Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 35.9s

Alternatives: 26

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = 4.7347766237564153e+36
  2. Ec = 4.864185675007253e+80
  3. Vef = 4.362517990528552e+257
  4. EDonor = -6.511772609389309e-98
  5. mu = 2.5882197820029283e+208
  6. KbT = -8.221068087434754e+92
  7. NaChar = 7.045862801179503e+35
  8. Ev = 3.1752881840656807e+21
  9. EAccept = -1.2302672808943075e-302

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{EAccept \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{mu}{KbT}}{EAccept}\right)}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ t_3 := \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} - \frac{1}{\frac{-1 - e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}}\\ \mathbf{if}\;mu \leq -8.2 \cdot 10^{+198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -2.55 \cdot 10^{+79}:\\ \;\;\;\;t\_0 + \frac{NaChar}{Vef \cdot \left(\frac{1}{KbT} + Ev \cdot \left(\frac{1}{Vef \cdot KbT} + \frac{\frac{2}{Vef} - \frac{\frac{mu - EAccept}{KbT}}{Vef}}{Ev}\right)\right)}\\ \mathbf{elif}\;mu \leq -1.16 \cdot 10^{+30}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;mu \leq -6.9 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq 1.2 \cdot 10^{-102}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;mu \leq 1.52 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1
         (+
          t_0
          (/
           NaChar
           (*
            EAccept
            (+
             (/ 1.0 KbT)
             (/ (- (+ 2.0 (+ (/ Ev KbT) (/ Vef KbT))) (/ mu KbT)) EAccept))))))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))))
        (t_3
         (-
          (/
           NdChar
           (-
            (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
            (/ Ec KbT)))
          (/
           1.0
           (/ (- -1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar)))))
   (if (<= mu -8.2e+198)
     t_2
     (if (<= mu -2.55e+79)
       (+
        t_0
        (/
         NaChar
         (*
          Vef
          (+
           (/ 1.0 KbT)
           (*
            Ev
            (+
             (/ 1.0 (* Vef KbT))
             (/ (- (/ 2.0 Vef) (/ (/ (- mu EAccept) KbT) Vef)) Ev)))))))
       (if (<= mu -1.16e+30)
         t_3
         (if (<= mu -6.9e-217)
           t_1
           (if (<= mu 1.2e-102) t_3 (if (<= mu 1.52e+62) t_1 t_2))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (EAccept * ((1.0 / KbT) + (((2.0 + ((Ev / KbT) + (Vef / KbT))) - (mu / KbT)) / EAccept))));
	double t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	double t_3 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar));
	double tmp;
	if (mu <= -8.2e+198) {
		tmp = t_2;
	} else if (mu <= -2.55e+79) {
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) + (Ev * ((1.0 / (Vef * KbT)) + (((2.0 / Vef) - (((mu - EAccept) / KbT) / Vef)) / Ev))))));
	} else if (mu <= -1.16e+30) {
		tmp = t_3;
	} else if (mu <= -6.9e-217) {
		tmp = t_1;
	} else if (mu <= 1.2e-102) {
		tmp = t_3;
	} else if (mu <= 1.52e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = t_0 + (nachar / (eaccept * ((1.0d0 / kbt) + (((2.0d0 + ((ev / kbt) + (vef / kbt))) - (mu / kbt)) / eaccept))))
    t_2 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    t_3 = (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt))) - (1.0d0 / (((-1.0d0) - exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar))
    if (mu <= (-8.2d+198)) then
        tmp = t_2
    else if (mu <= (-2.55d+79)) then
        tmp = t_0 + (nachar / (vef * ((1.0d0 / kbt) + (ev * ((1.0d0 / (vef * kbt)) + (((2.0d0 / vef) - (((mu - eaccept) / kbt) / vef)) / ev))))))
    else if (mu <= (-1.16d+30)) then
        tmp = t_3
    else if (mu <= (-6.9d-217)) then
        tmp = t_1
    else if (mu <= 1.2d-102) then
        tmp = t_3
    else if (mu <= 1.52d+62) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (EAccept * ((1.0 / KbT) + (((2.0 + ((Ev / KbT) + (Vef / KbT))) - (mu / KbT)) / EAccept))));
	double t_2 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	double t_3 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar));
	double tmp;
	if (mu <= -8.2e+198) {
		tmp = t_2;
	} else if (mu <= -2.55e+79) {
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) + (Ev * ((1.0 / (Vef * KbT)) + (((2.0 / Vef) - (((mu - EAccept) / KbT) / Vef)) / Ev))))));
	} else if (mu <= -1.16e+30) {
		tmp = t_3;
	} else if (mu <= -6.9e-217) {
		tmp = t_1;
	} else if (mu <= 1.2e-102) {
		tmp = t_3;
	} else if (mu <= 1.52e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = t_0 + (NaChar / (EAccept * ((1.0 / KbT) + (((2.0 + ((Ev / KbT) + (Vef / KbT))) - (mu / KbT)) / EAccept))))
	t_2 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	t_3 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar))
	tmp = 0
	if mu <= -8.2e+198:
		tmp = t_2
	elif mu <= -2.55e+79:
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) + (Ev * ((1.0 / (Vef * KbT)) + (((2.0 / Vef) - (((mu - EAccept) / KbT) / Vef)) / Ev))))))
	elif mu <= -1.16e+30:
		tmp = t_3
	elif mu <= -6.9e-217:
		tmp = t_1
	elif mu <= 1.2e-102:
		tmp = t_3
	elif mu <= 1.52e+62:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(EAccept * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Ev / KbT) + Float64(Vef / KbT))) - Float64(mu / KbT)) / EAccept)))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))))
	t_3 = Float64(Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))) - Float64(1.0 / Float64(Float64(-1.0 - exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)))
	tmp = 0.0
	if (mu <= -8.2e+198)
		tmp = t_2;
	elseif (mu <= -2.55e+79)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(Ev * Float64(Float64(1.0 / Float64(Vef * KbT)) + Float64(Float64(Float64(2.0 / Vef) - Float64(Float64(Float64(mu - EAccept) / KbT) / Vef)) / Ev)))))));
	elseif (mu <= -1.16e+30)
		tmp = t_3;
	elseif (mu <= -6.9e-217)
		tmp = t_1;
	elseif (mu <= 1.2e-102)
		tmp = t_3;
	elseif (mu <= 1.52e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = t_0 + (NaChar / (EAccept * ((1.0 / KbT) + (((2.0 + ((Ev / KbT) + (Vef / KbT))) - (mu / KbT)) / EAccept))));
	t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	t_3 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar));
	tmp = 0.0;
	if (mu <= -8.2e+198)
		tmp = t_2;
	elseif (mu <= -2.55e+79)
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) + (Ev * ((1.0 / (Vef * KbT)) + (((2.0 / Vef) - (((mu - EAccept) / KbT) / Vef)) / Ev))))));
	elseif (mu <= -1.16e+30)
		tmp = t_3;
	elseif (mu <= -6.9e-217)
		tmp = t_1;
	elseif (mu <= 1.2e-102)
		tmp = t_3;
	elseif (mu <= 1.52e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(EAccept * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision] / EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[(N[(-1.0 - N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -8.2e+198], t$95$2, If[LessEqual[mu, -2.55e+79], N[(t$95$0 + N[(NaChar / N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(Ev * N[(N[(1.0 / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(2.0 / Vef), $MachinePrecision] - N[(N[(N[(mu - EAccept), $MachinePrecision] / KbT), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision] / Ev), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -1.16e+30], t$95$3, If[LessEqual[mu, -6.9e-217], t$95$1, If[LessEqual[mu, 1.2e-102], t$95$3, If[LessEqual[mu, 1.52e+62], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if mu < -8.2000000000000003e198 or 1.51999999999999998e62 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 91.0%

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

      1. associate-*r/ 91.0%

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

      2. mul-1-neg 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in mu around inf 81.9%

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

   if -8.2000000000000003e198 < mu < -2.5500000000000001e79

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 47.3%

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

      1. associate-+r+ 47.3%

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

   7. Simplified 47.3%

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

   8. Taylor expanded in Vef around -inf 62.5%

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

   9. Taylor expanded in Ev around -inf 67.1%

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

       1. associate-*r* 67.1%

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

       2. mul-1-neg 67.1%

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

       3. associate-*r/ 67.1%

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

       4. mul-1-neg 67.1%

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

       5. associate--l+ 67.1%

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

       6. associate-*r/ 67.1%

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

       7. metadata-eval 67.1%

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

       8. associate-/r* 67.1%

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

       9. associate-/r* 67.0%

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

       10. div-sub 67.0%

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

       11. div-sub 67.1%

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

       12. *-commutative 67.1%

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

   11. Simplified 67.1%

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

   if -2.5500000000000001e79 < mu < -1.16e30 or -6.89999999999999974e-217 < mu < 1.2e-102

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*r/ 100.0%

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

      5. *-commutative 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-+l- 100.0%

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

   6. Applied egg-rr 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in KbT around inf 72.6%

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

   if -1.16e30 < mu < -6.89999999999999974e-217 or 1.2e-102 < mu < 1.51999999999999998e62

