tmp = t_2 + (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + t_0) - (Ec / KbT))))
	elif NaChar <= 1.25e+32:
		tmp = t_1 + (NaChar / 2.0)
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(mu / KbT) + Float64(Vef / KbT))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_3 = Float64(t_2 + Float64(NdChar / Float64(Float64(2.0 + t_0) - Float64(Ec / KbT))))
	tmp = 0.0
	if (NaChar <= -8.5e-33)
		tmp = t_3;
	elseif (NaChar <= 1.95e-218)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NaChar <= 9.2e+21)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + Float64(Float64(Float64(1.0 + Float64(EDonor / KbT)) + t_0) - Float64(Ec / KbT)))));
	elseif (NaChar <= 1.25e+32)
		tmp = Float64(t_1 + Float64(NaChar / 2.0));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (mu / KbT) + (Vef / KbT);
	t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_2 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_3 = t_2 + (NdChar / ((2.0 + t_0) - (Ec / KbT)));
	tmp = 0.0;
	if (NaChar <= -8.5e-33)
		tmp = t_3;
	elseif (NaChar <= 1.95e-218)
		tmp = t_1 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NaChar <= 9.2e+21)
		tmp = t_2 + (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + t_0) - (Ec / KbT))));
	elseif (NaChar <= 1.25e+32)
		tmp = t_1 + (NaChar / 2.0);
	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[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(NdChar / N[(N[(2.0 + t$95$0), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -8.5e-33], t$95$3, If[LessEqual[NaChar, 1.95e-218], N[(t$95$1 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 9.2e+21], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(N[(N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.25e+32], N[(t$95$1 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -8.49999999999999945e-33 or 1.2499999999999999e32 < NaChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 68.2%

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

      1. associate-+r+ 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in EDonor around 0 70.0%

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

   if -8.49999999999999945e-33 < NaChar < 1.95e-218

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 69.9%

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

   if 1.95e-218 < NaChar < 9.2e21

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.0%

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

      1. associate-+r+ 67.0%

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

   7. Simplified 67.0%

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

   if 9.2e21 < NaChar < 1.2499999999999999e32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 88.4%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 9.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.25 \cdot 10^{+32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -3.4 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 4500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 2.65 \cdot 10^{+39}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5.7 \cdot 10^{+138}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0))))
   (if (<= NdChar -3.4e-32)
     t_1
     (if (<= NdChar 8.5e-83)
       (+ t_0 (/ NdChar (+ 1.0 (/ EDonor KbT))))
       (if (<= NdChar 5e-30)
         (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
         (if (<= NdChar 4500000.0)
           t_1
           (if (<= NdChar 2.65e+39)
             (+
              (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT))))
              (/
               NaChar
               (-
                (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
                (/ mu KbT))))
             (if (<= NdChar 5.7e+138)
               (+ t_0 (/ NdChar (+ 1.0 (+ 1.0 (/ Vef KbT)))))
               t_1))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.4e-32) {
		tmp = t_1;
	} else if (NdChar <= 8.5e-83) {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NdChar <= 5e-30) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if (NdChar <= 4500000.0) {
		tmp = t_1;
	} else if (NdChar <= 2.65e+39) {
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 5.7e+138) {
		tmp = t_0 + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    if (ndchar <= (-3.4d-32)) then
        tmp = t_1
    else if (ndchar <= 8.5d-83) then
        tmp = t_0 + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (ndchar <= 5d-30) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if (ndchar <= 4500000.0d0) then
        tmp = t_1
    else if (ndchar <= 2.65d+39) then
        tmp = (ndchar / (1.0d0 + exp((-ec / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (ndchar <= 5.7d+138) then
        tmp = t_0 + (ndchar / (1.0d0 + (1.0d0 + (vef / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.4e-32) {
		tmp = t_1;
	} else if (NdChar <= 8.5e-83) {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NdChar <= 5e-30) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if (NdChar <= 4500000.0) {
		tmp = t_1;
	} else if (NdChar <= 2.65e+39) {
		tmp = (NdChar / (1.0 + Math.exp((-Ec / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 5.7e+138) {
		tmp = t_0 + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -3.4e-32:
		tmp = t_1
	elif NdChar <= 8.5e-83:
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)))
	elif NdChar <= 5e-30:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif NdChar <= 4500000.0:
		tmp = t_1
	elif NdChar <= 2.65e+39:
		tmp = (NdChar / (1.0 + math.exp((-Ec / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NdChar <= 5.7e+138:
		tmp = t_0 + (NdChar / (1.0 + (1.0 + (Vef / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -3.4e-32)
		tmp = t_1;
	elseif (NdChar <= 8.5e-83)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (NdChar <= 5e-30)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif (NdChar <= 4500000.0)
		tmp = t_1;
	elseif (NdChar <= 2.65e+39)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NdChar <= 5.7e+138)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(Vef / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -3.4e-32)
		tmp = t_1;
	elseif (NdChar <= 8.5e-83)
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (NdChar <= 5e-30)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif (NdChar <= 4500000.0)
		tmp = t_1;
	elseif (NdChar <= 2.65e+39)
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NdChar <= 5.7e+138)
		tmp = t_0 + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.4e-32], t$95$1, If[LessEqual[NdChar, 8.5e-83], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 5e-30], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 4500000.0], t$95$1, If[LessEqual[NdChar, 2.65e+39], N[(N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 5.7e+138], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -3.39999999999999978e-32 or 4.99999999999999972e-30 < NdChar < 4.5e6 or 5.69999999999999986e138 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 57.9%

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

   if -3.39999999999999978e-32 < NdChar < 8.49999999999999938e-83

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.7%

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

      1. associate-+r+ 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in EDonor around inf 74.5%

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

   if 8.49999999999999938e-83 < NdChar < 4.99999999999999972e-30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 16.1%

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

   6. Taylor expanded in Vef around inf 8.4%

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

   7. Taylor expanded in NdChar around inf 63.8%

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

   if 4.5e6 < NdChar < 2.64999999999999989e39

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in Ec around inf 97.3%

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

      1. associate-*r/ 66.6%

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

      2. mul-1-neg 66.6%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in KbT around inf 83.9%

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

   if 2.64999999999999989e39 < NdChar < 5.69999999999999986e138

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in Vef around inf 87.5%

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

   6. Taylor expanded in Vef around 0 77.3%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.4 \cdot 10^{-32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 4500000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 2.65 \cdot 10^{+39}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5.7 \cdot 10^{+138}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -6 \cdot 10^{-32} \lor \neg \left(NaChar \leq 1.5 \cdot 10^{-218}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -6e-32) (not (<= NaChar 1.5e-218)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar (- (+ 2.0 (+ (/ mu KbT) (/ Vef KbT))) (/ Ec KbT))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ 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 ((NaChar <= -6e-32) || !(NaChar <= 1.5e-218)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (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 ((nachar <= (-6d-32)) .or. (.not. (nachar <= 1.5d-218))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((2.0d0 + ((mu / kbt) + (vef / kbt))) - (ec / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (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 ((NaChar <= -6e-32) || !(NaChar <= 1.5e-218)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -6e-32) or not (NaChar <= 1.5e-218):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -6e-32) || !(NaChar <= 1.5e-218))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(mu / KbT) + Float64(Vef / KbT))) - Float64(Ec / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - 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 ((NaChar <= -6e-32) || ~((NaChar <= 1.5e-218)))
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -6e-32], N[Not[LessEqual[NaChar, 1.5e-218]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(2.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -6.0000000000000001e-32 or 1.4999999999999999e-218 < NaChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 65.9%

