Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 27.5s

Alternatives: 28

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -2.116754892504179e-237
  2. Ec = -6.1392032740913765e+106
  3. Vef = 4.5301606376594274e+86
  4. EDonor = -8.134286874407024e-184
  5. mu = -4.383466993818131e-28
  6. KbT = -1.6526595281035106e+80
  7. NaChar = 5.844266264502463e-237
  8. Ev = 3.0508334620814556e+287
  9. EAccept = -2.461099122366534e-129

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: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{Vef}{KbT} + \frac{mu}{KbT}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;t\_2 + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + t\_1\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -1.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - t\_0\\ \mathbf{elif}\;NaChar \leq -7 \cdot 10^{-73}:\\ \;\;\;\;t\_2 + \frac{NdChar}{Vef \cdot \left(\frac{1}{KbT} + \left(\left(\left(\frac{mu}{Vef \cdot KbT} + \frac{EDonor}{Vef \cdot KbT}\right) + \frac{2}{Vef}\right) - \frac{Ec}{Vef \cdot KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq -1.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - t\_0\\ \mathbf{elif}\;NaChar \leq 2.55:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + t\_1\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (+ (/ Vef KbT) (/ mu KbT)))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
   (if (<= NaChar -1.95e+86)
     (+
      t_2
      (/ NdChar (* Ec (+ (/ (+ 2.0 (+ (/ EDonor KbT) t_1)) Ec) (/ -1.0 KbT)))))
     (if (<= NaChar -1.7e-15)
       (- (/ 1.0 (/ (+ 2.0 (/ Vef KbT)) NaChar)) t_0)
       (if (<= NaChar -7e-73)
         (+
          t_2
          (/
           NdChar
           (*
            Vef
            (+
             (/ 1.0 KbT)
             (-
              (+ (+ (/ mu (* Vef KbT)) (/ EDonor (* Vef KbT))) (/ 2.0 Vef))
              (/ Ec (* Vef KbT)))))))
         (if (<= NaChar -1.6e-123)
           (-
            (/ -1.0 (* Vef (- (/ -1.0 (* KbT NaChar)) (/ 2.0 (* Vef NaChar)))))
            t_0)
           (if (<= NaChar 2.55)
             (+
              (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
              (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
             (+
              t_2
              (/
               NdChar
               (*
                EDonor
                (+ (/ 1.0 KbT) (/ (- (+ 2.0 t_1) (/ Ec KbT)) EDonor))))))))))))

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 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.95e+86) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -1.7e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if (NaChar <= -7e-73) {
		tmp = t_2 + (NdChar / (Vef * ((1.0 / KbT) + ((((mu / (Vef * KbT)) + (EDonor / (Vef * KbT))) + (2.0 / Vef)) - (Ec / (Vef * KbT))))));
	} else if (NaChar <= -1.6e-123) {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	} else if (NaChar <= 2.55) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	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 = (vef / kbt) + (mu / kbt)
    t_2 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    if (nachar <= (-1.95d+86)) then
        tmp = t_2 + (ndchar / (ec * (((2.0d0 + ((edonor / kbt) + t_1)) / ec) + ((-1.0d0) / kbt))))
    else if (nachar <= (-1.7d-15)) then
        tmp = (1.0d0 / ((2.0d0 + (vef / kbt)) / nachar)) - t_0
    else if (nachar <= (-7d-73)) then
        tmp = t_2 + (ndchar / (vef * ((1.0d0 / kbt) + ((((mu / (vef * kbt)) + (edonor / (vef * kbt))) + (2.0d0 / vef)) - (ec / (vef * kbt))))))
    else if (nachar <= (-1.6d-123)) then
        tmp = ((-1.0d0) / (vef * (((-1.0d0) / (kbt * nachar)) - (2.0d0 / (vef * nachar))))) - t_0
    else if (nachar <= 2.55d0) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = t_2 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + t_1) - (ec / kbt)) / edonor))))
    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 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.95e+86) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -1.7e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if (NaChar <= -7e-73) {
		tmp = t_2 + (NdChar / (Vef * ((1.0 / KbT) + ((((mu / (Vef * KbT)) + (EDonor / (Vef * KbT))) + (2.0 / Vef)) - (Ec / (Vef * KbT))))));
	} else if (NaChar <= -1.6e-123) {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	} else if (NaChar <= 2.55) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	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 = (Vef / KbT) + (mu / KbT)
	t_2 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	tmp = 0
	if NaChar <= -1.95e+86:
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))))
	elif NaChar <= -1.7e-15:
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0
	elif NaChar <= -7e-73:
		tmp = t_2 + (NdChar / (Vef * ((1.0 / KbT) + ((((mu / (Vef * KbT)) + (EDonor / (Vef * KbT))) + (2.0 / Vef)) - (Ec / (Vef * KbT))))))
	elif NaChar <= -1.6e-123:
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0
	elif NaChar <= 2.55:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))))
	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(Vef / KbT) + Float64(mu / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.95e+86)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + t_1)) / Ec) + Float64(-1.0 / KbT)))));
	elseif (NaChar <= -1.7e-15)
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 + Float64(Vef / KbT)) / NaChar)) - t_0);
	elseif (NaChar <= -7e-73)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(Float64(mu / Float64(Vef * KbT)) + Float64(EDonor / Float64(Vef * KbT))) + Float64(2.0 / Vef)) - Float64(Ec / Float64(Vef * KbT)))))));
	elseif (NaChar <= -1.6e-123)
		tmp = Float64(Float64(-1.0 / Float64(Vef * Float64(Float64(-1.0 / Float64(KbT * NaChar)) - Float64(2.0 / Float64(Vef * NaChar))))) - t_0);
	elseif (NaChar <= 2.55)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(t_2 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + t_1) - Float64(Ec / KbT)) / EDonor)))));
	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 = (Vef / KbT) + (mu / KbT);
	t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.95e+86)
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	elseif (NaChar <= -1.7e-15)
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	elseif (NaChar <= -7e-73)
		tmp = t_2 + (NdChar / (Vef * ((1.0 / KbT) + ((((mu / (Vef * KbT)) + (EDonor / (Vef * KbT))) + (2.0 / Vef)) - (Ec / (Vef * KbT))))));
	elseif (NaChar <= -1.6e-123)
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	elseif (NaChar <= 2.55)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	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[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.95e+86], N[(t$95$2 + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.7e-15], N[(N[(1.0 / N[(N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, -7e-73], N[(t$95$2 + N[(NdChar / N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(N[(mu / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 / Vef), $MachinePrecision]), $MachinePrecision] - N[(Ec / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.6e-123], N[(N[(-1.0 / N[(Vef * N[(N[(-1.0 / N[(KbT * NaChar), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(Vef * NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, 2.55], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + t$95$1), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if NaChar < -1.9500000000000001e86