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.7%

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

      1. associate-+r+ 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in EAccept around -inf 69.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -8.2 \cdot 10^{+198}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -2.55 \cdot 10^{+79}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{Vef \cdot \left(\frac{1}{KbT} + Ev \cdot \left(\frac{1}{Vef \cdot KbT} + \frac{\frac{2}{Vef} - \frac{\frac{mu - EAccept}{KbT}}{Vef}}{Ev}\right)\right)}\\ \mathbf{elif}\;mu \leq -1.16 \cdot 10^{+30}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} - \frac{1}{\frac{-1 - e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}}\\ \mathbf{elif}\;mu \leq -6.9 \cdot 10^{-217}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{EAccept \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{mu}{KbT}}{EAccept}\right)}\\ \mathbf{elif}\;mu \leq 1.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} - \frac{1}{\frac{-1 - e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}}\\ \mathbf{elif}\;mu \leq 1.52 \cdot 10^{+62}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{EAccept \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{mu}{KbT}}{EAccept}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -3.3 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq 1.95 \cdot 10^{-208}:\\ \;\;\;\;t\_0 + \frac{NaChar}{Vef \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{KbT} - \left(2 + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)\right)}{Vef}\right)}\\ \mathbf{elif}\;Vef \leq 4.7 \cdot 10^{-130}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;Vef \leq 6.8 \cdot 10^{+75}:\\ \;\;\;\;t\_0 - \frac{NaChar}{mu \cdot \left(\frac{1}{KbT} - \frac{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)}{mu}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor Vef) KbT)))))))
   (if (<= Vef -3.3e+28)
     t_1
     (if (<= Vef 1.95e-208)
       (+
        t_0
        (/
         NaChar
         (*
          Vef
          (-
           (/ 1.0 KbT)
           (/ (- (/ mu KbT) (+ 2.0 (+ (/ Ev KbT) (/ EAccept KbT)))) Vef)))))
       (if (<= Vef 4.7e-130)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))
         (if (<= Vef 6.8e+75)
           (-
            t_0
            (/
             NaChar
             (*
              mu
              (-
               (/ 1.0 KbT)
               (/
                (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))))
                mu)))))
           t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((EDonor + Vef) / KbT))));
	double tmp;
	if (Vef <= -3.3e+28) {
		tmp = t_1;
	} else if (Vef <= 1.95e-208) {
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))));
	} else if (Vef <= 4.7e-130) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	} else if (Vef <= 6.8e+75) {
		tmp = t_0 - (NaChar / (mu * ((1.0 / KbT) - ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) / mu))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp(((edonor + vef) / kbt))))
    if (vef <= (-3.3d+28)) then
        tmp = t_1
    else if (vef <= 1.95d-208) then
        tmp = t_0 + (nachar / (vef * ((1.0d0 / kbt) - (((mu / kbt) - (2.0d0 + ((ev / kbt) + (eaccept / kbt)))) / vef))))
    else if (vef <= 4.7d-130) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    else if (vef <= 6.8d+75) then
        tmp = t_0 - (nachar / (mu * ((1.0d0 / kbt) - ((2.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) / mu))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp(((EDonor + Vef) / KbT))));
	double tmp;
	if (Vef <= -3.3e+28) {
		tmp = t_1;
	} else if (Vef <= 1.95e-208) {
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))));
	} else if (Vef <= 4.7e-130) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	} else if (Vef <= 6.8e+75) {
		tmp = t_0 - (NaChar / (mu * ((1.0 / KbT) - ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) / mu))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp(((EDonor + Vef) / KbT))))
	tmp = 0
	if Vef <= -3.3e+28:
		tmp = t_1
	elif Vef <= 1.95e-208:
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))))
	elif Vef <= 4.7e-130:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	elif Vef <= 6.8e+75:
		tmp = t_0 - (NaChar / (mu * ((1.0 / KbT) - ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) / mu))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Vef) / KbT)))))
	tmp = 0.0
	if (Vef <= -3.3e+28)
		tmp = t_1;
	elseif (Vef <= 1.95e-208)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Vef * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(mu / KbT) - Float64(2.0 + Float64(Float64(Ev / KbT) + Float64(EAccept / KbT)))) / Vef)))));
	elseif (Vef <= 4.7e-130)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))));
	elseif (Vef <= 6.8e+75)
		tmp = Float64(t_0 - Float64(NaChar / Float64(mu * Float64(Float64(1.0 / KbT) - Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) / mu)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((EDonor + Vef) / KbT))));
	tmp = 0.0;
	if (Vef <= -3.3e+28)
		tmp = t_1;
	elseif (Vef <= 1.95e-208)
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))));
	elseif (Vef <= 4.7e-130)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	elseif (Vef <= 6.8e+75)
		tmp = t_0 - (NaChar / (mu * ((1.0 / KbT) - ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) / mu))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + Vef), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -3.3e+28], t$95$1, If[LessEqual[Vef, 1.95e-208], N[(t$95$0 + N[(NaChar / N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(mu / KbT), $MachinePrecision] - N[(2.0 + N[(N[(Ev / KbT), $MachinePrecision] + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 4.7e-130], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 6.8e+75], N[(t$95$0 - N[(NaChar / N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -3.3e28 or 6.80000000000000022e75 < 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%

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

   5. Taylor expanded in Vef around inf 87.6%

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

   6. Taylor expanded in Vef around inf 80.0%

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

   if -3.3e28 < Vef < 1.95000000000000002e-208

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.6%

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

      1. associate-+r+ 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in Vef around -inf 68.7%

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

   if 1.95000000000000002e-208 < Vef < 4.69999999999999968e-130

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 93.8%

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

      1. associate-*r/ 93.8%

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

      2. mul-1-neg 93.8%

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

   7. Simplified 93.8%

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

   8. Taylor expanded in mu around inf 93.8%

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

   if 4.69999999999999968e-130 < Vef < 6.80000000000000022e75

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.6%

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

      1. associate-+r+ 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in mu around -inf 72.2%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.3 \cdot 10^{+28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.95 \cdot 10^{-208}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{Vef \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{KbT} - \left(2 + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)\right)}{Vef}\right)}\\ \mathbf{elif}\;Vef \leq 4.7 \cdot 10^{-130}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;Vef \leq 6.8 \cdot 10^{+75}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} - \frac{NaChar}{mu \cdot \left(\frac{1}{KbT} - \frac{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)}{mu}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -8 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.3 \cdot 10^{+76}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor Vef) KbT)))))))
   (if (<= Vef -8e+171)
     t_0
     (if (<= Vef -1.3e+15)
       (+
        (/ NaChar (+ 1.0 (exp (/ (- (+ Vef EAccept) mu) KbT))))
        (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
       (if (<= Vef 1.3e+76)
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((EDonor + Vef) / KbT))));
	double tmp;
	if (Vef <= -8e+171) {
		tmp = t_0;
	} else if (Vef <= -1.3e+15) {
		tmp = (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (Vef <= 1.3e+76) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp(((edonor + vef) / kbt))))
    if (vef <= (-8d+171)) then
        tmp = t_0
    else if (vef <= (-1.3d+15)) then
        tmp = (nachar / (1.0d0 + exp((((vef + eaccept) - mu) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (vef <= 1.3d+76) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp(((EDonor + Vef) / KbT))));
	double tmp;
	if (Vef <= -8e+171) {
		tmp = t_0;
	} else if (Vef <= -1.3e+15) {
		tmp = (NaChar / (1.0 + Math.exp((((Vef + EAccept) - mu) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (Vef <= 1.3e+76) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp(((EDonor + Vef) / KbT))))
	tmp = 0
	if Vef <= -8e+171:
		tmp = t_0
	elif Vef <= -1.3e+15:
		tmp = (NaChar / (1.0 + math.exp((((Vef + EAccept) - mu) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif Vef <= 1.3e+76:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Vef) / KbT)))))
	tmp = 0.0
	if (Vef <= -8e+171)
		tmp = t_0;
	elseif (Vef <= -1.3e+15)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + EAccept) - mu) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (Vef <= 1.3e+76)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((EDonor + Vef) / KbT))));
	tmp = 0.0;
	if (Vef <= -8e+171)
		tmp = t_0;
	elseif (Vef <= -1.3e+15)
		tmp = (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (Vef <= 1.3e+76)
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + Vef), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -8e+171], t$95$0, If[LessEqual[Vef, -1.3e+15], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.3e+76], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -7.99999999999999963e171 or 1.3e76 < 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%

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

   5. Taylor expanded in Vef around inf 89.7%

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

   6. Taylor expanded in Vef around inf 84.0%

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

   if -7.99999999999999963e171 < Vef < -1.3e15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around 0 92.9%