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

      1. associate-+r+ 65.9%

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

   7. Simplified 65.9%

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

   8. Taylor expanded in EDonor around 0 66.8%

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

   if -6.0000000000000001e-32 < NaChar < 1.4999999999999999e-218

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 69.9%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6 \cdot 10^{-32} \lor \neg \left(NaChar \leq 1.5 \cdot 10^{-218}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -1.06 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 9 \cdot 10^{-18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq 1.35 \cdot 10^{+75}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT}}\\ \mathbf{elif}\;NdChar \leq 8.6 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 1.05 \cdot 10^{+170} \lor \neg \left(NdChar \leq 5.2 \cdot 10^{+229}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (* NdChar 0.5)))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0))))
   (if (<= NdChar -1.06e-32)
     t_2
     (if (<= NdChar 8.5e-83)
       t_1
       (if (<= NdChar 9e-18)
         t_0
         (if (<= NdChar 2.4e+71)
           t_2
           (if (<= NdChar 1.35e+75)
             (+ (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))) (/ NaChar (/ Vef KbT)))
             (if (<= NdChar 8.6e+134)
               t_1
               (if (or (<= NdChar 1.05e+170) (not (<= NdChar 5.2e+229)))
                 t_2
                 t_0)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((Vef / KbT)));
	double t_1 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	double t_2 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -1.06e-32) {
		tmp = t_2;
	} else if (NdChar <= 8.5e-83) {
		tmp = t_1;
	} else if (NdChar <= 9e-18) {
		tmp = t_0;
	} else if (NdChar <= 2.4e+71) {
		tmp = t_2;
	} else if (NdChar <= 1.35e+75) {
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (Vef / KbT));
	} else if (NdChar <= 8.6e+134) {
		tmp = t_1;
	} else if ((NdChar <= 1.05e+170) || !(NdChar <= 5.2e+229)) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((vef / kbt)))
    t_1 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    t_2 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    if (ndchar <= (-1.06d-32)) then
        tmp = t_2
    else if (ndchar <= 8.5d-83) then
        tmp = t_1
    else if (ndchar <= 9d-18) then
        tmp = t_0
    else if (ndchar <= 2.4d+71) then
        tmp = t_2
    else if (ndchar <= 1.35d+75) then
        tmp = (ndchar / (1.0d0 + exp((-ec / kbt)))) + (nachar / (vef / kbt))
    else if (ndchar <= 8.6d+134) then
        tmp = t_1
    else if ((ndchar <= 1.05d+170) .or. (.not. (ndchar <= 5.2d+229))) then
        tmp = t_2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((Vef / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	double t_2 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -1.06e-32) {
		tmp = t_2;
	} else if (NdChar <= 8.5e-83) {
		tmp = t_1;
	} else if (NdChar <= 9e-18) {
		tmp = t_0;
	} else if (NdChar <= 2.4e+71) {
		tmp = t_2;
	} else if (NdChar <= 1.35e+75) {
		tmp = (NdChar / (1.0 + Math.exp((-Ec / KbT)))) + (NaChar / (Vef / KbT));
	} else if (NdChar <= 8.6e+134) {
		tmp = t_1;
	} else if ((NdChar <= 1.05e+170) || !(NdChar <= 5.2e+229)) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((Vef / KbT)))
	t_1 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	t_2 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -1.06e-32:
		tmp = t_2
	elif NdChar <= 8.5e-83:
		tmp = t_1
	elif NdChar <= 9e-18:
		tmp = t_0
	elif NdChar <= 2.4e+71:
		tmp = t_2
	elif NdChar <= 1.35e+75:
		tmp = (NdChar / (1.0 + math.exp((-Ec / KbT)))) + (NaChar / (Vef / KbT))
	elif NdChar <= 8.6e+134:
		tmp = t_1
	elif (NdChar <= 1.05e+170) or not (NdChar <= 5.2e+229):
		tmp = t_2
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -1.06e-32)
		tmp = t_2;
	elseif (NdChar <= 8.5e-83)
		tmp = t_1;
	elseif (NdChar <= 9e-18)
		tmp = t_0;
	elseif (NdChar <= 2.4e+71)
		tmp = t_2;
	elseif (NdChar <= 1.35e+75)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))) + Float64(NaChar / Float64(Vef / KbT)));
	elseif (NdChar <= 8.6e+134)
		tmp = t_1;
	elseif ((NdChar <= 1.05e+170) || !(NdChar <= 5.2e+229))
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((Vef / KbT)));
	t_1 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	t_2 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -1.06e-32)
		tmp = t_2;
	elseif (NdChar <= 8.5e-83)
		tmp = t_1;
	elseif (NdChar <= 9e-18)
		tmp = t_0;
	elseif (NdChar <= 2.4e+71)
		tmp = t_2;
	elseif (NdChar <= 1.35e+75)
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (Vef / KbT));
	elseif (NdChar <= 8.6e+134)
		tmp = t_1;
	elseif ((NdChar <= 1.05e+170) || ~((NdChar <= 5.2e+229)))
		tmp = t_2;
	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[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.06e-32], t$95$2, If[LessEqual[NdChar, 8.5e-83], t$95$1, If[LessEqual[NdChar, 9e-18], t$95$0, If[LessEqual[NdChar, 2.4e+71], t$95$2, If[LessEqual[NdChar, 1.35e+75], N[(N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 8.6e+134], t$95$1, If[Or[LessEqual[NdChar, 1.05e+170], N[Not[LessEqual[NdChar, 5.2e+229]], $MachinePrecision]], t$95$2, t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -1.05999999999999994e-32 or 8.99999999999999987e-18 < NdChar < 2.39999999999999981e71 or 8.6000000000000001e134 < NdChar < 1.04999999999999999e170 or 5.2e229 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 60.3%

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

   if -1.05999999999999994e-32 < NdChar < 8.49999999999999938e-83 or 1.34999999999999999e75 < NdChar < 8.6000000000000001e134

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 81.9%

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

   6. Taylor expanded in mu around 0 68.0%

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

   7. Taylor expanded in mu around 0 62.1%

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

   if 8.49999999999999938e-83 < NdChar < 8.99999999999999987e-18 or 1.04999999999999999e170 < NdChar < 5.2e229

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 37.8%

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

   6. Taylor expanded in Vef around inf 28.6%

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

   7. Taylor expanded in NdChar around inf 64.5%

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

   if 2.39999999999999981e71 < NdChar < 1.34999999999999999e75

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 100.0%

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

      1. associate-*r/ 37.4%

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

      2. mul-1-neg 37.4%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in KbT around inf 33.3%