   1. Initial program 100.0%

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

   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 75.0%

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

   6. Taylor expanded in Ec around -inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. *-commutative 77.2%

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

      3. distribute-rgt-neg-in 77.2%

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

      4. +-commutative 77.2%

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

      5. mul-1-neg 77.2%

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

      6. unsub-neg 77.2%

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

   8. Simplified 77.2%

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

   if -1.9500000000000001e86 < NaChar < -1.7e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.4%

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

   6. Taylor expanded in Vef around 0 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. associate-+r+ 82.9%

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

      4. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   10. Simplified 82.9%

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

   if -1.7e-15 < NaChar < -6.9999999999999995e-73

   1. Initial program 100.0%

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

   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 56.1%

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

   6. Taylor expanded in Vef around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. +-commutative 62.3%

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

      3. *-commutative 62.3%

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

      4. *-commutative 62.3%

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

      5. associate-*r/ 62.3%

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

      6. metadata-eval 62.3%

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

      7. *-commutative 62.3%

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

   8. Simplified 62.3%

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

   if -6.9999999999999995e-73 < NaChar < -1.59999999999999989e-123

   1. Initial program 100.0%

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

   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 76.0%

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

   6. Taylor expanded in Vef around 0 68.5%

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

      1. clear-num 68.3%

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

      2. inv-pow 68.3%

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

      3. associate-+r+ 68.3%

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

      4. metadata-eval 68.3%

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

   8. Applied egg-rr 68.3%

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

      1. unpow-1 68.3%

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

   10. Simplified 68.3%

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

   11. Taylor expanded in Vef around inf 92.2%

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

       1. associate-*r/ 92.2%

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

       2. metadata-eval 92.2%

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

   13. Simplified 92.2%

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

   if -1.59999999999999989e-123 < NaChar < 2.5499999999999998

   1. Initial program 100.0%

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

   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 77.4%

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

   6. Taylor expanded in EDonor around 0 70.5%

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

   if 2.5499999999999998 < 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 KbT around inf 71.8%