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

   6. Taylor expanded in EDonor around inf 78.7%

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

   if -1.3e15 < Vef < 1.3e76

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 75.1%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -8 \cdot 10^{+171}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.3 \cdot 10^{+76}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.3 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-186}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;t\_0 + \frac{NaChar}{Vef \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{KbT} - \left(2 + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)\right)}{Vef}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (- (+ Vef EAccept) mu) KbT))))
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= NaChar -1.3e-104)
     t_1
     (if (<= NaChar 1.85e-186)
       (+ t_0 (* KbT (/ NaChar (+ (+ Ev EAccept) (- Vef mu)))))
       (if (<= NaChar 6.5e+18)
         (+
          t_0
          (/
           NaChar
           (*
            Vef
            (-
             (/ 1.0 KbT)
             (/ (- (/ mu KbT) (+ 2.0 (+ (/ Ev KbT) (/ EAccept KbT)))) Vef)))))
         t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (NaChar <= -1.3e-104) {
		tmp = t_1;
	} else if (NaChar <= 1.85e-186) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 6.5e+18) {
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = (nachar / (1.0d0 + exp((((vef + eaccept) - mu) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (nachar <= (-1.3d-104)) then
        tmp = t_1
    else if (nachar <= 1.85d-186) then
        tmp = t_0 + (kbt * (nachar / ((ev + eaccept) + (vef - mu))))
    else if (nachar <= 6.5d+18) then
        tmp = t_0 + (nachar / (vef * ((1.0d0 / kbt) - (((mu / kbt) - (2.0d0 + ((ev / kbt) + (eaccept / kbt)))) / vef))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((((Vef + EAccept) - mu) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (NaChar <= -1.3e-104) {
		tmp = t_1;
	} else if (NaChar <= 1.85e-186) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 6.5e+18) {
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp((((Vef + EAccept) - mu) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if NaChar <= -1.3e-104:
		tmp = t_1
	elif NaChar <= 1.85e-186:
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))))
	elif NaChar <= 6.5e+18:
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + EAccept) - mu) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (NaChar <= -1.3e-104)
		tmp = t_1;
	elseif (NaChar <= 1.85e-186)
		tmp = Float64(t_0 + Float64(KbT * Float64(NaChar / Float64(Float64(Ev + EAccept) + Float64(Vef - mu)))));
	elseif (NaChar <= 6.5e+18)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Vef * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(mu / KbT) - Float64(2.0 + Float64(Float64(Ev / KbT) + Float64(EAccept / KbT)))) / Vef)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (NaChar <= -1.3e-104)
		tmp = t_1;
	elseif (NaChar <= 1.85e-186)
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	elseif (NaChar <= 6.5e+18)
		tmp = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.3e-104], t$95$1, If[LessEqual[NaChar, 1.85e-186], N[(t$95$0 + N[(KbT * N[(NaChar / N[(N[(Ev + EAccept), $MachinePrecision] + N[(Vef - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 6.5e+18], N[(t$95$0 + N[(NaChar / N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(mu / KbT), $MachinePrecision] - N[(2.0 + N[(N[(Ev / KbT), $MachinePrecision] + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.30000000000000001e-104 or 6.5e18 < 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%

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

   5. Taylor expanded in Ev around 0 94.7%

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

   6. Taylor expanded in EDonor around inf 71.0%

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

   if -1.30000000000000001e-104 < NaChar < 1.8500000000000001e-186

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 75.1%

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

      1. associate-+r+ 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in KbT around 0 81.6%

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

      1. associate-/l* 88.3%

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

      2. associate--l+ 88.3%

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

      3. associate--l+ 88.3%

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

      4. sub-neg 88.3%

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

      5. neg-mul-1 88.3%

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

      6. associate-+r+ 88.3%

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

      7. +-commutative 88.3%

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

      8. neg-mul-1 88.3%

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

      9. sub-neg 88.3%

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

   10. Simplified 88.3%

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

   if 1.8500000000000001e-186 < NaChar < 6.5e18

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.5%

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

      1. associate-+r+ 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in Vef around -inf 77.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.3 \cdot 10^{-104}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-186}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{Vef \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{KbT} - \left(2 + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)\right)}{Vef}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;EAccept \leq -5500000:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.5 \cdot 10^{+89}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= EAccept -5500000.0)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= EAccept 3.5e+89)
       (+ t_0 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))
       (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept 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 + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (EAccept <= -5500000.0) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (EAccept <= 3.5e+89) {
		tmp = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (eaccept <= (-5500000.0d0)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (eaccept <= 3.5d+89) then
        tmp = t_0 + (nachar / (1.0d0 + exp((vef / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (EAccept <= -5500000.0) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (EAccept <= 3.5e+89) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if EAccept <= -5500000.0:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif EAccept <= 3.5e+89:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (EAccept <= -5500000.0)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (EAccept <= 3.5e+89)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / 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 + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (EAccept <= -5500000.0)
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (EAccept <= 3.5e+89)
		tmp = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -5500000.0], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.5e+89], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < -5.5e6

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 70.5%

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

   if -5.5e6 < EAccept < 3.5000000000000001e89

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 79.5%

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

   if 3.5000000000000001e89 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 89.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -5500000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;Ev \leq -6.5 \cdot 10^{+164}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= Ev -6.5e+164)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ 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) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (Ev <= -6.5e+164) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((((Vef + EAccept) - 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(((edonor + (mu + (vef - ec))) / kbt)))
    if (ev <= (-6.5d+164)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((((vef + eaccept) - 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(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (Ev <= -6.5e+164) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((((Vef + EAccept) - mu) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if Ev <= -6.5e+164:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((((Vef + EAccept) - 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(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (Ev <= -6.5e+164)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + EAccept) - 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(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (Ev <= -6.5e+164)
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((((Vef + EAccept) - 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[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -6.5e+164], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if Ev < -6.5000000000000003e164

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 100.0%

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

   if -6.5000000000000003e164 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around 0 95.1%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -6.5 \cdot 10^{+164}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} - \frac{1}{\frac{-1 - e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}}\\ t_2 := t\_0 + \frac{NaChar}{Vef \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{KbT} - \left(2 + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)\right)}{Vef}\right)}\\ \mathbf{if}\;NaChar \leq -5.2 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -4 \cdot 10^{-101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 9 \cdot 10^{-191}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1
         (-
          (/
           NdChar
           (-
            (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
            (/ Ec KbT)))
          (/
           1.0
           (/ (- -1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))))
        (t_2
         (+
          t_0
          (/
           NaChar
           (*
            Vef
            (-
             (/ 1.0 KbT)
             (/
              (- (/ mu KbT) (+ 2.0 (+ (/ Ev KbT) (/ EAccept KbT))))
              Vef)))))))
   (if (<= NaChar -5.2e+56)
     t_1
     (if (<= NaChar -4e-101)
       t_2
       (if (<= NaChar 9e-191)
         (+ t_0 (* KbT (/ NaChar (+ (+ Ev EAccept) (- Vef mu)))))
         (if (<= NaChar 1.5e+50) t_2 t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar));
	double t_2 = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))));
	double tmp;
	if (NaChar <= -5.2e+56) {
		tmp = t_1;
	} else if (NaChar <= -4e-101) {
		tmp = t_2;
	} else if (NaChar <= 9e-191) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 1.5e+50) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt))) - (1.0d0 / (((-1.0d0) - exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar))
    t_2 = t_0 + (nachar / (vef * ((1.0d0 / kbt) - (((mu / kbt) - (2.0d0 + ((ev / kbt) + (eaccept / kbt)))) / vef))))
    if (nachar <= (-5.2d+56)) then
        tmp = t_1
    else if (nachar <= (-4d-101)) then
        tmp = t_2
    else if (nachar <= 9d-191) then
        tmp = t_0 + (kbt * (nachar / ((ev + eaccept) + (vef - mu))))
    else if (nachar <= 1.5d+50) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar));
	double t_2 = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))));
	double tmp;
	if (NaChar <= -5.2e+56) {
		tmp = t_1;
	} else if (NaChar <= -4e-101) {
		tmp = t_2;
	} else if (NaChar <= 9e-191) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 1.5e+50) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar))
	t_2 = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))))
	tmp = 0
	if NaChar <= -5.2e+56:
		tmp = t_1
	elif NaChar <= -4e-101:
		tmp = t_2
	elif NaChar <= 9e-191:
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))))
	elif NaChar <= 1.5e+50:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))) - Float64(1.0 / Float64(Float64(-1.0 - exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)))
	t_2 = Float64(t_0 + Float64(NaChar / Float64(Vef * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(mu / KbT) - Float64(2.0 + Float64(Float64(Ev / KbT) + Float64(EAccept / KbT)))) / Vef)))))
	tmp = 0.0
	if (NaChar <= -5.2e+56)
		tmp = t_1;
	elseif (NaChar <= -4e-101)
		tmp = t_2;
	elseif (NaChar <= 9e-191)
		tmp = Float64(t_0 + Float64(KbT * Float64(NaChar / Float64(Float64(Ev + EAccept) + Float64(Vef - mu)))));
	elseif (NaChar <= 1.5e+50)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar));
	t_2 = t_0 + (NaChar / (Vef * ((1.0 / KbT) - (((mu / KbT) - (2.0 + ((Ev / KbT) + (EAccept / KbT)))) / Vef))));
	tmp = 0.0;
	if (NaChar <= -5.2e+56)
		tmp = t_1;
	elseif (NaChar <= -4e-101)
		tmp = t_2;
	elseif (NaChar <= 9e-191)
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	elseif (NaChar <= 1.5e+50)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[(N[(-1.0 - N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NaChar / N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(mu / KbT), $MachinePrecision] - N[(2.0 + N[(N[(Ev / KbT), $MachinePrecision] + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -5.2e+56], t$95$1, If[LessEqual[NaChar, -4e-101], t$95$2, If[LessEqual[NaChar, 9e-191], N[(t$95$0 + N[(KbT * N[(NaChar / N[(N[(Ev + EAccept), $MachinePrecision] + N[(Vef - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.5e+50], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -5.20000000000000022e56 or 1.4999999999999999e50 < 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%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 60.1%

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

   if -5.20000000000000022e56 < NaChar < -4.00000000000000021e-101 or 9.00000000000000017e-191 < NaChar < 1.4999999999999999e50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.1%

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

      1. associate-+r+ 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in Vef around -inf 75.0%

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

   if -4.00000000000000021e-101 < NaChar < 9.00000000000000017e-191

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 74.0%

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

      1. associate-+r+ 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in KbT around 0 80.4%