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

   9. Taylor expanded in Vef around inf 100.0%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.06 \cdot 10^{-32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 9 \cdot 10^{-18}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+71}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 1.35 \cdot 10^{+75}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT}}\\ \mathbf{elif}\;NdChar \leq 8.6 \cdot 10^{+134}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 1.05 \cdot 10^{+170} \lor \neg \left(NdChar \leq 5.2 \cdot 10^{+229}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 6 \cdot 10^{-83}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5.8 \cdot 10^{-39}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.55 \cdot 10^{+70} \lor \neg \left(NdChar \leq 8 \cdot 10^{+138}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0))))
   (if (<= NdChar -2.25e-29)
     t_1
     (if (<= NdChar 6e-83)
       (+ t_0 (/ NdChar (+ 1.0 (/ EDonor KbT))))
       (if (<= NdChar 5.8e-39)
         (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
         (if (or (<= NdChar 1.55e+70) (not (<= NdChar 8e+138)))
           t_1
           (+ t_0 (/ NdChar (+ 1.0 (+ 1.0 (/ Vef KbT)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -2.25e-29) {
		tmp = t_1;
	} else if (NdChar <= 6e-83) {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NdChar <= 5.8e-39) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if ((NdChar <= 1.55e+70) || !(NdChar <= 8e+138)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    if (ndchar <= (-2.25d-29)) then
        tmp = t_1
    else if (ndchar <= 6d-83) then
        tmp = t_0 + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (ndchar <= 5.8d-39) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if ((ndchar <= 1.55d+70) .or. (.not. (ndchar <= 8d+138))) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (1.0d0 + (1.0d0 + (vef / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -2.25e-29) {
		tmp = t_1;
	} else if (NdChar <= 6e-83) {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NdChar <= 5.8e-39) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if ((NdChar <= 1.55e+70) || !(NdChar <= 8e+138)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -2.25e-29:
		tmp = t_1
	elif NdChar <= 6e-83:
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)))
	elif NdChar <= 5.8e-39:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif (NdChar <= 1.55e+70) or not (NdChar <= 8e+138):
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (1.0 + (1.0 + (Vef / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -2.25e-29)
		tmp = t_1;
	elseif (NdChar <= 6e-83)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (NdChar <= 5.8e-39)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif ((NdChar <= 1.55e+70) || !(NdChar <= 8e+138))
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(Vef / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -2.25e-29)
		tmp = t_1;
	elseif (NdChar <= 6e-83)
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (NdChar <= 5.8e-39)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif ((NdChar <= 1.55e+70) || ~((NdChar <= 8e+138)))
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (1.0 + (1.0 + (Vef / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -2.25e-29], t$95$1, If[LessEqual[NdChar, 6e-83], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 5.8e-39], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NdChar, 1.55e+70], N[Not[LessEqual[NdChar, 8e+138]], $MachinePrecision]], t$95$1, N[(t$95$0 + N[(NdChar / N[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -2.2499999999999999e-29 or 5.79999999999999975e-39 < NdChar < 1.55000000000000015e70 or 8.0000000000000003e138 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 59.8%

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

   if -2.2499999999999999e-29 < NdChar < 6.00000000000000021e-83

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.7%

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

      1. associate-+r+ 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in EDonor around inf 74.5%

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

   if 6.00000000000000021e-83 < NdChar < 5.79999999999999975e-39

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 16.1%

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

   6. Taylor expanded in Vef around inf 8.4%

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

   7. Taylor expanded in NdChar around inf 63.8%

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

   if 1.55000000000000015e70 < NdChar < 8.0000000000000003e138

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in Vef around inf 85.2%

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

   6. Taylor expanded in Vef around 0 73.1%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 6 \cdot 10^{-83}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5.8 \cdot 10^{-39}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.55 \cdot 10^{+70} \lor \neg \left(NdChar \leq 8 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -3.25 \cdot 10^{+193}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;mu \leq 1.7 \cdot 10^{+118}:\\ \;\;\;\;t_0 + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (<= mu -3.25e+193)
     (+ t_0 (/ NdChar (- 1.0 (/ Ec KbT))))
     (if (<= mu 1.7e+118)
       (+ t_0 (/ NdChar (- (+ 2.0 (+ (/ mu KbT) (/ Vef KbT))) (/ Ec KbT))))
       (+ t_0 (/ NdChar (+ 1.0 (/ EDonor KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (mu <= -3.25e+193) {
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)));
	} else if (mu <= 1.7e+118) {
		tmp = t_0 + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	} else {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    if (mu <= (-3.25d+193)) then
        tmp = t_0 + (ndchar / (1.0d0 - (ec / kbt)))
    else if (mu <= 1.7d+118) then
        tmp = t_0 + (ndchar / ((2.0d0 + ((mu / kbt) + (vef / kbt))) - (ec / kbt)))
    else
        tmp = t_0 + (ndchar / (1.0d0 + (edonor / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (mu <= -3.25e+193) {
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)));
	} else if (mu <= 1.7e+118) {
		tmp = t_0 + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	} else {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	tmp = 0
	if mu <= -3.25e+193:
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)))
	elif mu <= 1.7e+118:
		tmp = t_0 + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)))
	else:
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	tmp = 0.0
	if (mu <= -3.25e+193)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 - Float64(Ec / KbT))));
	elseif (mu <= 1.7e+118)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(mu / KbT) + Float64(Vef / KbT))) - Float64(Ec / KbT))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if (mu <= -3.25e+193)
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)));
	elseif (mu <= 1.7e+118)
		tmp = t_0 + (NdChar / ((2.0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)));
	else
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -3.25e+193], N[(t$95$0 + N[(NdChar / N[(1.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.7e+118], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -3.2499999999999999e193

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 38.8%

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

      1. associate-+r+ 38.8%

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

   7. Simplified 38.8%

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

   8. Taylor expanded in Ec around inf 64.8%

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

      1. mul-1-neg 64.8%

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

   10. Simplified 64.8%

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

   if -3.2499999999999999e193 < mu < 1.69999999999999993e118

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 66.2%

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

      1. associate-+r+ 66.2%

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

   7. Simplified 66.2%

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

   8. Taylor expanded in EDonor around 0 66.2%

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

   if 1.69999999999999993e118 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 37.2%

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

      1. associate-+r+ 37.2%

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

   7. Simplified 37.2%

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

   8. Taylor expanded in EDonor around inf 60.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -3.25 \cdot 10^{+193}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;mu \leq 1.7 \cdot 10^{+118}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -2.05 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 9.5 \cdot 10^{+68} \lor \neg \left(NdChar \leq 10^{+135}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0))))
   (if (<= NdChar -2.05e-29)
     t_1
     (if (<= NdChar 8.5e-83)
       (+ t_0 (/ NdChar (+ 1.0 (/ EDonor KbT))))
       (if (<= NdChar 3.2e-39)
         (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
         (if (or (<= NdChar 9.5e+68) (not (<= NdChar 1e+135)))
           t_1
           (+ t_0 (/ NdChar (+ 1.0 (/ Vef KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -2.05e-29) {
		tmp = t_1;
	} else if (NdChar <= 8.5e-83) {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NdChar <= 3.2e-39) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if ((NdChar <= 9.5e+68) || !(NdChar <= 1e+135)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    if (ndchar <= (-2.05d-29)) then
        tmp = t_1
    else if (ndchar <= 8.5d-83) then
        tmp = t_0 + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (ndchar <= 3.2d-39) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if ((ndchar <= 9.5d+68) .or. (.not. (ndchar <= 1d+135))) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -2.05e-29) {
		tmp = t_1;
	} else if (NdChar <= 8.5e-83) {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NdChar <= 3.2e-39) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if ((NdChar <= 9.5e+68) || !(NdChar <= 1e+135)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -2.05e-29:
		tmp = t_1
	elif NdChar <= 8.5e-83:
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)))
	elif NdChar <= 3.2e-39:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif (NdChar <= 9.5e+68) or not (NdChar <= 1e+135):
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -2.05e-29)
		tmp = t_1;
	elseif (NdChar <= 8.5e-83)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (NdChar <= 3.2e-39)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif ((NdChar <= 9.5e+68) || !(NdChar <= 1e+135))
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -2.05e-29)
		tmp = t_1;
	elseif (NdChar <= 8.5e-83)
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (NdChar <= 3.2e-39)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif ((NdChar <= 9.5e+68) || ~((NdChar <= 1e+135)))
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -2.05e-29], t$95$1, If[LessEqual[NdChar, 8.5e-83], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.2e-39], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NdChar, 9.5e+68], N[Not[LessEqual[NdChar, 1e+135]], $MachinePrecision]], t$95$1, N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -2.0499999999999999e-29 or 3.1999999999999998e-39 < NdChar < 9.50000000000000069e68 or 9.99999999999999962e134 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 59.8%

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

   if -2.0499999999999999e-29 < NdChar < 8.49999999999999938e-83

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.7%

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

      1. associate-+r+ 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in EDonor around inf 74.5%