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

   6. Taylor expanded in EDonor around -inf 84.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -1.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -7 \cdot 10^{-73}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{Vef \cdot \left(\frac{1}{KbT} + \left(\left(\left(\frac{mu}{Vef \cdot KbT} + \frac{EDonor}{Vef \cdot KbT}\right) + \frac{2}{Vef}\right) - \frac{Ec}{Vef \cdot KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq -1.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 2.55:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - t\_0\\ t_2 := \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;EAccept \leq 2.4 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;EAccept \leq 3 \cdot 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (- (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_0))
        (t_2
         (+
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))))
   (if (<= EAccept 2.4e-304)
     t_1
     (if (<= EAccept 3.2e-107)
       t_2
       (if (<= EAccept 5.6e-64)
         t_1
         (if (<= EAccept 3e+180)
           t_2
           (- (/ 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 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + exp((Ev / KbT)))) - t_0;
	double t_2 = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (EAccept <= 2.4e-304) {
		tmp = t_1;
	} else if (EAccept <= 3.2e-107) {
		tmp = t_2;
	} else if (EAccept <= 5.6e-64) {
		tmp = t_1;
	} else if (EAccept <= 3e+180) {
		tmp = t_2;
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = (nachar / (1.0d0 + exp((ev / kbt)))) - t_0
    t_2 = (nachar / (1.0d0 + exp((mu / -kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    if (eaccept <= 2.4d-304) then
        tmp = t_1
    else if (eaccept <= 3.2d-107) then
        tmp = t_2
    else if (eaccept <= 5.6d-64) then
        tmp = t_1
    else if (eaccept <= 3d+180) then
        tmp = t_2
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) - t_0;
	double t_2 = (NaChar / (1.0 + Math.exp((mu / -KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (EAccept <= 2.4e-304) {
		tmp = t_1;
	} else if (EAccept <= 3.2e-107) {
		tmp = t_2;
	} else if (EAccept <= 5.6e-64) {
		tmp = t_1;
	} else if (EAccept <= 3e+180) {
		tmp = t_2;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) - t_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)))
	t_1 = (NaChar / (1.0 + math.exp((Ev / KbT)))) - t_0
	t_2 = (NaChar / (1.0 + math.exp((mu / -KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	tmp = 0
	if EAccept <= 2.4e-304:
		tmp = t_1
	elif EAccept <= 3.2e-107:
		tmp = t_2
	elif EAccept <= 5.6e-64:
		tmp = t_1
	elif EAccept <= 3e+180:
		tmp = t_2
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) - t_0)
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))))
	tmp = 0.0
	if (EAccept <= 2.4e-304)
		tmp = t_1;
	elseif (EAccept <= 3.2e-107)
		tmp = t_2;
	elseif (EAccept <= 5.6e-64)
		tmp = t_1;
	elseif (EAccept <= 3e+180)
		tmp = t_2;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = (NaChar / (1.0 + exp((Ev / KbT)))) - t_0;
	t_2 = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	tmp = 0.0;
	if (EAccept <= 2.4e-304)
		tmp = t_1;
	elseif (EAccept <= 3.2e-107)
		tmp = t_2;
	elseif (EAccept <= 5.6e-64)
		tmp = t_1;
	elseif (EAccept <= 3e+180)
		tmp = t_2;
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(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[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, 2.4e-304], t$95$1, If[LessEqual[EAccept, 3.2e-107], t$95$2, If[LessEqual[EAccept, 5.6e-64], t$95$1, If[LessEqual[EAccept, 3e+180], t$95$2, N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 2.4000000000000001e-304 or 3.20000000000000013e-107 < EAccept < 5.60000000000000008e-64

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 72.2%

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

   if 2.4000000000000001e-304 < EAccept < 3.20000000000000013e-107 or 5.60000000000000008e-64 < EAccept < 3.00000000000000003e180

   1. Initial program 100.0%

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

   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 74.4%

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

      1. associate-*r/ 74.4%

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

      2. mul-1-neg 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in EDonor around 0 72.6%