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

      1. associate-/l* 87.0%

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

      2. associate--l+ 87.0%

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

      3. associate--l+ 87.0%

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

      4. sub-neg 87.0%

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

      5. neg-mul-1 87.0%

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

      6. associate-+r+ 87.0%

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

      7. +-commutative 87.0%

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

      8. neg-mul-1 87.0%

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

      9. sub-neg 87.0%

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

   10. Simplified 87.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} - \frac{1}{\frac{-1 - e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}}\\ \mathbf{elif}\;NaChar \leq -4 \cdot 10^{-101}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{Vef \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{KbT} - \left(2 + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)\right)}{Vef}\right)}\\ \mathbf{elif}\;NaChar \leq 9 \cdot 10^{-191}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{Vef \cdot \left(\frac{1}{KbT} - \frac{\frac{mu}{KbT} - \left(2 + \left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right)\right)}{Vef}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} - \frac{1}{\frac{-1 - e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} - \frac{1}{\frac{-1 - e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}}\\ t_2 := t\_0 + \frac{NaChar}{\frac{\left(EAccept + \left(Ev + \left(Vef + KbT \cdot 2\right)\right)\right) - mu}{KbT}}\\ \mathbf{if}\;NaChar \leq -6.5 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -3.2 \cdot 10^{-101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 2.5 \cdot 10^{-185}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 1.52 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1
         (-
          (/
           NdChar
           (-
            (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
            (/ Ec KbT)))
          (/
           1.0
           (/ (- -1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))))
        (t_2
         (+
          t_0
          (/ NaChar (/ (- (+ EAccept (+ Ev (+ Vef (* KbT 2.0)))) mu) KbT)))))
   (if (<= NaChar -6.5e+56)
     t_1
     (if (<= NaChar -3.2e-101)
       t_2
       (if (<= NaChar 2.5e-185)
         (+ t_0 (* KbT (/ NaChar (+ (+ Ev EAccept) (- Vef mu)))))
         (if (<= NaChar 1.52e+50) t_2 t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar));
	double t_2 = t_0 + (NaChar / (((EAccept + (Ev + (Vef + (KbT * 2.0)))) - mu) / KbT));
	double tmp;
	if (NaChar <= -6.5e+56) {
		tmp = t_1;
	} else if (NaChar <= -3.2e-101) {
		tmp = t_2;
	} else if (NaChar <= 2.5e-185) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 1.52e+50) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt))) - (1.0d0 / (((-1.0d0) - exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar))
    t_2 = t_0 + (nachar / (((eaccept + (ev + (vef + (kbt * 2.0d0)))) - mu) / kbt))
    if (nachar <= (-6.5d+56)) then
        tmp = t_1
    else if (nachar <= (-3.2d-101)) then
        tmp = t_2
    else if (nachar <= 2.5d-185) then
        tmp = t_0 + (kbt * (nachar / ((ev + eaccept) + (vef - mu))))
    else if (nachar <= 1.52d+50) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar));
	double t_2 = t_0 + (NaChar / (((EAccept + (Ev + (Vef + (KbT * 2.0)))) - mu) / KbT));
	double tmp;
	if (NaChar <= -6.5e+56) {
		tmp = t_1;
	} else if (NaChar <= -3.2e-101) {
		tmp = t_2;
	} else if (NaChar <= 2.5e-185) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 1.52e+50) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar))
	t_2 = t_0 + (NaChar / (((EAccept + (Ev + (Vef + (KbT * 2.0)))) - mu) / KbT))
	tmp = 0
	if NaChar <= -6.5e+56:
		tmp = t_1
	elif NaChar <= -3.2e-101:
		tmp = t_2
	elif NaChar <= 2.5e-185:
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))))
	elif NaChar <= 1.52e+50:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))) - Float64(1.0 / Float64(Float64(-1.0 - exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)))
	t_2 = Float64(t_0 + Float64(NaChar / Float64(Float64(Float64(EAccept + Float64(Ev + Float64(Vef + Float64(KbT * 2.0)))) - mu) / KbT)))
	tmp = 0.0
	if (NaChar <= -6.5e+56)
		tmp = t_1;
	elseif (NaChar <= -3.2e-101)
		tmp = t_2;
	elseif (NaChar <= 2.5e-185)
		tmp = Float64(t_0 + Float64(KbT * Float64(NaChar / Float64(Float64(Ev + EAccept) + Float64(Vef - mu)))));
	elseif (NaChar <= 1.52e+50)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) - (1.0 / ((-1.0 - exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar));
	t_2 = t_0 + (NaChar / (((EAccept + (Ev + (Vef + (KbT * 2.0)))) - mu) / KbT));
	tmp = 0.0;
	if (NaChar <= -6.5e+56)
		tmp = t_1;
	elseif (NaChar <= -3.2e-101)
		tmp = t_2;
	elseif (NaChar <= 2.5e-185)
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	elseif (NaChar <= 1.52e+50)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[(N[(-1.0 - N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NaChar / N[(N[(N[(EAccept + N[(Ev + N[(Vef + N[(KbT * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.5e+56], t$95$1, If[LessEqual[NaChar, -3.2e-101], t$95$2, If[LessEqual[NaChar, 2.5e-185], N[(t$95$0 + N[(KbT * N[(NaChar / N[(N[(Ev + EAccept), $MachinePrecision] + N[(Vef - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.52e+50], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -6.5000000000000001e56 or 1.5199999999999999e50 < 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%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 60.1%

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

   if -6.5000000000000001e56 < NaChar < -3.19999999999999978e-101 or 2.5000000000000001e-185 < NaChar < 1.5199999999999999e50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.7%

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

      1. associate-+r+ 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in KbT around 0 72.6%

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

   if -3.19999999999999978e-101 < NaChar < 2.5000000000000001e-185

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.1%

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

      1. associate-+r+ 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in KbT around 0 79.4%

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

      1. associate-/l* 87.2%

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

      2. associate--l+ 87.2%

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

      3. associate--l+ 87.2%

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

      4. sub-neg 87.2%

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

      5. neg-mul-1 87.2%

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

      6. associate-+r+ 87.2%

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

      7. +-commutative 87.2%

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

      8. neg-mul-1 87.2%

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

      9. sub-neg 87.2%

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

   10. Simplified 87.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} - \frac{1}{\frac{-1 - e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}}\\ \mathbf{elif}\;NaChar \leq -3.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{\left(EAccept + \left(Ev + \left(Vef + KbT \cdot 2\right)\right)\right) - mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.5 \cdot 10^{-185}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 1.52 \cdot 10^{+50}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{\left(EAccept + \left(Ev + \left(Vef + KbT \cdot 2\right)\right)\right) - mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} - \frac{1}{\frac{-1 - e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)}\\ t_2 := \frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -5 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -4.4 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 2.45 \cdot 10^{-185}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 1.95 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1
         (+
          t_0
          (/ NaChar (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT)))))))
        (t_2
         (+
          (/
           1.0
           (/ (+ 1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))
          (* NdChar 0.5))))
   (if (<= NaChar -5e+42)
     t_2
     (if (<= NaChar -4.4e-101)
       t_1
       (if (<= NaChar 2.45e-185)
         (+ t_0 (* KbT (/ NaChar (+ (+ Ev EAccept) (- Vef mu)))))
         (if (<= NaChar 1.95e+50) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))));
	double t_2 = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -5e+42) {
		tmp = t_2;
	} else if (NaChar <= -4.4e-101) {
		tmp = t_1;
	} else if (NaChar <= 2.45e-185) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 1.95e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = t_0 + (nachar / (2.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))))
    t_2 = (1.0d0 / ((1.0d0 + exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar)) + (ndchar * 0.5d0)
    if (nachar <= (-5d+42)) then
        tmp = t_2
    else if (nachar <= (-4.4d-101)) then
        tmp = t_1
    else if (nachar <= 2.45d-185) then
        tmp = t_0 + (kbt * (nachar / ((ev + eaccept) + (vef - mu))))
    else if (nachar <= 1.95d+50) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))));
	double t_2 = (1.0 / ((1.0 + Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -5e+42) {
		tmp = t_2;
	} else if (NaChar <= -4.4e-101) {
		tmp = t_1;
	} else if (NaChar <= 2.45e-185) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 1.95e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = t_0 + (NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))))
	t_2 = (1.0 / ((1.0 + math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5)
	tmp = 0
	if NaChar <= -5e+42:
		tmp = t_2
	elif NaChar <= -4.4e-101:
		tmp = t_1
	elif NaChar <= 2.45e-185:
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))))
	elif NaChar <= 1.95e+50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT))))))
	t_2 = Float64(Float64(1.0 / Float64(Float64(1.0 + exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)) + Float64(NdChar * 0.5))
	tmp = 0.0
	if (NaChar <= -5e+42)
		tmp = t_2;
	elseif (NaChar <= -4.4e-101)
		tmp = t_1;
	elseif (NaChar <= 2.45e-185)
		tmp = Float64(t_0 + Float64(KbT * Float64(NaChar / Float64(Float64(Ev + EAccept) + Float64(Vef - mu)))));
	elseif (NaChar <= 1.95e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = t_0 + (NaChar / (2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))));
	t_2 = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	tmp = 0.0;
	if (NaChar <= -5e+42)
		tmp = t_2;
	elseif (NaChar <= -4.4e-101)
		tmp = t_1;
	elseif (NaChar <= 2.45e-185)
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	elseif (NaChar <= 1.95e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 / N[(N[(1.0 + N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -5e+42], t$95$2, If[LessEqual[NaChar, -4.4e-101], t$95$1, If[LessEqual[NaChar, 2.45e-185], N[(t$95$0 + N[(KbT * N[(NaChar / N[(N[(Ev + EAccept), $MachinePrecision] + N[(Vef - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.95e+50], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -5.00000000000000007e42 or 1.94999999999999984e50 < 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%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 54.6%