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

   if 8.49999999999999938e-83 < NdChar < 3.1999999999999998e-39

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 16.1%

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

   6. Taylor expanded in Vef around inf 8.4%

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

   7. Taylor expanded in NdChar around inf 63.8%

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

   if 9.50000000000000069e68 < NdChar < 9.99999999999999962e134

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 61.1%

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

      1. associate-+r+ 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in Vef around inf 65.5%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.05 \cdot 10^{-29}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 9.5 \cdot 10^{+68} \lor \neg \left(NdChar \leq 10^{+135}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -8.5 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.55 \cdot 10^{-31}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 2.6 \cdot 10^{+75}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.6 \cdot 10^{+143}:\\ \;\;\;\;t_0 + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0))))
   (if (<= NdChar -8.5e-31)
     t_1
     (if (<= NdChar 8.5e-83)
       (+ t_0 (/ NdChar (+ 1.0 (/ EDonor KbT))))
       (if (<= NdChar 1.55e-31)
         (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
         (if (<= NdChar 2.4e+71)
           t_1
           (if (<= NdChar 2.6e+75)
             (+ (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))) (/ NaChar (/ Vef KbT)))
             (if (<= NdChar 1.6e+143) (+ t_0 (* NdChar 0.5)) t_1))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -8.5e-31) {
		tmp = t_1;
	} else if (NdChar <= 8.5e-83) {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NdChar <= 1.55e-31) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if (NdChar <= 2.4e+71) {
		tmp = t_1;
	} else if (NdChar <= 2.6e+75) {
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (Vef / KbT));
	} else if (NdChar <= 1.6e+143) {
		tmp = t_0 + (NdChar * 0.5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    if (ndchar <= (-8.5d-31)) then
        tmp = t_1
    else if (ndchar <= 8.5d-83) then
        tmp = t_0 + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (ndchar <= 1.55d-31) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if (ndchar <= 2.4d+71) then
        tmp = t_1
    else if (ndchar <= 2.6d+75) then
        tmp = (ndchar / (1.0d0 + exp((-ec / kbt)))) + (nachar / (vef / kbt))
    else if (ndchar <= 1.6d+143) then
        tmp = t_0 + (ndchar * 0.5d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -8.5e-31) {
		tmp = t_1;
	} else if (NdChar <= 8.5e-83) {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NdChar <= 1.55e-31) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if (NdChar <= 2.4e+71) {
		tmp = t_1;
	} else if (NdChar <= 2.6e+75) {
		tmp = (NdChar / (1.0 + Math.exp((-Ec / KbT)))) + (NaChar / (Vef / KbT));
	} else if (NdChar <= 1.6e+143) {
		tmp = t_0 + (NdChar * 0.5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -8.5e-31:
		tmp = t_1
	elif NdChar <= 8.5e-83:
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)))
	elif NdChar <= 1.55e-31:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif NdChar <= 2.4e+71:
		tmp = t_1
	elif NdChar <= 2.6e+75:
		tmp = (NdChar / (1.0 + math.exp((-Ec / KbT)))) + (NaChar / (Vef / KbT))
	elif NdChar <= 1.6e+143:
		tmp = t_0 + (NdChar * 0.5)
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -8.5e-31)
		tmp = t_1;
	elseif (NdChar <= 8.5e-83)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (NdChar <= 1.55e-31)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif (NdChar <= 2.4e+71)
		tmp = t_1;
	elseif (NdChar <= 2.6e+75)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))) + Float64(NaChar / Float64(Vef / KbT)));
	elseif (NdChar <= 1.6e+143)
		tmp = Float64(t_0 + Float64(NdChar * 0.5));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -8.5e-31)
		tmp = t_1;
	elseif (NdChar <= 8.5e-83)
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (NdChar <= 1.55e-31)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif (NdChar <= 2.4e+71)
		tmp = t_1;
	elseif (NdChar <= 2.6e+75)
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / (Vef / KbT));
	elseif (NdChar <= 1.6e+143)
		tmp = t_0 + (NdChar * 0.5);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -8.5e-31], t$95$1, If[LessEqual[NdChar, 8.5e-83], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.55e-31], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.4e+71], t$95$1, If[LessEqual[NdChar, 2.6e+75], N[(N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.6e+143], N[(t$95$0 + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -8.5000000000000007e-31 or 1.55e-31 < NdChar < 2.39999999999999981e71 or 1.60000000000000008e143 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 60.0%

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

   if -8.5000000000000007e-31 < NdChar < 8.49999999999999938e-83

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.7%

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

      1. associate-+r+ 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in EDonor around inf 74.5%

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

   if 8.49999999999999938e-83 < NdChar < 1.55e-31

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 16.1%

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

   6. Taylor expanded in Vef around inf 8.4%

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

   7. Taylor expanded in NdChar around inf 63.8%

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

   if 2.39999999999999981e71 < NdChar < 2.59999999999999985e75

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 100.0%

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

      1. associate-*r/ 37.4%

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

      2. mul-1-neg 37.4%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in KbT around inf 33.3%

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

   9. Taylor expanded in Vef around inf 100.0%

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

   if 2.59999999999999985e75 < NdChar < 1.60000000000000008e143

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in mu around inf 72.9%

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

   6. Taylor expanded in mu around 0 60.1%

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

   7. Taylor expanded in mu around 0 54.9%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -8.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.55 \cdot 10^{-31}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+71}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 2.6 \cdot 10^{+75}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.6 \cdot 10^{+143}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -0.00092:\\ \;\;\;\;t_1 + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq -5.6 \cdot 10^{-84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -1 \cdot 10^{-114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;KbT \leq -3.8 \cdot 10^{-307}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.25 \cdot 10^{-14}:\\ \;\;\;\;t_1 + \frac{KbT}{\frac{EDonor}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0)))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (<= KbT -0.00092)
     (+ t_1 (* NdChar 0.5))
     (if (<= KbT -5.6e-84)
       t_0
       (if (<= KbT -1e-114)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT))))
          (* NdChar (/ KbT mu)))
         (if (<= KbT -3.8e-307)
           (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
           (if (<= KbT 1.25e-14) (+ t_1 (/ KbT (/ EDonor NdChar))) t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double t_1 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (KbT <= -0.00092) {
		tmp = t_1 + (NdChar * 0.5);
	} else if (KbT <= -5.6e-84) {
		tmp = t_0;
	} else if (KbT <= -1e-114) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	} else if (KbT <= -3.8e-307) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if (KbT <= 1.25e-14) {
		tmp = t_1 + (KbT / (EDonor / NdChar));
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    t_1 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    if (kbt <= (-0.00092d0)) then
        tmp = t_1 + (ndchar * 0.5d0)
    else if (kbt <= (-5.6d-84)) then
        tmp = t_0
    else if (kbt <= (-1d-114)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt)))) + (ndchar * (kbt / mu))
    else if (kbt <= (-3.8d-307)) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if (kbt <= 1.25d-14) then
        tmp = t_1 + (kbt / (edonor / ndchar))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (KbT <= -0.00092) {
		tmp = t_1 + (NdChar * 0.5);
	} else if (KbT <= -5.6e-84) {
		tmp = t_0;
	} else if (KbT <= -1e-114) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	} else if (KbT <= -3.8e-307) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if (KbT <= 1.25e-14) {
		tmp = t_1 + (KbT / (EDonor / NdChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	t_1 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	tmp = 0
	if KbT <= -0.00092:
		tmp = t_1 + (NdChar * 0.5)
	elif KbT <= -5.6e-84:
		tmp = t_0
	elif KbT <= -1e-114:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu))
	elif KbT <= -3.8e-307:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif KbT <= 1.25e-14:
		tmp = t_1 + (KbT / (EDonor / NdChar))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	tmp = 0.0
	if (KbT <= -0.00092)
		tmp = Float64(t_1 + Float64(NdChar * 0.5));
	elseif (KbT <= -5.6e-84)
		tmp = t_0;
	elseif (KbT <= -1e-114)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT)))) + Float64(NdChar * Float64(KbT / mu)));
	elseif (KbT <= -3.8e-307)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif (KbT <= 1.25e-14)
		tmp = Float64(t_1 + Float64(KbT / Float64(EDonor / NdChar)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	t_1 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if (KbT <= -0.00092)
		tmp = t_1 + (NdChar * 0.5);
	elseif (KbT <= -5.6e-84)
		tmp = t_0;
	elseif (KbT <= -1e-114)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	elseif (KbT <= -3.8e-307)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif (KbT <= 1.25e-14)
		tmp = t_1 + (KbT / (EDonor / NdChar));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -0.00092], N[(t$95$1 + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -5.6e-84], t$95$0, If[LessEqual[KbT, -1e-114], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * N[(KbT / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -3.8e-307], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.25e-14], N[(t$95$1 + N[(KbT / N[(EDonor / NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if KbT < -9.2000000000000003e-4