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

   if 3.00000000000000003e180 < 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 88.9%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 2.4 \cdot 10^{-304}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{-107}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3 \cdot 10^{+180}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} - t\_0\\ \mathbf{if}\;EAccept \leq 8 \cdot 10^{-302}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - t\_0\\ \mathbf{elif}\;EAccept \leq 9 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;EAccept \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (- (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) t_0)))
   (if (<= EAccept 8e-302)
     (- (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_0)
     (if (<= EAccept 9e+24)
       t_1
       (if (<= EAccept 1.15e+73)
         (+
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
         (if (<= EAccept 3e+180)
           t_1
           (- (/ 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 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) - t_0;
	double tmp;
	if (EAccept <= 8e-302) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - t_0;
	} else if (EAccept <= 9e+24) {
		tmp = t_1;
	} else if (EAccept <= 1.15e+73) {
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else if (EAccept <= 3e+180) {
		tmp = t_1;
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = (nachar / (1.0d0 + exp((vef / kbt)))) - t_0
    if (eaccept <= 8d-302) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) - t_0
    else if (eaccept <= 9d+24) then
        tmp = t_1
    else if (eaccept <= 1.15d+73) then
        tmp = (nachar / (1.0d0 + exp((mu / -kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else if (eaccept <= 3d+180) then
        tmp = t_1
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) - t_0;
	double tmp;
	if (EAccept <= 8e-302) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) - t_0;
	} else if (EAccept <= 9e+24) {
		tmp = t_1;
	} else if (EAccept <= 1.15e+73) {
		tmp = (NaChar / (1.0 + Math.exp((mu / -KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else if (EAccept <= 3e+180) {
		tmp = t_1;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) - t_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)))
	t_1 = (NaChar / (1.0 + math.exp((Vef / KbT)))) - t_0
	tmp = 0
	if EAccept <= 8e-302:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) - t_0
	elif EAccept <= 9e+24:
		tmp = t_1
	elif EAccept <= 1.15e+73:
		tmp = (NaChar / (1.0 + math.exp((mu / -KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	elif EAccept <= 3e+180:
		tmp = t_1
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - t_0)
	tmp = 0.0
	if (EAccept <= 8e-302)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) - t_0);
	elseif (EAccept <= 9e+24)
		tmp = t_1;
	elseif (EAccept <= 1.15e+73)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	elseif (EAccept <= 3e+180)
		tmp = t_1;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) - t_0;
	tmp = 0.0;
	if (EAccept <= 8e-302)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - t_0;
	elseif (EAccept <= 9e+24)
		tmp = t_1;
	elseif (EAccept <= 1.15e+73)
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	elseif (EAccept <= 3e+180)
		tmp = t_1;
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(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] - t$95$0), $MachinePrecision]}, If[LessEqual[EAccept, 8e-302], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[EAccept, 9e+24], t$95$1, If[LessEqual[EAccept, 1.15e+73], N[(N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3e+180], t$95$1, N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if EAccept < 7.9999999999999997e-302

   1. Initial program 100.0%

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

   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 71.9%

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

   if 7.9999999999999997e-302 < EAccept < 9.00000000000000039e24 or 1.15e73 < EAccept < 3.00000000000000003e180

   1. Initial program 100.0%

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

   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 71.6%

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

   if 9.00000000000000039e24 < EAccept < 1.15e73

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in mu around inf 78.0%

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

      1. associate-*r/ 78.0%

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

      2. mul-1-neg 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in EDonor around 0 78.0%

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

   if 3.00000000000000003e180 < 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 88.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 8 \cdot 10^{-302}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 9 \cdot 10^{+24}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3 \cdot 10^{+180}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EAccept}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;mu \leq -9.6 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq 1.18 \cdot 10^{-39}:\\ \;\;\;\;\frac{NaChar}{1 + t\_0} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 3.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + Vef \cdot \left(\frac{1}{KbT} + \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;mu \leq 6 \cdot 10^{+139}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - t\_0}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ EAccept KbT)))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))))
   (if (<= mu -9.6e+95)
     t_1
     (if (<= mu 1.18e-39)
       (-
        (/ NaChar (+ 1.0 t_0))
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (if (<= mu 3.2e+35)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
          (/
           NdChar
           (-
            (+
             2.0
             (+ (/ EDonor KbT) (* Vef (+ (/ 1.0 KbT) (/ mu (* Vef KbT))))))
            (/ Ec KbT))))
         (if (<= mu 6e+139)
           (- (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (/ NaChar (- -1.0 t_0)))
           t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp((EAccept / KbT));
	double t_1 = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (mu <= -9.6e+95) {
		tmp = t_1;
	} else if (mu <= 1.18e-39) {
		tmp = (NaChar / (1.0 + t_0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (mu <= 3.2e+35) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT)));
	} else if (mu <= 6e+139) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) - (NaChar / (-1.0 - t_0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = exp((eaccept / kbt))
    t_1 = (nachar / (1.0d0 + exp((mu / -kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    if (mu <= (-9.6d+95)) then
        tmp = t_1
    else if (mu <= 1.18d-39) then
        tmp = (nachar / (1.0d0 + t_0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else if (mu <= 3.2d+35) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / ((2.0d0 + ((edonor / kbt) + (vef * ((1.0d0 / kbt) + (mu / (vef * kbt)))))) - (ec / kbt)))
    else if (mu <= 6d+139) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) - (nachar / ((-1.0d0) - t_0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp((EAccept / KbT));
	double t_1 = (NaChar / (1.0 + Math.exp((mu / -KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (mu <= -9.6e+95) {
		tmp = t_1;
	} else if (mu <= 1.18e-39) {
		tmp = (NaChar / (1.0 + t_0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (mu <= 3.2e+35) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT)));
	} else if (mu <= 6e+139) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) - (NaChar / (-1.0 - t_0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp((EAccept / KbT))
	t_1 = (NaChar / (1.0 + math.exp((mu / -KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	tmp = 0
	if mu <= -9.6e+95:
		tmp = t_1
	elif mu <= 1.18e-39:
		tmp = (NaChar / (1.0 + t_0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	elif mu <= 3.2e+35:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT)))
	elif mu <= 6e+139:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) - (NaChar / (-1.0 - t_0))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(EAccept / KbT))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))))
	tmp = 0.0
	if (mu <= -9.6e+95)
		tmp = t_1;
	elseif (mu <= 1.18e-39)
		tmp = Float64(Float64(NaChar / Float64(1.0 + t_0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	elseif (mu <= 3.2e+35)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(mu / Float64(Vef * KbT)))))) - Float64(Ec / KbT))));
	elseif (mu <= 6e+139)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - Float64(NaChar / Float64(-1.0 - t_0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp((EAccept / KbT));
	t_1 = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	tmp = 0.0;
	if (mu <= -9.6e+95)
		tmp = t_1;
	elseif (mu <= 1.18e-39)
		tmp = (NaChar / (1.0 + t_0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	elseif (mu <= 3.2e+35)
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + (Vef * ((1.0 / KbT) + (mu / (Vef * KbT)))))) - (Ec / KbT)));
	elseif (mu <= 6e+139)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) - (NaChar / (-1.0 - t_0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -9.6e+95], t$95$1, If[LessEqual[mu, 1.18e-39], N[(N[(NaChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 3.2e+35], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(mu / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 6e+139], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if mu < -9.6000000000000002e95 or 5.9999999999999999e139 < 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 89.8%