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

   if -5.00000000000000007e42 < NaChar < -4.3999999999999998e-101 or 2.4500000000000001e-185 < NaChar < 1.94999999999999984e50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 69.0%

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

      1. associate-+r+ 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in mu around 0 71.5%

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

   if -4.3999999999999998e-101 < NaChar < 2.4500000000000001e-185

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.1%

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

      1. associate-+r+ 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in KbT around 0 79.4%

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

      1. associate-/l* 87.2%

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

      2. associate--l+ 87.2%

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

      3. associate--l+ 87.2%

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

      4. sub-neg 87.2%

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

      5. neg-mul-1 87.2%

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

      6. associate-+r+ 87.2%

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

      7. +-commutative 87.2%

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

      8. neg-mul-1 87.2%

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

      9. sub-neg 87.2%

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

   10. Simplified 87.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5 \cdot 10^{+42}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -4.4 \cdot 10^{-101}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq 2.45 \cdot 10^{-185}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 1.95 \cdot 10^{+50}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{\frac{\left(EAccept + \left(Ev + \left(Vef + KbT \cdot 2\right)\right)\right) - mu}{KbT}}\\ t_2 := \frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -3.5 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 9.6 \cdot 10^{-186}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1
         (+
          t_0
          (/ NaChar (/ (- (+ EAccept (+ Ev (+ Vef (* KbT 2.0)))) mu) KbT))))
        (t_2
         (+
          (/
           1.0
           (/ (+ 1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))
          (* NdChar 0.5))))
   (if (<= NaChar -1.5e+43)
     t_2
     (if (<= NaChar -3.5e-101)
       t_1
       (if (<= NaChar 9.6e-186)
         (+ t_0 (* KbT (/ NaChar (+ (+ Ev EAccept) (- Vef mu)))))
         (if (<= NaChar 1.8e+50) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (((EAccept + (Ev + (Vef + (KbT * 2.0)))) - mu) / KbT));
	double t_2 = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -1.5e+43) {
		tmp = t_2;
	} else if (NaChar <= -3.5e-101) {
		tmp = t_1;
	} else if (NaChar <= 9.6e-186) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 1.8e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = t_0 + (nachar / (((eaccept + (ev + (vef + (kbt * 2.0d0)))) - mu) / kbt))
    t_2 = (1.0d0 / ((1.0d0 + exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar)) + (ndchar * 0.5d0)
    if (nachar <= (-1.5d+43)) then
        tmp = t_2
    else if (nachar <= (-3.5d-101)) then
        tmp = t_1
    else if (nachar <= 9.6d-186) then
        tmp = t_0 + (kbt * (nachar / ((ev + eaccept) + (vef - mu))))
    else if (nachar <= 1.8d+50) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (((EAccept + (Ev + (Vef + (KbT * 2.0)))) - mu) / KbT));
	double t_2 = (1.0 / ((1.0 + Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -1.5e+43) {
		tmp = t_2;
	} else if (NaChar <= -3.5e-101) {
		tmp = t_1;
	} else if (NaChar <= 9.6e-186) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 1.8e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = t_0 + (NaChar / (((EAccept + (Ev + (Vef + (KbT * 2.0)))) - mu) / KbT))
	t_2 = (1.0 / ((1.0 + math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5)
	tmp = 0
	if NaChar <= -1.5e+43:
		tmp = t_2
	elif NaChar <= -3.5e-101:
		tmp = t_1
	elif NaChar <= 9.6e-186:
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))))
	elif NaChar <= 1.8e+50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(Float64(Float64(EAccept + Float64(Ev + Float64(Vef + Float64(KbT * 2.0)))) - mu) / KbT)))
	t_2 = Float64(Float64(1.0 / Float64(Float64(1.0 + exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)) + Float64(NdChar * 0.5))
	tmp = 0.0
	if (NaChar <= -1.5e+43)
		tmp = t_2;
	elseif (NaChar <= -3.5e-101)
		tmp = t_1;
	elseif (NaChar <= 9.6e-186)
		tmp = Float64(t_0 + Float64(KbT * Float64(NaChar / Float64(Float64(Ev + EAccept) + Float64(Vef - mu)))));
	elseif (NaChar <= 1.8e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = t_0 + (NaChar / (((EAccept + (Ev + (Vef + (KbT * 2.0)))) - mu) / KbT));
	t_2 = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	tmp = 0.0;
	if (NaChar <= -1.5e+43)
		tmp = t_2;
	elseif (NaChar <= -3.5e-101)
		tmp = t_1;
	elseif (NaChar <= 9.6e-186)
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	elseif (NaChar <= 1.8e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(N[(N[(EAccept + N[(Ev + N[(Vef + N[(KbT * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 / N[(N[(1.0 + N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.5e+43], t$95$2, If[LessEqual[NaChar, -3.5e-101], t$95$1, If[LessEqual[NaChar, 9.6e-186], N[(t$95$0 + N[(KbT * N[(NaChar / N[(N[(Ev + EAccept), $MachinePrecision] + N[(Vef - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.8e+50], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.50000000000000008e43 or 1.79999999999999993e50 < 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%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 54.6%

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

   if -1.50000000000000008e43 < NaChar < -3.49999999999999994e-101 or 9.60000000000000012e-186 < NaChar < 1.79999999999999993e50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 69.0%

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

      1. associate-+r+ 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in KbT around 0 74.0%

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

   if -3.49999999999999994e-101 < NaChar < 9.60000000000000012e-186

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.1%

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

      1. associate-+r+ 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in KbT around 0 79.4%

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

      1. associate-/l* 87.2%

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

      2. associate--l+ 87.2%

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

      3. associate--l+ 87.2%

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

      4. sub-neg 87.2%

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

      5. neg-mul-1 87.2%

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

      6. associate-+r+ 87.2%

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

      7. +-commutative 87.2%

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

      8. neg-mul-1 87.2%

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

      9. sub-neg 87.2%

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

   10. Simplified 87.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -3.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{\left(EAccept + \left(Ev + \left(Vef + KbT \cdot 2\right)\right)\right) - mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 9.6 \cdot 10^{-186}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{\left(EAccept + \left(Ev + \left(Vef + KbT \cdot 2\right)\right)\right) - mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ t_2 := \frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -4.2 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 4.5 \cdot 10^{-254}:\\ \;\;\;\;t\_0 + \left(-1 + \left(1 - \frac{NaChar}{\frac{mu}{KbT}}\right)\right)\\ \mathbf{elif}\;NaChar \leq 7.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0))))
        (t_2
         (+
          (/
           1.0
           (/ (+ 1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))
          (* NdChar 0.5))))
   (if (<= NaChar -2.3e+35)
     t_2
     (if (<= NaChar -4.2e-106)
       t_1
       (if (<= NaChar 4.5e-254)
         (+ t_0 (+ -1.0 (- 1.0 (/ NaChar (/ mu KbT)))))
         (if (<= NaChar 7.2e+48) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -2.3e+35) {
		tmp = t_2;
	} else if (NaChar <= -4.2e-106) {
		tmp = t_1;
	} else if (NaChar <= 4.5e-254) {
		tmp = t_0 + (-1.0 + (1.0 - (NaChar / (mu / KbT))));
	} else if (NaChar <= 7.2e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    t_2 = (1.0d0 / ((1.0d0 + exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar)) + (ndchar * 0.5d0)
    if (nachar <= (-2.3d+35)) then
        tmp = t_2
    else if (nachar <= (-4.2d-106)) then
        tmp = t_1
    else if (nachar <= 4.5d-254) then
        tmp = t_0 + ((-1.0d0) + (1.0d0 - (nachar / (mu / kbt))))
    else if (nachar <= 7.2d+48) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = (1.0 / ((1.0 + Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -2.3e+35) {
		tmp = t_2;
	} else if (NaChar <= -4.2e-106) {
		tmp = t_1;
	} else if (NaChar <= 4.5e-254) {
		tmp = t_0 + (-1.0 + (1.0 - (NaChar / (mu / KbT))));
	} else if (NaChar <= 7.2e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	t_2 = (1.0 / ((1.0 + math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5)
	tmp = 0
	if NaChar <= -2.3e+35:
		tmp = t_2
	elif NaChar <= -4.2e-106:
		tmp = t_1
	elif NaChar <= 4.5e-254:
		tmp = t_0 + (-1.0 + (1.0 - (NaChar / (mu / KbT))))
	elif NaChar <= 7.2e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)))
	t_2 = Float64(Float64(1.0 / Float64(Float64(1.0 + exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)) + Float64(NdChar * 0.5))
	tmp = 0.0
	if (NaChar <= -2.3e+35)
		tmp = t_2;
	elseif (NaChar <= -4.2e-106)
		tmp = t_1;
	elseif (NaChar <= 4.5e-254)
		tmp = Float64(t_0 + Float64(-1.0 + Float64(1.0 - Float64(NaChar / Float64(mu / KbT)))));
	elseif (NaChar <= 7.2e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	t_2 = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	tmp = 0.0;
	if (NaChar <= -2.3e+35)
		tmp = t_2;
	elseif (NaChar <= -4.2e-106)
		tmp = t_1;
	elseif (NaChar <= 4.5e-254)
		tmp = t_0 + (-1.0 + (1.0 - (NaChar / (mu / KbT))));
	elseif (NaChar <= 7.2e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 / N[(N[(1.0 + N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.3e+35], t$95$2, If[LessEqual[NaChar, -4.2e-106], t$95$1, If[LessEqual[NaChar, 4.5e-254], N[(t$95$0 + N[(-1.0 + N[(1.0 - N[(NaChar / N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 7.2e+48], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2.2999999999999998e35 or 7.19999999999999967e48 < 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%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 54.7%