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 80.9%

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

   6. Taylor expanded in mu around 0 67.8%

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

   7. Taylor expanded in mu around 0 67.3%

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

   if -9.2000000000000003e-4 < KbT < -5.59999999999999964e-84 or 1.25e-14 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 58.3%

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

   if -5.59999999999999964e-84 < KbT < -1.0000000000000001e-114

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 86.5%

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

      1. associate-+r+ 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in mu around inf 86.8%

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

      1. expm1-log1p-u 86.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{KbT \cdot NdChar}{mu}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      2. expm1-udef 86.8%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{KbT \cdot NdChar}{mu}\right)} - 1\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. associate-/l* 87.0%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{KbT}{\frac{mu}{NdChar}}}\right)} - 1\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   10. Applied egg-rr 87.0%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{KbT}{\frac{mu}{NdChar}}\right)} - 1\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   11. Step-by-step derivation

       1. expm1-def 87.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{KbT}{\frac{mu}{NdChar}}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

       2. expm1-log1p 87.0%

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

       3. associate-/r/ 86.8%

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

       4. *-commutative 86.8%

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

   12. Simplified 86.8%

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

   13. Taylor expanded in Ev around 0 86.8%

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

       1. +-commutative 86.8%

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

       2. sub-neg 86.8%

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

       3. associate-+l+ 86.8%

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

       4. mul-1-neg 86.8%

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

       5. +-commutative 86.8%

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

       6. mul-1-neg 86.8%

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

       7. sub-neg 86.8%

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

       8. associate--r- 86.8%

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

   15. Simplified 86.8%

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

   if -1.0000000000000001e-114 < KbT < -3.79999999999999985e-307

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 38.1%

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

   6. Taylor expanded in Vef around inf 19.7%

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

   7. Taylor expanded in NdChar around inf 51.1%

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

   if -3.79999999999999985e-307 < KbT < 1.25e-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%

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

   5. Taylor expanded in KbT around inf 60.4%

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

      1. associate-+r+ 60.4%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in EDonor around inf 55.5%

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

      1. associate-/l* 52.6%

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

   10. Simplified 52.6%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -0.00092:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq -5.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -1 \cdot 10^{-114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;KbT \leq -3.8 \cdot 10^{-307}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.25 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{KbT}{\frac{EDonor}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -7.2 \cdot 10^{-5}:\\ \;\;\;\;t_1 + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -5 \cdot 10^{-114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;KbT \leq -1.22 \cdot 10^{-290}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;KbT \leq 8.5 \cdot 10^{-16}:\\ \;\;\;\;t_1 + \frac{KbT}{\frac{Vef}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0)))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (<= KbT -7.2e-5)
     (+ t_1 (* NdChar 0.5))
     (if (<= KbT -3.3e-84)
       t_0
       (if (<= KbT -5e-114)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT))))
          (* NdChar (/ KbT mu)))
         (if (<= KbT -1.22e-290)
           (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
           (if (<= KbT 8.5e-16) (+ t_1 (/ KbT (/ Vef NdChar))) t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double t_1 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (KbT <= -7.2e-5) {
		tmp = t_1 + (NdChar * 0.5);
	} else if (KbT <= -3.3e-84) {
		tmp = t_0;
	} else if (KbT <= -5e-114) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	} else if (KbT <= -1.22e-290) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if (KbT <= 8.5e-16) {
		tmp = t_1 + (KbT / (Vef / NdChar));
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    t_1 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    if (kbt <= (-7.2d-5)) then
        tmp = t_1 + (ndchar * 0.5d0)
    else if (kbt <= (-3.3d-84)) then
        tmp = t_0
    else if (kbt <= (-5d-114)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt)))) + (ndchar * (kbt / mu))
    else if (kbt <= (-1.22d-290)) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if (kbt <= 8.5d-16) then
        tmp = t_1 + (kbt / (vef / ndchar))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (KbT <= -7.2e-5) {
		tmp = t_1 + (NdChar * 0.5);
	} else if (KbT <= -3.3e-84) {
		tmp = t_0;
	} else if (KbT <= -5e-114) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	} else if (KbT <= -1.22e-290) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if (KbT <= 8.5e-16) {
		tmp = t_1 + (KbT / (Vef / NdChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	t_1 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	tmp = 0
	if KbT <= -7.2e-5:
		tmp = t_1 + (NdChar * 0.5)
	elif KbT <= -3.3e-84:
		tmp = t_0
	elif KbT <= -5e-114:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu))
	elif KbT <= -1.22e-290:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif KbT <= 8.5e-16:
		tmp = t_1 + (KbT / (Vef / NdChar))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	tmp = 0.0
	if (KbT <= -7.2e-5)
		tmp = Float64(t_1 + Float64(NdChar * 0.5));
	elseif (KbT <= -3.3e-84)
		tmp = t_0;
	elseif (KbT <= -5e-114)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT)))) + Float64(NdChar * Float64(KbT / mu)));
	elseif (KbT <= -1.22e-290)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif (KbT <= 8.5e-16)
		tmp = Float64(t_1 + Float64(KbT / Float64(Vef / NdChar)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	t_1 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if (KbT <= -7.2e-5)
		tmp = t_1 + (NdChar * 0.5);
	elseif (KbT <= -3.3e-84)
		tmp = t_0;
	elseif (KbT <= -5e-114)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	elseif (KbT <= -1.22e-290)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif (KbT <= 8.5e-16)
		tmp = t_1 + (KbT / (Vef / NdChar));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -7.2e-5], N[(t$95$1 + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -3.3e-84], t$95$0, If[LessEqual[KbT, -5e-114], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * N[(KbT / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -1.22e-290], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 8.5e-16], N[(t$95$1 + N[(KbT / N[(Vef / NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if KbT < -7.20000000000000018e-5

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 80.9%

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

   6. Taylor expanded in mu around 0 67.8%

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

   7. Taylor expanded in mu around 0 67.3%

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

   if -7.20000000000000018e-5 < KbT < -3.29999999999999984e-84 or 8.5000000000000001e-16 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 58.3%

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

   if -3.29999999999999984e-84 < KbT < -4.99999999999999989e-114

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 86.5%

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

      1. associate-+r+ 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in mu around inf 86.8%

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

      1. expm1-log1p-u 86.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{KbT \cdot NdChar}{mu}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      2. expm1-udef 86.8%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{KbT \cdot NdChar}{mu}\right)} - 1\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. associate-/l* 87.0%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{KbT}{\frac{mu}{NdChar}}}\right)} - 1\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   10. Applied egg-rr 87.0%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{KbT}{\frac{mu}{NdChar}}\right)} - 1\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   11. Step-by-step derivation

       1. expm1-def 87.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{KbT}{\frac{mu}{NdChar}}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