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

      1. associate-*r/ 89.8%

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

      2. mul-1-neg 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in EDonor around 0 87.7%

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

   if -9.6000000000000002e95 < mu < 1.17999999999999993e-39

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 73.6%

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

   if 1.17999999999999993e-39 < mu < 3.19999999999999983e35

   1. Initial program 100.0%

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

   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 84.6%

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

   6. Taylor expanded in Vef around inf 89.8%

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

      1. *-commutative 89.8%

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

   8. Simplified 89.8%

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

   if 3.19999999999999983e35 < mu < 5.9999999999999999e139

   1. Initial program 100.0%

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

   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 78.3%

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

   6. Taylor expanded in Vef around inf 78.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -9.6 \cdot 10^{+95}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.18 \cdot 10^{-39}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 3.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + Vef \cdot \left(\frac{1}{KbT} + \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;mu \leq 6 \cdot 10^{+139}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{Vef}{KbT} + \frac{mu}{KbT}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -5 \cdot 10^{+167}:\\ \;\;\;\;t\_2 + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + t\_1\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-307}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} - t\_0\\ \mathbf{elif}\;NaChar \leq 2:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + t\_1\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (+ (/ Vef KbT) (/ mu KbT)))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
   (if (<= NaChar -5e+167)
     (+
      t_2
      (/ NdChar (* Ec (+ (/ (+ 2.0 (+ (/ EDonor KbT) t_1)) Ec) (/ -1.0 KbT)))))
     (if (<= NaChar -2.3e-307)
       (- (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))) t_0)
       (if (<= NaChar 2.0)
         (- (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_0)
         (+
          t_2
          (/
           NdChar
           (*
            EDonor
            (+ (/ 1.0 KbT) (/ (- (+ 2.0 t_1) (/ Ec KbT)) EDonor))))))))))

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 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -5e+167) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -2.3e-307) {
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) - t_0;
	} else if (NaChar <= 2.0) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - t_0;
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	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 = (vef / kbt) + (mu / kbt)
    t_2 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    if (nachar <= (-5d+167)) then
        tmp = t_2 + (ndchar / (ec * (((2.0d0 + ((edonor / kbt) + t_1)) / ec) + ((-1.0d0) / kbt))))
    else if (nachar <= (-2.3d-307)) then
        tmp = (nachar / (1.0d0 + exp((mu / -kbt)))) - t_0
    else if (nachar <= 2.0d0) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) - t_0
    else
        tmp = t_2 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + t_1) - (ec / kbt)) / edonor))))
    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 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -5e+167) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -2.3e-307) {
		tmp = (NaChar / (1.0 + Math.exp((mu / -KbT)))) - t_0;
	} else if (NaChar <= 2.0) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) - t_0;
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	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 = (Vef / KbT) + (mu / KbT)
	t_2 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	tmp = 0
	if NaChar <= -5e+167:
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))))
	elif NaChar <= -2.3e-307:
		tmp = (NaChar / (1.0 + math.exp((mu / -KbT)))) - t_0
	elif NaChar <= 2.0:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) - t_0
	else:
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))))
	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(Vef / KbT) + Float64(mu / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	tmp = 0.0
	if (NaChar <= -5e+167)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + t_1)) / Ec) + Float64(-1.0 / KbT)))));
	elseif (NaChar <= -2.3e-307)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))) - t_0);
	elseif (NaChar <= 2.0)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) - t_0);
	else
		tmp = Float64(t_2 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + t_1) - Float64(Ec / KbT)) / EDonor)))));
	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 = (Vef / KbT) + (mu / KbT);
	t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -5e+167)
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	elseif (NaChar <= -2.3e-307)
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) - t_0;
	elseif (NaChar <= 2.0)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - t_0;
	else
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	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[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -5e+167], N[(t$95$2 + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2.3e-307], N[(N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, 2.0], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(t$95$2 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + t$95$1), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -4.9999999999999997e167