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

   if -2.2999999999999998e35 < NaChar < -4.20000000000000007e-106 or 4.5e-254 < NaChar < 7.19999999999999967e48

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 74.2%

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

   6. Taylor expanded in Vef around 0 69.5%

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

   if -4.20000000000000007e-106 < NaChar < 4.5e-254

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 78.1%

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

      1. associate-+r+ 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in Vef around -inf 81.9%

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

   9. Taylor expanded in mu around inf 61.2%

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

       1. expm1-log1p-u 59.3%

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

       2. expm1-undefine 82.0%

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

       3. mul-1-neg 82.0%

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

   11. Applied egg-rr 82.0%

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

       1. sub-neg 82.0%

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

       2. log1p-undefine 82.0%

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

       3. rem-exp-log 83.9%

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

       4. distribute-frac-neg2 83.9%

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

       5. unsub-neg 83.9%

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

       6. metadata-eval 83.9%

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

   13. Simplified 83.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -4.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.5 \cdot 10^{-254}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \left(-1 + \left(1 - \frac{NaChar}{\frac{mu}{KbT}}\right)\right)\\ \mathbf{elif}\;NaChar \leq 7.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ t_2 := \frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -3.6 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -6 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 2.25 \cdot 10^{-185}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 2.15 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0))))
        (t_2
         (+
          (/
           1.0
           (/ (+ 1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))
          (* NdChar 0.5))))
   (if (<= NaChar -3.6e+35)
     t_2
     (if (<= NaChar -6e-102)
       t_1
       (if (<= NaChar 2.25e-185)
         (+ t_0 (* KbT (/ NaChar (+ (+ Ev EAccept) (- Vef mu)))))
         (if (<= NaChar 2.15e+49) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -3.6e+35) {
		tmp = t_2;
	} else if (NaChar <= -6e-102) {
		tmp = t_1;
	} else if (NaChar <= 2.25e-185) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 2.15e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    t_2 = (1.0d0 / ((1.0d0 + exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar)) + (ndchar * 0.5d0)
    if (nachar <= (-3.6d+35)) then
        tmp = t_2
    else if (nachar <= (-6d-102)) then
        tmp = t_1
    else if (nachar <= 2.25d-185) then
        tmp = t_0 + (kbt * (nachar / ((ev + eaccept) + (vef - mu))))
    else if (nachar <= 2.15d+49) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = (1.0 / ((1.0 + Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -3.6e+35) {
		tmp = t_2;
	} else if (NaChar <= -6e-102) {
		tmp = t_1;
	} else if (NaChar <= 2.25e-185) {
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	} else if (NaChar <= 2.15e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	t_2 = (1.0 / ((1.0 + math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5)
	tmp = 0
	if NaChar <= -3.6e+35:
		tmp = t_2
	elif NaChar <= -6e-102:
		tmp = t_1
	elif NaChar <= 2.25e-185:
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))))
	elif NaChar <= 2.15e+49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)))
	t_2 = Float64(Float64(1.0 / Float64(Float64(1.0 + exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)) + Float64(NdChar * 0.5))
	tmp = 0.0
	if (NaChar <= -3.6e+35)
		tmp = t_2;
	elseif (NaChar <= -6e-102)
		tmp = t_1;
	elseif (NaChar <= 2.25e-185)
		tmp = Float64(t_0 + Float64(KbT * Float64(NaChar / Float64(Float64(Ev + EAccept) + Float64(Vef - mu)))));
	elseif (NaChar <= 2.15e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	t_2 = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	tmp = 0.0;
	if (NaChar <= -3.6e+35)
		tmp = t_2;
	elseif (NaChar <= -6e-102)
		tmp = t_1;
	elseif (NaChar <= 2.25e-185)
		tmp = t_0 + (KbT * (NaChar / ((Ev + EAccept) + (Vef - mu))));
	elseif (NaChar <= 2.15e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 / N[(N[(1.0 + N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -3.6e+35], t$95$2, If[LessEqual[NaChar, -6e-102], t$95$1, If[LessEqual[NaChar, 2.25e-185], N[(t$95$0 + N[(KbT * N[(NaChar / N[(N[(Ev + EAccept), $MachinePrecision] + N[(Vef - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.15e+49], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -3.6e35 or 2.15e49 < 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%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 54.7%

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

   if -3.6e35 < NaChar < -6e-102 or 2.2500000000000001e-185 < NaChar < 2.15e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 74.9%

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

   6. Taylor expanded in Vef around 0 70.1%

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

   if -6e-102 < NaChar < 2.2500000000000001e-185

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 74.1%

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

      1. associate-+r+ 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in KbT around 0 80.6%

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

      1. associate-/l* 88.5%

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

      2. associate--l+ 88.5%

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

      3. associate--l+ 88.5%

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

      4. sub-neg 88.5%

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

      5. neg-mul-1 88.5%

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

      6. associate-+r+ 88.5%

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

      7. +-commutative 88.5%

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

      8. neg-mul-1 88.5%

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

      9. sub-neg 88.5%

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

   10. Simplified 88.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.6 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -6 \cdot 10^{-102}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 2.25 \cdot 10^{-185}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + KbT \cdot \frac{NaChar}{\left(Ev + EAccept\right) + \left(Vef - mu\right)}\\ \mathbf{elif}\;NaChar \leq 2.15 \cdot 10^{+49}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.15 \cdot 10^{+35} \lor \neg \left(NaChar \leq 3.9 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.15e+35) (not (<= NaChar 3.9e+56)))
   (+
    (/ 1.0 (/ (+ 1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))
    (* NdChar 0.5))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ Ev KbT) 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.15e+35) || !(NaChar <= 3.9e+56)) {
		tmp = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-2.15d+35)) .or. (.not. (nachar <= 3.9d+56))) then
        tmp = (1.0d0 / ((1.0d0 + exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar)) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / ((ev / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.15e+35) || !(NaChar <= 3.9e+56)) {
		tmp = (1.0 / ((1.0 + Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2.15e+35) or not (NaChar <= 3.9e+56):
		tmp = (1.0 / ((1.0 + math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -2.15e+35) || !(NaChar <= 3.9e+56))
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -2.15e+35) || ~((NaChar <= 3.9e+56)))
		tmp = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -2.15e+35], N[Not[LessEqual[NaChar, 3.9e+56]], $MachinePrecision]], N[(N[(1.0 / N[(N[(1.0 + N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.1499999999999999e35 or 3.89999999999999994e56 < 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%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. div-inv 99.9%

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

      4. associate-*r/ 99.9%

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

      5. *-commutative 99.9%

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

      6. *-un-lft-identity 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l- 99.9%

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

   6. Applied egg-rr 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in KbT around inf 55.6%

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

   if -2.1499999999999999e35 < NaChar < 3.89999999999999994e56

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 79.0%

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

   6. Taylor expanded in Ev around 0 67.6%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.15 \cdot 10^{+35} \lor \neg \left(NaChar \leq 3.9 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.25 \cdot 10^{+35} \lor \neg \left(NaChar \leq 1.45 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.25e+35) (not (<= NaChar 1.45e+49)))
   (+
    (/ 1.0 (/ (+ 1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))
    (* NdChar 0.5))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ Vef KbT) 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.25e+35) || !(NaChar <= 1.45e+49)) {
		tmp = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-1.25d+35)) .or. (.not. (nachar <= 1.45d+49))) then
        tmp = (1.0d0 / ((1.0d0 + exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar)) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.25e+35) || !(NaChar <= 1.45e+49)) {
		tmp = (1.0 / ((1.0 + Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.25e+35) or not (NaChar <= 1.45e+49):
		tmp = (1.0 / ((1.0 + math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.25e+35) || !(NaChar <= 1.45e+49))
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1.25e+35) || ~((NaChar <= 1.45e+49)))
		tmp = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.25e+35], N[Not[LessEqual[NaChar, 1.45e+49]], $MachinePrecision]], N[(N[(1.0 / N[(N[(1.0 + N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.25000000000000005e35 or 1.45e49 < 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%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 54.7%

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

   if -1.25000000000000005e35 < NaChar < 1.45e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 77.4%

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

   6. Taylor expanded in Vef around 0 71.7%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.25 \cdot 10^{+35} \lor \neg \left(NaChar \leq 1.45 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -7.5 \cdot 10^{+121} \lor \neg \left(NdChar \leq 1.25 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -7.5e+121) (not (<= NdChar 1.25e-20)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/ NaChar 2.0))
   (+
    (/ 1.0 (/ (+ 1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))
    (* NdChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -7.5e+121) || !(NdChar <= 1.25e-20)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-7.5d+121)) .or. (.not. (ndchar <= 1.25d-20))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (1.0d0 / ((1.0d0 + exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar)) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -7.5e+121) || !(NdChar <= 1.25e-20)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (1.0 / ((1.0 + Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -7.5e+121) or not (NdChar <= 1.25e-20):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (1.0 / ((1.0 + math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -7.5e+121) || !(NdChar <= 1.25e-20))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -7.5e+121) || ~((NdChar <= 1.25e-20)))
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	else
		tmp = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -7.5e+121], N[Not[LessEqual[NdChar, 1.25e-20]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[(1.0 + N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -7.49999999999999965e121 or 1.25e-20 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.0%