       2. expm1-log1p 87.0%

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

       3. associate-/r/ 86.8%

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

       4. *-commutative 86.8%

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

   12. Simplified 86.8%

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

   13. Taylor expanded in Ev around 0 86.8%

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

       1. +-commutative 86.8%

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

       2. sub-neg 86.8%

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

       3. associate-+l+ 86.8%

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

       4. mul-1-neg 86.8%

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

       5. +-commutative 86.8%

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

       6. mul-1-neg 86.8%

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

       7. sub-neg 86.8%

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

       8. associate--r- 86.8%

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

   15. Simplified 86.8%

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

   if -4.99999999999999989e-114 < KbT < -1.22e-290

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 40.8%

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

   6. Taylor expanded in Vef around inf 20.4%

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

   7. Taylor expanded in NdChar around inf 52.7%

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

   if -1.22e-290 < KbT < 8.5000000000000001e-16

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.6%

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

      1. associate-+r+ 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in Vef around inf 61.9%

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

      1. associate-/l* 57.3%

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

   10. Simplified 57.3%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -7.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -5 \cdot 10^{-114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;KbT \leq -1.22 \cdot 10^{-290}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;KbT \leq 8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{KbT}{\frac{Vef}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -0.00029:\\ \;\;\;\;t_1 + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq -1.6 \cdot 10^{-84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -6.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;KbT \leq -4.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.12 \cdot 10^{-14}:\\ \;\;\;\;t_1 + \frac{NdChar \cdot KbT}{Vef}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0)))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (<= KbT -0.00029)
     (+ t_1 (* NdChar 0.5))
     (if (<= KbT -1.6e-84)
       t_0
       (if (<= KbT -6.5e-114)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT))))
          (* NdChar (/ KbT mu)))
         (if (<= KbT -4.5e-289)
           (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
           (if (<= KbT 1.12e-14) (+ t_1 (/ (* NdChar KbT) Vef)) t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double t_1 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (KbT <= -0.00029) {
		tmp = t_1 + (NdChar * 0.5);
	} else if (KbT <= -1.6e-84) {
		tmp = t_0;
	} else if (KbT <= -6.5e-114) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	} else if (KbT <= -4.5e-289) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if (KbT <= 1.12e-14) {
		tmp = t_1 + ((NdChar * KbT) / Vef);
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    t_1 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    if (kbt <= (-0.00029d0)) then
        tmp = t_1 + (ndchar * 0.5d0)
    else if (kbt <= (-1.6d-84)) then
        tmp = t_0
    else if (kbt <= (-6.5d-114)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt)))) + (ndchar * (kbt / mu))
    else if (kbt <= (-4.5d-289)) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if (kbt <= 1.12d-14) then
        tmp = t_1 + ((ndchar * kbt) / vef)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (KbT <= -0.00029) {
		tmp = t_1 + (NdChar * 0.5);
	} else if (KbT <= -1.6e-84) {
		tmp = t_0;
	} else if (KbT <= -6.5e-114) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	} else if (KbT <= -4.5e-289) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if (KbT <= 1.12e-14) {
		tmp = t_1 + ((NdChar * KbT) / Vef);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	t_1 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	tmp = 0
	if KbT <= -0.00029:
		tmp = t_1 + (NdChar * 0.5)
	elif KbT <= -1.6e-84:
		tmp = t_0
	elif KbT <= -6.5e-114:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu))
	elif KbT <= -4.5e-289:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif KbT <= 1.12e-14:
		tmp = t_1 + ((NdChar * KbT) / Vef)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	tmp = 0.0
	if (KbT <= -0.00029)
		tmp = Float64(t_1 + Float64(NdChar * 0.5));
	elseif (KbT <= -1.6e-84)
		tmp = t_0;
	elseif (KbT <= -6.5e-114)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT)))) + Float64(NdChar * Float64(KbT / mu)));
	elseif (KbT <= -4.5e-289)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif (KbT <= 1.12e-14)
		tmp = Float64(t_1 + Float64(Float64(NdChar * KbT) / Vef));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	t_1 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if (KbT <= -0.00029)
		tmp = t_1 + (NdChar * 0.5);
	elseif (KbT <= -1.6e-84)
		tmp = t_0;
	elseif (KbT <= -6.5e-114)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	elseif (KbT <= -4.5e-289)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif (KbT <= 1.12e-14)
		tmp = t_1 + ((NdChar * KbT) / Vef);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -0.00029], N[(t$95$1 + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -1.6e-84], t$95$0, If[LessEqual[KbT, -6.5e-114], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * N[(KbT / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -4.5e-289], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.12e-14], N[(t$95$1 + N[(N[(NdChar * KbT), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if KbT < -2.9e-4

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 80.9%

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

   6. Taylor expanded in mu around 0 67.8%

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

   7. Taylor expanded in mu around 0 67.3%

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

   if -2.9e-4 < KbT < -1.6e-84 or 1.12000000000000006e-14 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 58.3%

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

   if -1.6e-84 < KbT < -6.4999999999999998e-114

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 86.5%

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

      1. associate-+r+ 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in mu around inf 86.8%

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

      1. expm1-log1p-u 86.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{KbT \cdot NdChar}{mu}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      2. expm1-udef 86.8%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{KbT \cdot NdChar}{mu}\right)} - 1\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. associate-/l* 87.0%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{KbT}{\frac{mu}{NdChar}}}\right)} - 1\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   10. Applied egg-rr 87.0%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{KbT}{\frac{mu}{NdChar}}\right)} - 1\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   11. Step-by-step derivation

       1. expm1-def 87.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{KbT}{\frac{mu}{NdChar}}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

       2. expm1-log1p 87.0%

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

       3. associate-/r/ 86.8%

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

       4. *-commutative 86.8%

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

   12. Simplified 86.8%

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

   13. Taylor expanded in Ev around 0 86.8%

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

       1. +-commutative 86.8%

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

       2. sub-neg 86.8%

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

       3. associate-+l+ 86.8%

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

       4. mul-1-neg 86.8%

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

       5. +-commutative 86.8%

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

       6. mul-1-neg 86.8%

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

       7. sub-neg 86.8%

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

       8. associate--r- 86.8%

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

   15. Simplified 86.8%

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

   if -6.4999999999999998e-114 < KbT < -4.5000000000000002e-289

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 40.8%

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

   6. Taylor expanded in Vef around inf 20.4%

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

   7. Taylor expanded in NdChar around inf 52.7%

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

   if -4.5000000000000002e-289 < KbT < 1.12000000000000006e-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%