   1. Initial program 100.0%

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

   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 80.0%

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

   6. Taylor expanded in Ec around -inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. +-commutative 83.2%

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

      5. mul-1-neg 83.2%

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

      6. unsub-neg 83.2%

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

   8. Simplified 83.2%

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

   if -4.9999999999999997e167 < NaChar < -2.2999999999999999e-307

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 78.9%

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

      1. associate-*r/ 78.9%

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

      2. mul-1-neg 78.9%

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

   7. Simplified 78.9%

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

   if -2.2999999999999999e-307 < NaChar < 2

   1. Initial program 100.0%

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

   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 81.4%

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

   if 2 < 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 KbT around inf 71.8%

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

   6. Taylor expanded in EDonor around -inf 84.3%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5 \cdot 10^{+167}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-307}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 2:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ t_1 := \frac{Vef}{KbT} + \frac{mu}{KbT}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+164}:\\ \;\;\;\;t\_2 + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + t\_1\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + t\_0\\ \mathbf{elif}\;NaChar \leq 8.5:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + t\_1\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
        (t_1 (+ (/ Vef KbT) (/ mu KbT)))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
   (if (<= NaChar -1.9e+164)
     (+
      t_2
      (/ NdChar (* Ec (+ (/ (+ 2.0 (+ (/ EDonor KbT) t_1)) Ec) (/ -1.0 KbT)))))
     (if (<= NaChar 4.8e-305)
       (+ (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))) t_0)
       (if (<= NaChar 8.5)
         (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_0)
         (+
          t_2
          (/
           NdChar
           (*
            EDonor
            (+ (/ 1.0 KbT) (/ (- (+ 2.0 t_1) (/ Ec KbT)) EDonor))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	double t_1 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.9e+164) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= 4.8e-305) {
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + t_0;
	} else if (NaChar <= 8.5) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	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((((mu + vef) - ec) / kbt)))
    t_1 = (vef / kbt) + (mu / kbt)
    t_2 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    if (nachar <= (-1.9d+164)) then
        tmp = t_2 + (ndchar / (ec * (((2.0d0 + ((edonor / kbt) + t_1)) / ec) + ((-1.0d0) / kbt))))
    else if (nachar <= 4.8d-305) then
        tmp = (nachar / (1.0d0 + exp((mu / -kbt)))) + t_0
    else if (nachar <= 8.5d0) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + t_0
    else
        tmp = t_2 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + t_1) - (ec / kbt)) / edonor))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)));
	double t_1 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.9e+164) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= 4.8e-305) {
		tmp = (NaChar / (1.0 + Math.exp((mu / -KbT)))) + t_0;
	} else if (NaChar <= 8.5) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + t_0;
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))
	t_1 = (Vef / KbT) + (mu / KbT)
	t_2 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	tmp = 0
	if NaChar <= -1.9e+164:
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))))
	elif NaChar <= 4.8e-305:
		tmp = (NaChar / (1.0 + math.exp((mu / -KbT)))) + t_0
	elif NaChar <= 8.5:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + t_0
	else:
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))))
	t_1 = Float64(Float64(Vef / KbT) + Float64(mu / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.9e+164)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + t_1)) / Ec) + Float64(-1.0 / KbT)))));
	elseif (NaChar <= 4.8e-305)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))) + t_0);
	elseif (NaChar <= 8.5)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + t_0);
	else
		tmp = Float64(t_2 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + t_1) - Float64(Ec / KbT)) / EDonor)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	t_1 = (Vef / KbT) + (mu / KbT);
	t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.9e+164)
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	elseif (NaChar <= 4.8e-305)
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + t_0;
	elseif (NaChar <= 8.5)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	else
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.9e+164], N[(t$95$2 + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.8e-305], N[(N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[NaChar, 8.5], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], N[(t$95$2 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + t$95$1), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.90000000000000011e164

   1. Initial program 100.0%

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

   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 80.0%

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

   6. Taylor expanded in Ec around -inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. +-commutative 83.2%

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

      5. mul-1-neg 83.2%

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

      6. unsub-neg 83.2%

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

   8. Simplified 83.2%

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

   if -1.90000000000000011e164 < NaChar < 4.80000000000000039e-305

   1. Initial program 100.0%

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

   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 78.9%

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

      1. associate-*r/ 78.9%

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

      2. mul-1-neg 78.9%

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

   7. Simplified 78.9%

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

   8. Taylor expanded in EDonor around 0 71.8%

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

   if 4.80000000000000039e-305 < NaChar < 8.5

   1. Initial program 100.0%

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

   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 81.4%

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

   6. Taylor expanded in EDonor around 0 75.8%

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

   if 8.5 < 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 KbT around inf 71.8%