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

   if -7.49999999999999965e121 < NdChar < 1.25e-20

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. div-inv 99.9%

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

      4. associate-*r/ 99.9%

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

      5. *-commutative 99.9%

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

      6. *-un-lft-identity 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l- 99.9%

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

   6. Applied egg-rr 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in KbT around inf 52.3%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{1}{\frac{1 + e^{\frac{EAccept + \left(Vef - \left(mu - Ev\right)\right)}{KbT}}}{NaChar}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -7.5 \cdot 10^{+121} \lor \neg \left(NdChar \leq 1.25 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 56.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -6 \cdot 10^{+122}:\\ \;\;\;\;t\_0 + \frac{1}{\frac{2}{NaChar}}\\ \mathbf{elif}\;NdChar \leq 3 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NdChar -6e+122)
     (+ t_0 (/ 1.0 (/ 2.0 NaChar)))
     (if (<= NdChar 3e-23)
       (+
        (/ 1.0 (/ (+ 1.0 (exp (/ (- EAccept (- (- mu Ev) Vef)) KbT))) NaChar))
        (* NdChar 0.5))
       (+ t_0 (/ NaChar 2.0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -6e+122) {
		tmp = t_0 + (1.0 / (2.0 / NaChar));
	} else if (NdChar <= 3e-23) {
		tmp = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	} else {
		tmp = t_0 + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (ndchar <= (-6d+122)) then
        tmp = t_0 + (1.0d0 / (2.0d0 / nachar))
    else if (ndchar <= 3d-23) then
        tmp = (1.0d0 / ((1.0d0 + exp(((eaccept - ((mu - ev) - vef)) / kbt))) / nachar)) + (ndchar * 0.5d0)
    else
        tmp = t_0 + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -6e+122) {
		tmp = t_0 + (1.0 / (2.0 / NaChar));
	} else if (NdChar <= 3e-23) {
		tmp = (1.0 / ((1.0 + Math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	} else {
		tmp = t_0 + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -6e+122:
		tmp = t_0 + (1.0 / (2.0 / NaChar))
	elif NdChar <= 3e-23:
		tmp = (1.0 / ((1.0 + math.exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5)
	else:
		tmp = t_0 + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -6e+122)
		tmp = Float64(t_0 + Float64(1.0 / Float64(2.0 / NaChar)));
	elseif (NdChar <= 3e-23)
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + exp(Float64(Float64(EAccept - Float64(Float64(mu - Ev) - Vef)) / KbT))) / NaChar)) + Float64(NdChar * 0.5));
	else
		tmp = Float64(t_0 + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -6e+122)
		tmp = t_0 + (1.0 / (2.0 / NaChar));
	elseif (NdChar <= 3e-23)
		tmp = (1.0 / ((1.0 + exp(((EAccept - ((mu - Ev) - Vef)) / KbT))) / NaChar)) + (NdChar * 0.5);
	else
		tmp = t_0 + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -6e+122], N[(t$95$0 + N[(1.0 / N[(2.0 / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3e-23], N[(N[(1.0 / N[(N[(1.0 + N[Exp[N[(N[(EAccept - N[(N[(mu - Ev), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -5.99999999999999972e122

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. div-inv 99.9%

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

      4. associate-*r/ 99.9%

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

      5. *-commutative 99.9%

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

      6. *-un-lft-identity 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l- 99.9%

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

   6. Applied egg-rr 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in KbT around inf 62.4%

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

   if -5.99999999999999972e122 < NdChar < 3.00000000000000003e-23

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. div-inv 99.9%

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

      4. associate-*r/ 99.9%

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

      5. *-commutative 99.9%

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

      6. *-un-lft-identity 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l- 99.9%

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

   6. Applied egg-rr 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in KbT around inf 52.3%

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

   if 3.00000000000000003e-23 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.4%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6 \cdot 10^{+122}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2}{NaChar}}\\ \mathbf{elif}\;NdChar \leq 3 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{\frac{1 + e^{\frac{EAccept - \left(\left(mu - Ev\right) - Vef\right)}{KbT}}}{NaChar}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.1 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{+189}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -1.1e+44)
   (+ (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))) (* NdChar 0.5))
   (if (<= NaChar 1.7e+189)
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
      (/ NaChar 2.0))
     (- (* NdChar 0.5) (/ NaChar (- -1.0 (exp (/ Ev KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.1e+44) {
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar * 0.5);
	} else if (NaChar <= 1.7e+189) {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-1.1d+44)) then
        tmp = (nachar / (1.0d0 + exp((mu / -kbt)))) + (ndchar * 0.5d0)
    else if (nachar <= 1.7d+189) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (ndchar * 0.5d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.1e+44) {
		tmp = (NaChar / (1.0 + Math.exp((mu / -KbT)))) + (NdChar * 0.5);
	} else if (NaChar <= 1.7e+189) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -1.1e+44:
		tmp = (NaChar / (1.0 + math.exp((mu / -KbT)))) + (NdChar * 0.5)
	elif NaChar <= 1.7e+189:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -1.1e+44)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))) + Float64(NdChar * 0.5));
	elseif (NaChar <= 1.7e+189)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -1.1e+44)
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar * 0.5);
	elseif (NaChar <= 1.7e+189)
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -1.1e+44], N[(N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.7e+189], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.09999999999999998e44

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 60.3%

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

      1. associate-*r/ 60.3%

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

      2. mul-1-neg 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in KbT around inf 42.4%

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

   if -1.09999999999999998e44 < NaChar < 1.69999999999999992e189

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.8%

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

   if 1.69999999999999992e189 < 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%

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

   5. Taylor expanded in Ev around inf 64.4%

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

   6. Taylor expanded in KbT around inf 34.5%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.1 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{+189}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -8.8 \cdot 10^{-125} \lor \neg \left(KbT \leq 6.6 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} - \frac{KbT \cdot NaChar}{mu}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -8.8e-125) (not (<= KbT 6.6e-105)))
   (+ (/ NdChar (+ 1.0 (exp (/ (+ EDonor Vef) KbT)))) (/ NaChar 2.0))
   (- (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (/ (* KbT NaChar) mu))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -8.8e-125) || !(KbT <= 6.6e-105)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + Vef) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) - ((KbT * NaChar) / mu);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((kbt <= (-8.8d-125)) .or. (.not. (kbt <= 6.6d-105))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + vef) / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) - ((kbt * nachar) / mu)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -8.8e-125) || !(KbT <= 6.6e-105)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + Vef) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) - ((KbT * NaChar) / mu);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -8.8e-125) or not (KbT <= 6.6e-105):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + Vef) / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) - ((KbT * NaChar) / mu)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -8.8e-125) || !(KbT <= 6.6e-105))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Vef) / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) - Float64(Float64(KbT * NaChar) / mu));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -8.8e-125) || ~((KbT <= 6.6e-105)))
		tmp = (NdChar / (1.0 + exp(((EDonor + Vef) / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) - ((KbT * NaChar) / mu);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -8.8e-125], N[Not[LessEqual[KbT, 6.6e-105]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + Vef), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(KbT * NaChar), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -8.79999999999999979e-125 or 6.5999999999999997e-105 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 51.7%

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

   6. Taylor expanded in Vef around inf 44.5%

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

   if -8.79999999999999979e-125 < KbT < 6.5999999999999997e-105

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 44.4%

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

      1. associate-+r+ 44.4%

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

   7. Simplified 44.4%

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

   8. Taylor expanded in mu around inf 25.4%

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

   9. Taylor expanded in mu around inf 36.7%

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

       1. associate-*r/ 36.7%

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

       2. mul-1-neg 36.7%

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

       3. *-commutative 36.7%

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

   11. Simplified 36.7%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -8.8 \cdot 10^{-125} \lor \neg \left(KbT \leq 6.6 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} - \frac{KbT \cdot NaChar}{mu}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 3.4 \cdot 10^{+77}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -4.5e+41)
   (+ (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))) (* NdChar 0.5))
   (if (<= NaChar 3.4e+77)
     (+ (/ NdChar (+ 1.0 (exp (/ (+ EDonor Vef) KbT)))) (/ NaChar 2.0))
     (- (* NdChar 0.5) (/ NaChar (- -1.0 (exp (/ Ev KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -4.5e+41) {
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar * 0.5);
	} else if (NaChar <= 3.4e+77) {
		tmp = (NdChar / (1.0 + exp(((EDonor + Vef) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-4.5d+41)) then
        tmp = (nachar / (1.0d0 + exp((mu / -kbt)))) + (ndchar * 0.5d0)
    else if (nachar <= 3.4d+77) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + vef) / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (ndchar * 0.5d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -4.5e+41) {
		tmp = (NaChar / (1.0 + Math.exp((mu / -KbT)))) + (NdChar * 0.5);
	} else if (NaChar <= 3.4e+77) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + Vef) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -4.5e+41:
		tmp = (NaChar / (1.0 + math.exp((mu / -KbT)))) + (NdChar * 0.5)
	elif NaChar <= 3.4e+77:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + Vef) / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -4.5e+41)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))) + Float64(NdChar * 0.5));
	elseif (NaChar <= 3.4e+77)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Vef) / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -4.5e+41)
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar * 0.5);
	elseif (NaChar <= 3.4e+77)
		tmp = (NdChar / (1.0 + exp(((EDonor + Vef) / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -4.5e+41], N[(N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.4e+77], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + Vef), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -4.5000000000000001e41