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

   5. Taylor expanded in KbT around inf 60.6%

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

      1. associate-+r+ 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in Vef around inf 61.9%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -0.00029:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq -1.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -6.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;KbT \leq -4.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.12 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar \cdot KbT}{Vef}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 48.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;KbT \leq -7.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq -5.2 \cdot 10^{-84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -1.25 \cdot 10^{-114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;KbT \leq -7.2 \cdot 10^{-291}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;KbT \leq 8 \cdot 10^{-77}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef - mu\right)}{KbT}}} + \frac{NdChar \cdot KbT}{mu}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0))))
   (if (<= KbT -7.3e-6)
     (+
      (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
      (* NdChar 0.5))
     (if (<= KbT -5.2e-84)
       t_0
       (if (<= KbT -1.25e-114)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- EAccept mu)) KbT))))
          (* NdChar (/ KbT mu)))
         (if (<= KbT -7.2e-291)
           (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
           (if (<= KbT 8e-77)
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Ev (- Vef mu)) KbT))))
              (/ (* NdChar KbT) mu))
             t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (KbT <= -7.3e-6) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else if (KbT <= -5.2e-84) {
		tmp = t_0;
	} else if (KbT <= -1.25e-114) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	} else if (KbT <= -7.2e-291) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if (KbT <= 8e-77) {
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef - mu)) / KbT)))) + ((NdChar * KbT) / mu);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    if (kbt <= (-7.3d-6)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    else if (kbt <= (-5.2d-84)) then
        tmp = t_0
    else if (kbt <= (-1.25d-114)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept - mu)) / kbt)))) + (ndchar * (kbt / mu))
    else if (kbt <= (-7.2d-291)) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if (kbt <= 8d-77) then
        tmp = (nachar / (1.0d0 + exp(((ev + (vef - mu)) / kbt)))) + ((ndchar * kbt) / mu)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (KbT <= -7.3e-6) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else if (KbT <= -5.2e-84) {
		tmp = t_0;
	} else if (KbT <= -1.25e-114) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	} else if (KbT <= -7.2e-291) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if (KbT <= 8e-77) {
		tmp = (NaChar / (1.0 + Math.exp(((Ev + (Vef - mu)) / KbT)))) + ((NdChar * KbT) / mu);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	tmp = 0
	if KbT <= -7.3e-6:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	elif KbT <= -5.2e-84:
		tmp = t_0
	elif KbT <= -1.25e-114:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu))
	elif KbT <= -7.2e-291:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif KbT <= 8e-77:
		tmp = (NaChar / (1.0 + math.exp(((Ev + (Vef - mu)) / KbT)))) + ((NdChar * KbT) / mu)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (KbT <= -7.3e-6)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5));
	elseif (KbT <= -5.2e-84)
		tmp = t_0;
	elseif (KbT <= -1.25e-114)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept - mu)) / KbT)))) + Float64(NdChar * Float64(KbT / mu)));
	elseif (KbT <= -7.2e-291)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif (KbT <= 8e-77)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef - mu)) / KbT)))) + Float64(Float64(NdChar * KbT) / mu));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	tmp = 0.0;
	if (KbT <= -7.3e-6)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	elseif (KbT <= -5.2e-84)
		tmp = t_0;
	elseif (KbT <= -1.25e-114)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept - mu)) / KbT)))) + (NdChar * (KbT / mu));
	elseif (KbT <= -7.2e-291)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif (KbT <= 8e-77)
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef - mu)) / KbT)))) + ((NdChar * KbT) / mu);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -7.3e-6], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -5.2e-84], t$95$0, If[LessEqual[KbT, -1.25e-114], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * N[(KbT / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -7.2e-291], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 8e-77], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(NdChar * KbT), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if KbT < -7.30000000000000041e-6

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 80.9%

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

   6. Taylor expanded in mu around 0 67.8%

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

   7. Taylor expanded in mu around 0 67.3%

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

   if -7.30000000000000041e-6 < KbT < -5.2e-84 or 7.9999999999999994e-77 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.0%

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

   if -5.2e-84 < KbT < -1.24999999999999997e-114

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 86.5%

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

      1. associate-+r+ 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in mu around inf 86.8%

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

      1. expm1-log1p-u 86.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{KbT \cdot NdChar}{mu}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      2. expm1-udef 86.8%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{KbT \cdot NdChar}{mu}\right)} - 1\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. associate-/l* 87.0%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{KbT}{\frac{mu}{NdChar}}}\right)} - 1\right) + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   10. Applied egg-rr 87.0%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{KbT}{\frac{mu}{NdChar}}\right)} - 1\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
   11. Step-by-step derivation

       1. expm1-def 87.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{KbT}{\frac{mu}{NdChar}}\right)\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

       2. expm1-log1p 87.0%

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

       3. associate-/r/ 86.8%

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

       4. *-commutative 86.8%

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

   12. Simplified 86.8%

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

   13. Taylor expanded in Ev around 0 86.8%

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

       1. +-commutative 86.8%

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

       2. sub-neg 86.8%

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

       3. associate-+l+ 86.8%

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

       4. mul-1-neg 86.8%

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

       5. +-commutative 86.8%

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

       6. mul-1-neg 86.8%

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

       7. sub-neg 86.8%

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

       8. associate--r- 86.8%

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

   15. Simplified 86.8%

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

   if -1.24999999999999997e-114 < KbT < -7.1999999999999993e-291

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 40.8%

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

   6. Taylor expanded in Vef around inf 20.4%

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

   7. Taylor expanded in NdChar around inf 52.7%

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

   if -7.1999999999999993e-291 < KbT < 7.9999999999999994e-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%

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

   5. Taylor expanded in KbT around inf 57.7%

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

      1. associate-+r+ 57.7%

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

   7. Simplified 57.7%

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

   8. Taylor expanded in mu around inf 53.8%

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

   9. Taylor expanded in EAccept around 0 50.5%

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

       1. +-commutative 50.5%

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

       2. associate--l+ 50.5%

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

   11. Simplified 50.5%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -7.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq -5.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -1.25 \cdot 10^{-114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;KbT \leq -7.2 \cdot 10^{-291}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;KbT \leq 8 \cdot 10^{-77}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef - mu\right)}{KbT}}} + \frac{NdChar \cdot KbT}{mu}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 50.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -4.2 \cdot 10^{+17} \lor \neg \left(NaChar \leq 1.95 \cdot 10^{-218}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -4.2e+17) (not (<= NaChar 1.95e-218)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (* NdChar 0.5))
   (/ NdChar (+ 1.0 (exp (/ Vef KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -4.2e+17) || !(NaChar <= 1.95e-218)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-4.2d+17)) .or. (.not. (nachar <= 1.95d-218))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -4.2e+17) || !(NaChar <= 1.95e-218)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -4.2e+17) or not (NaChar <= 1.95e-218):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -4.2e+17) || !(NaChar <= 1.95e-218))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -4.2e+17) || ~((NaChar <= 1.95e-218)))
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar * 0.5);
	else
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -4.2e+17], N[Not[LessEqual[NaChar, 1.95e-218]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.2e17 or 1.95e-218 < NaChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 77.3%

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

   6. Taylor expanded in mu around 0 63.3%

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

   7. Taylor expanded in mu around 0 57.8%

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

   if -4.2e17 < NaChar < 1.95e-218

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.1%

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

   6. Taylor expanded in Vef around inf 32.8%

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

   7. Taylor expanded in NdChar around inf 45.8%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.2 \cdot 10^{+17} \lor \neg \left(NaChar \leq 1.95 \cdot 10^{-218}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 44.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -8.5 \cdot 10^{+18} \lor \neg \left(Vef \leq 0.062\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Vef -8.5e+18) (not (<= Vef 0.062)))
   (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
   (+ (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))) (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -8.5e+18) || !(Vef <= 0.062)) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((vef <= (-8.5d+18)) .or. (.not. (vef <= 0.062d0))) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp((-ec / kbt)))) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -8.5e+18) || !(Vef <= 0.062)) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((-Ec / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Vef <= -8.5e+18) or not (Vef <= 0.062):
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp((-Ec / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Vef <= -8.5e+18) || !(Vef <= 0.062))
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Vef <= -8.5e+18) || ~((Vef <= 0.062)))
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	else
		tmp = (NdChar / (1.0 + exp((-Ec / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Vef, -8.5e+18], N[Not[LessEqual[Vef, 0.062]], $MachinePrecision]], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -8.5e18 or 0.062 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 34.3%

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

   6. Taylor expanded in Vef around inf 26.5%

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

   7. Taylor expanded in NdChar around inf 49.2%

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

   if -8.5e18 < Vef < 0.062

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 54.8%

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

   6. Taylor expanded in Ec around inf 45.5%

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

      1. associate-*r/ 45.5%

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

      2. mul-1-neg 45.5%

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

   8. Simplified 45.5%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -8.5 \cdot 10^{+18} \lor \neg \left(Vef \leq 0.062\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 44.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -25000000000 \lor \neg \left(Vef \leq 23000\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Vef -25000000000.0) (not (<= Vef 23000.0)))
   (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -25000000000.0) || !(Vef <= 23000.0)) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((vef <= (-25000000000.0d0)) .or. (.not. (vef <= 23000.0d0))) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -25000000000.0) || !(Vef <= 23000.0)) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Vef <= -25000000000.0) or not (Vef <= 23000.0):
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Vef <= -25000000000.0) || !(Vef <= 23000.0))
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Vef <= -25000000000.0) || ~((Vef <= 23000.0)))
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	else
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Vef, -25000000000.0], N[Not[LessEqual[Vef, 23000.0]], $MachinePrecision]], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -2.5e10 or 23000 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 34.5%