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

   6. Taylor expanded in EDonor around -inf 84.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+164}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 8.5:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;t\_1 + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - t\_0\\ \mathbf{elif}\;NaChar \leq -1.85 \cdot 10^{-75}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.48 \cdot 10^{-12}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
   (if (<= NaChar -1.9e+86)
     (+
      t_1
      (/
       NdChar
       (*
        Ec
        (+
         (/ (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) Ec)
         (/ -1.0 KbT)))))
     (if (<= NaChar -2.3e-15)
       (- (/ 1.0 (/ (+ 2.0 (/ Vef KbT)) NaChar)) t_0)
       (if (<= NaChar -1.85e-75)
         (+ t_1 (/ NdChar (+ 2.0 (/ (- (+ EDonor (+ mu Vef)) Ec) KbT))))
         (if (<= NaChar 1.48e-12)
           (-
            (/ -1.0 (* Vef (- (/ -1.0 (* KbT NaChar)) (/ 2.0 (* Vef NaChar)))))
            t_0)
           (+
            t_1
            (/
             NdChar
             (-
              (+
               2.0
               (*
                EDonor
                (+
                 (/ 1.0 KbT)
                 (+ (/ (/ Vef EDonor) KbT) (/ (/ mu EDonor) KbT)))))
              (/ Ec KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.9e+86) {
		tmp = t_1 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -2.3e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if (NaChar <= -1.85e-75) {
		tmp = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	} else if (NaChar <= 1.48e-12) {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    if (nachar <= (-1.9d+86)) then
        tmp = t_1 + (ndchar / (ec * (((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) / ec) + ((-1.0d0) / kbt))))
    else if (nachar <= (-2.3d-15)) then
        tmp = (1.0d0 / ((2.0d0 + (vef / kbt)) / nachar)) - t_0
    else if (nachar <= (-1.85d-75)) then
        tmp = t_1 + (ndchar / (2.0d0 + (((edonor + (mu + vef)) - ec) / kbt)))
    else if (nachar <= 1.48d-12) then
        tmp = ((-1.0d0) / (vef * (((-1.0d0) / (kbt * nachar)) - (2.0d0 / (vef * nachar))))) - t_0
    else
        tmp = t_1 + (ndchar / ((2.0d0 + (edonor * ((1.0d0 / kbt) + (((vef / edonor) / kbt) + ((mu / edonor) / kbt))))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.9e+86) {
		tmp = t_1 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -2.3e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if (NaChar <= -1.85e-75) {
		tmp = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	} else if (NaChar <= 1.48e-12) {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	tmp = 0
	if NaChar <= -1.9e+86:
		tmp = t_1 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))))
	elif NaChar <= -2.3e-15:
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0
	elif NaChar <= -1.85e-75:
		tmp = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)))
	elif NaChar <= 1.48e-12:
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0
	else:
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.9e+86)
		tmp = Float64(t_1 + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / KbT)))));
	elseif (NaChar <= -2.3e-15)
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 + Float64(Vef / KbT)) / NaChar)) - t_0);
	elseif (NaChar <= -1.85e-75)
		tmp = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT))));
	elseif (NaChar <= 1.48e-12)
		tmp = Float64(Float64(-1.0 / Float64(Vef * Float64(Float64(-1.0 / Float64(KbT * NaChar)) - Float64(2.0 / Float64(Vef * NaChar))))) - t_0);
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(Vef / EDonor) / KbT) + Float64(Float64(mu / EDonor) / KbT))))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.9e+86)
		tmp = t_1 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))));
	elseif (NaChar <= -2.3e-15)
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	elseif (NaChar <= -1.85e-75)
		tmp = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	elseif (NaChar <= 1.48e-12)
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	else
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.9e+86], N[(t$95$1 + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2.3e-15], N[(N[(1.0 / N[(N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, -1.85e-75], N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.48e-12], N[(N[(-1.0 / N[(Vef * N[(N[(-1.0 / N[(KbT * NaChar), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(Vef * NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(t$95$1 + N[(NdChar / N[(N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(Vef / EDonor), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(mu / EDonor), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -1.89999999999999989e86

   1. Initial program 100.0%

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

   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 75.0%

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

   6. Taylor expanded in Ec around -inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. *-commutative 77.2%

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

      3. distribute-rgt-neg-in 77.2%

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

      4. +-commutative 77.2%

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

      5. mul-1-neg 77.2%

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

      6. unsub-neg 77.2%

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

   8. Simplified 77.2%

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

   if -1.89999999999999989e86 < NaChar < -2.2999999999999999e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.4%