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 60.3%

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

      1. associate-*r/ 60.3%

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

      2. mul-1-neg 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in KbT around inf 42.4%

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

   if -4.5000000000000001e41 < NaChar < 3.39999999999999997e77

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 59.4%

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

   6. Taylor expanded in Vef around inf 43.8%

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

   if 3.39999999999999997e77 < 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%

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

   5. Taylor expanded in Ev around inf 61.6%

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

   6. Taylor expanded in KbT around inf 33.9%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 3.4 \cdot 10^{+77}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + Vef}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.06 \cdot 10^{+24} \lor \neg \left(NaChar \leq 2 \cdot 10^{+76}\right):\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.06e+24) (not (<= NaChar 2e+76)))
   (- (* NdChar 0.5) (/ NaChar (- -1.0 (exp (/ Ev 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 ((NaChar <= -1.06e+24) || !(NaChar <= 2e+76)) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / 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 ((nachar <= (-1.06d+24)) .or. (.not. (nachar <= 2d+76))) then
        tmp = (ndchar * 0.5d0) - (nachar / ((-1.0d0) - exp((ev / 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 ((NaChar <= -1.06e+24) || !(NaChar <= 2e+76)) {
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - Math.exp((Ev / 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 (NaChar <= -1.06e+24) or not (NaChar <= 2e+76):
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - math.exp((Ev / 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 ((NaChar <= -1.06e+24) || !(NaChar <= 2e+76))
		tmp = Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / 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 ((NaChar <= -1.06e+24) || ~((NaChar <= 2e+76)))
		tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / 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[NaChar, -1.06e+24], N[Not[LessEqual[NaChar, 2e+76]], $MachinePrecision]], N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $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 NaChar < -1.06e24 or 2.0000000000000001e76 < 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%

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

   5. Taylor expanded in Ev around inf 61.0%

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

   6. Taylor expanded in KbT around inf 37.9%

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

   if -1.06e24 < NaChar < 2.0000000000000001e76

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 59.2%

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

   6. Taylor expanded in EDonor around inf 41.8%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.06 \cdot 10^{+24} \lor \neg \left(NaChar \leq 2 \cdot 10^{+76}\right):\\ \;\;\;\;NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq -9 \cdot 10^{+28} \lor \neg \left(EDonor \leq 6 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= EDonor -9e+28) (not (<= EDonor 6e+85)))
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
   (+ (/ NdChar (+ 1.0 (exp (/ mu 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 ((EDonor <= -9e+28) || !(EDonor <= 6e+85)) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((mu / 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 ((edonor <= (-9d+28)) .or. (.not. (edonor <= 6d+85))) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((mu / 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 ((EDonor <= -9e+28) || !(EDonor <= 6e+85)) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (EDonor <= -9e+28) or not (EDonor <= 6e+85):
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((EDonor <= -9e+28) || !(EDonor <= 6e+85))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / 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 ((EDonor <= -9e+28) || ~((EDonor <= 6e+85)))
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[EDonor, -9e+28], N[Not[LessEqual[EDonor, 6e+85]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -8.9999999999999994e28 or 6.0000000000000001e85 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 44.1%

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

   6. Taylor expanded in EDonor around inf 38.1%

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

   if -8.9999999999999994e28 < EDonor < 6.0000000000000001e85

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 48.2%

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

   6. Taylor expanded in mu around inf 41.1%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -9 \cdot 10^{+28} \lor \neg \left(EDonor \leq 6 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq -5 \cdot 10^{-79}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;EDonor \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EDonor -5e-79)
   (+ (/ NaChar 2.0) (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))))
   (if (<= EDonor 5.8e+84)
     (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (/ NaChar 2.0))
     (+ (/ 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 (EDonor <= -5e-79) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((Ec / -KbT))));
	} else if (EDonor <= 5.8e+84) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / 2.0);
	} 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 (edonor <= (-5d-79)) then
        tmp = (nachar / 2.0d0) + (ndchar / (1.0d0 + exp((ec / -kbt))))
    else if (edonor <= 5.8d+84) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / 2.0d0)
    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 (EDonor <= -5e-79) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + Math.exp((Ec / -KbT))));
	} else if (EDonor <= 5.8e+84) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / 2.0);
	} 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 EDonor <= -5e-79:
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + math.exp((Ec / -KbT))))
	elif EDonor <= 5.8e+84:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / 2.0)
	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 (EDonor <= -5e-79)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))));
	elseif (EDonor <= 5.8e+84)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / 2.0));
	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 (EDonor <= -5e-79)
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((Ec / -KbT))));
	elseif (EDonor <= 5.8e+84)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EDonor, -5e-79], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 5.8e+84], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EDonor < -4.99999999999999999e-79

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 48.4%

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

   6. Taylor expanded in Ec around inf 39.6%

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

      1. associate-*r/ 39.6%

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

      2. mul-1-neg 39.6%

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

   8. Simplified 39.6%

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

   if -4.99999999999999999e-79 < EDonor < 5.79999999999999977e84

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.6%

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

   6. Taylor expanded in mu around inf 40.6%

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

   if 5.79999999999999977e84 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.3%

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

   6. Taylor expanded in EDonor around inf 40.8%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -5 \cdot 10^{-79}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;EDonor \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 36.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (- (* NdChar 0.5) (/ NaChar (- -1.0 (exp (/ Ev KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / 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 * 0.5d0) - (nachar / ((-1.0d0) - exp((ev / 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 * 0.5) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar * 0.5) - (NaChar / (-1.0 - math.exp((Ev / KbT))))

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar * 0.5) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar * 0.5) - (NaChar / (-1.0 - exp((Ev / KbT))));
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar * 0.5), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in Ev around inf 70.6%

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

6. Taylor expanded in KbT around inf 36.0%

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

7. Final simplification 36.0%

   \[\leadsto NdChar \cdot 0.5 - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}} \]
8. Add Preprocessing

Alternative 25: 27.6% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 1.6 \cdot 10^{+170}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 1.6e+170)
   (* 0.5 (+ NdChar NaChar))
   (/ NdChar (- 2.0 (/ 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 (EAccept <= 1.6e+170) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NdChar / (2.0 - (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 (eaccept <= 1.6d+170) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = ndchar / (2.0d0 - (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 (EAccept <= 1.6e+170) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NdChar / (2.0 - (Ec / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 1.6e+170:
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NdChar / (2.0 - (Ec / KbT))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 1.6e+170)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NdChar / Float64(2.0 - 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 (EAccept <= 1.6e+170)
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NdChar / (2.0 - (Ec / KbT));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 1.6e+170], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 1.59999999999999989e170

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 47.8%

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

   6. Taylor expanded in Ec around inf 35.3%

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

      1. associate-*r/ 35.3%

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

      2. mul-1-neg 35.3%

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

   8. Simplified 35.3%

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

   9. Taylor expanded in Ec around 0 25.0%

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

       1. mul-1-neg 25.0%

          \[\leadsto \frac{NdChar}{2 + \color{blue}{\left(-\frac{Ec}{KbT}\right)}} + \frac{NaChar}{2} \]

       2. unsub-neg 25.0%

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

   11. Simplified 25.0%

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

   12. Taylor expanded in Ec around 0 26.9%

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

       1. distribute-lft-out 26.9%

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

   14. Simplified 26.9%

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

   if 1.59999999999999989e170 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 37.7%

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

   6. Taylor expanded in Ec around inf 32.3%

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

      1. associate-*r/ 32.3%

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

      2. mul-1-neg 32.3%

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

   8. Simplified 32.3%

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

   9. Taylor expanded in Ec around 0 23.5%

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

       1. mul-1-neg 23.5%

          \[\leadsto \frac{NdChar}{2 + \color{blue}{\left(-\frac{Ec}{KbT}\right)}} + \frac{NaChar}{2} \]

       2. unsub-neg 23.5%

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

   11. Simplified 23.5%

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

   12. Taylor expanded in NdChar around inf 34.8%

       \[\leadsto \color{blue}{\frac{NdChar}{2 - \frac{Ec}{KbT}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 1.6 \cdot 10^{+170}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 27.8% accurate, 45.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 46.5%

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

6. Taylor expanded in Ec around inf 35.0%

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

   1. associate-*r/ 35.0%

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

   2. mul-1-neg 35.0%

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

8. Simplified 35.0%

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

9. Taylor expanded in Ec around 0 24.8%

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

    1. mul-1-neg 24.8%

       \[\leadsto \frac{NdChar}{2 + \color{blue}{\left(-\frac{Ec}{KbT}\right)}} + \frac{NaChar}{2} \]

    2. unsub-neg 24.8%

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

11. Simplified 24.8%

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

12. Taylor expanded in Ec around 0 26.6%

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

    1. distribute-lft-out 26.6%

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

14. Simplified 26.6%

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

15. Final simplification 26.6%

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

Reproduce

herbie shell --seed 2024073 
(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))))))