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

   6. Taylor expanded in Vef around inf 26.7%

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

   7. Taylor expanded in NdChar around inf 49.6%

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

   if -2.5e10 < Vef < 23000

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 54.4%

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

   6. Taylor expanded in EDonor around inf 43.6%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -25000000000 \lor \neg \left(Vef \leq 23000\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 40.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -1 \cdot 10^{-17} \lor \neg \left(Vef \leq 1.55 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Vef -1e-17) (not (<= Vef 1.55e-64)))
   (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
   (+
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT)))
    (/ NdChar (+ 1.0 (/ Vef KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -1e-17) || !(Vef <= 1.55e-64)) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((vef <= (-1d-17)) .or. (.not. (vef <= 1.55d-64))) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else
        tmp = (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt))) + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -1e-17) || !(Vef <= 1.55e-64)) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Vef <= -1e-17) or not (Vef <= 1.55e-64):
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	else:
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Vef <= -1e-17) || !(Vef <= 1.55e-64))
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))) + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Vef <= -1e-17) || ~((Vef <= 1.55e-64)))
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	else
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Vef, -1e-17], N[Not[LessEqual[Vef, 1.55e-64]], $MachinePrecision]], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -1.00000000000000007e-17 or 1.55000000000000012e-64 < Vef

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 37.0%

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

   6. Taylor expanded in Vef around inf 28.3%

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

   7. Taylor expanded in NdChar around inf 46.7%

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

   if -1.00000000000000007e-17 < Vef < 1.55000000000000012e-64

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.2%

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

      1. associate-+r+ 65.2%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in KbT around inf 34.4%

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

   9. Taylor expanded in Vef around inf 38.2%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1 \cdot 10^{-17} \lor \neg \left(Vef \leq 1.55 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 27.4% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{EDonor}{KbT}\\ t_1 := 2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\\ \mathbf{if}\;Ec \leq -3 \cdot 10^{-13}:\\ \;\;\;\;\frac{NdChar}{t_0} + \frac{NaChar}{t_1 - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(t_0 + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ EDonor KbT)))
        (t_1 (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))))
   (if (<= Ec -3e-13)
     (+ (/ NdChar t_0) (/ NaChar (- t_1 (/ mu KbT))))
     (+
      (/ NdChar (+ 1.0 (- (+ t_0 (+ (/ mu KbT) (/ Vef KbT))) (/ Ec KbT))))
      (/ NaChar t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + (EDonor / KbT);
	double t_1 = 2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)));
	double tmp;
	if (Ec <= -3e-13) {
		tmp = (NdChar / t_0) + (NaChar / (t_1 - (mu / KbT)));
	} else {
		tmp = (NdChar / (1.0 + ((t_0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)))) + (NaChar / 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 = 1.0d0 + (edonor / kbt)
    t_1 = 2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))
    if (ec <= (-3d-13)) then
        tmp = (ndchar / t_0) + (nachar / (t_1 - (mu / kbt)))
    else
        tmp = (ndchar / (1.0d0 + ((t_0 + ((mu / kbt) + (vef / kbt))) - (ec / kbt)))) + (nachar / t_1)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + (EDonor / KbT);
	double t_1 = 2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)));
	double tmp;
	if (Ec <= -3e-13) {
		tmp = (NdChar / t_0) + (NaChar / (t_1 - (mu / KbT)));
	} else {
		tmp = (NdChar / (1.0 + ((t_0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)))) + (NaChar / t_1);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + (EDonor / KbT)
	t_1 = 2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))
	tmp = 0
	if Ec <= -3e-13:
		tmp = (NdChar / t_0) + (NaChar / (t_1 - (mu / KbT)))
	else:
		tmp = (NdChar / (1.0 + ((t_0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)))) + (NaChar / t_1)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + Float64(EDonor / KbT))
	t_1 = Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))))
	tmp = 0.0
	if (Ec <= -3e-13)
		tmp = Float64(Float64(NdChar / t_0) + Float64(NaChar / Float64(t_1 - Float64(mu / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(Float64(t_0 + Float64(Float64(mu / KbT) + Float64(Vef / KbT))) - Float64(Ec / KbT)))) + Float64(NaChar / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + (EDonor / KbT);
	t_1 = 2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)));
	tmp = 0.0;
	if (Ec <= -3e-13)
		tmp = (NdChar / t_0) + (NaChar / (t_1 - (mu / KbT)));
	else
		tmp = (NdChar / (1.0 + ((t_0 + ((mu / KbT) + (Vef / KbT))) - (Ec / KbT)))) + (NaChar / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ec, -3e-13], N[(N[(NdChar / t$95$0), $MachinePrecision] + N[(NaChar / N[(t$95$1 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[(N[(t$95$0 + N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if Ec < -2.99999999999999984e-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%

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

   5. Taylor expanded in KbT around inf 49.7%

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

      1. associate-+r+ 49.7%

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

   7. Simplified 49.7%

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

   8. Taylor expanded in KbT around inf 18.6%

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

   9. Taylor expanded in EDonor around inf 28.0%

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

   if -2.99999999999999984e-13 < 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%

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

   5. Taylor expanded in KbT around inf 61.5%

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

      1. associate-+r+ 61.5%

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

   7. Simplified 61.5%

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

   8. Taylor expanded in KbT around inf 30.5%

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

   9. Taylor expanded in mu around 0 32.4%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -3 \cdot 10^{-13}:\\ \;\;\;\;\frac{NdChar}{1 + \frac{EDonor}{KbT}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 27.4% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq -2.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{NdChar}{1 + \frac{EDonor}{KbT}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ec -2.5e-37)
   (+
    (/ NdChar (+ 1.0 (/ EDonor KbT)))
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ 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 (Ec <= -2.5e-37) {
		tmp = (NdChar / (1.0 + (EDonor / KbT))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (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 (ec <= (-2.5d-37)) then
        tmp = (ndchar / (1.0d0 + (edonor / kbt))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (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 (Ec <= -2.5e-37) {
		tmp = (NdChar / (1.0 + (EDonor / KbT))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (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 Ec <= -2.5e-37:
		tmp = (NdChar / (1.0 + (EDonor / KbT))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (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 (Ec <= -2.5e-37)
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - 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 (Ec <= -2.5e-37)
		tmp = (NdChar / (1.0 + (EDonor / KbT))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (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[Ec, -2.5e-37], N[(N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < -2.4999999999999999e-37

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 49.2%

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

      1. associate-+r+ 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in KbT around inf 19.4%

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

   9. Taylor expanded in EDonor around inf 28.4%

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

   if -2.4999999999999999e-37 < 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%

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

   5. Taylor expanded in KbT around inf 46.1%

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

   6. Taylor expanded in Vef around inf 36.0%

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

   7. Taylor expanded in Vef around 0 30.5%

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

      1. distribute-lft-out 30.5%

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

   9. Simplified 30.5%

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

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -2.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{NdChar}{1 + \frac{EDonor}{KbT}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 27.4% accurate, 45.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 44.7%

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

6. Taylor expanded in Vef around inf 31.4%

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

7. Taylor expanded in Vef around 0 26.8%

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

   1. distribute-lft-out 26.8%

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

9. Simplified 26.8%

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

10. Final simplification 26.8%

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

Alternative 29: 18.3% 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%

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

5. Taylor expanded in KbT around inf 44.7%

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

6. Taylor expanded in Vef around inf 31.4%

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

7. Taylor expanded in NdChar around 0 20.0%

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

8. Final simplification 20.0%

   \[\leadsto NaChar \cdot 0.5 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(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))))))