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

   6. Taylor expanded in Vef around 0 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. associate-+r+ 82.9%

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

      4. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   10. Simplified 82.9%

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

   if -2.2999999999999999e-15 < NaChar < -1.85000000000000012e-75

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.1%

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

   6. Taylor expanded in KbT around -inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   8. Simplified 61.6%

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

   if -1.85000000000000012e-75 < NaChar < 1.47999999999999995e-12

   1. Initial program 100.0%

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

   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 72.5%

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

   6. Taylor expanded in Vef around 0 69.4%

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

      1. clear-num 69.4%

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

      2. inv-pow 69.4%

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

      3. associate-+r+ 69.4%

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

      4. metadata-eval 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. unpow-1 69.4%

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

   10. Simplified 69.4%

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

   11. Taylor expanded in Vef around inf 71.6%

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

       1. associate-*r/ 71.6%

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

       2. metadata-eval 71.6%

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

   13. Simplified 71.6%

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

   if 1.47999999999999995e-12 < 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 KbT around inf 71.2%

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

   6. Taylor expanded in EDonor around inf 80.4%

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

      1. associate-/r* 80.4%

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

      2. associate-/r* 78.6%

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

   8. Simplified 78.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.85 \cdot 10^{-75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.48 \cdot 10^{-12}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{Vef}{KbT} + \frac{mu}{KbT}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;t\_2 + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + t\_1\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - t\_0\\ \mathbf{elif}\;NaChar \leq -3.5 \cdot 10^{-72}:\\ \;\;\;\;t\_2 + \frac{NdChar}{Vef \cdot \left(\frac{1}{KbT} + \left(\left(\left(\frac{mu}{Vef \cdot KbT} + \frac{EDonor}{Vef \cdot KbT}\right) + \frac{2}{Vef}\right) - \frac{Ec}{Vef \cdot KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq 2.7 \cdot 10^{-12}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + t\_1\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (+ (/ Vef KbT) (/ mu KbT)))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
   (if (<= NaChar -1.9e+86)
     (+
      t_2
      (/ NdChar (* Ec (+ (/ (+ 2.0 (+ (/ EDonor KbT) t_1)) Ec) (/ -1.0 KbT)))))
     (if (<= NaChar -3.2e-15)
       (- (/ 1.0 (/ (+ 2.0 (/ Vef KbT)) NaChar)) t_0)
       (if (<= NaChar -3.5e-72)
         (+
          t_2
          (/
           NdChar
           (*
            Vef
            (+
             (/ 1.0 KbT)
             (-
              (+ (+ (/ mu (* Vef KbT)) (/ EDonor (* Vef KbT))) (/ 2.0 Vef))
              (/ Ec (* Vef KbT)))))))
         (if (<= NaChar 2.7e-12)
           (-
            (/ -1.0 (* Vef (- (/ -1.0 (* KbT NaChar)) (/ 2.0 (* Vef NaChar)))))
            t_0)
           (+
            t_2
            (/
             NdChar
             (*
              EDonor
              (+ (/ 1.0 KbT) (/ (- (+ 2.0 t_1) (/ Ec KbT)) EDonor)))))))))))

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 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.9e+86) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -3.2e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if (NaChar <= -3.5e-72) {
		tmp = t_2 + (NdChar / (Vef * ((1.0 / KbT) + ((((mu / (Vef * KbT)) + (EDonor / (Vef * KbT))) + (2.0 / Vef)) - (Ec / (Vef * KbT))))));
	} else if (NaChar <= 2.7e-12) {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	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 = (vef / kbt) + (mu / kbt)
    t_2 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    if (nachar <= (-1.9d+86)) then
        tmp = t_2 + (ndchar / (ec * (((2.0d0 + ((edonor / kbt) + t_1)) / ec) + ((-1.0d0) / kbt))))
    else if (nachar <= (-3.2d-15)) then
        tmp = (1.0d0 / ((2.0d0 + (vef / kbt)) / nachar)) - t_0
    else if (nachar <= (-3.5d-72)) then
        tmp = t_2 + (ndchar / (vef * ((1.0d0 / kbt) + ((((mu / (vef * kbt)) + (edonor / (vef * kbt))) + (2.0d0 / vef)) - (ec / (vef * kbt))))))
    else if (nachar <= 2.7d-12) then
        tmp = ((-1.0d0) / (vef * (((-1.0d0) / (kbt * nachar)) - (2.0d0 / (vef * nachar))))) - t_0
    else
        tmp = t_2 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + t_1) - (ec / kbt)) / edonor))))
    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 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -1.9e+86) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -3.2e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if (NaChar <= -3.5e-72) {
		tmp = t_2 + (NdChar / (Vef * ((1.0 / KbT) + ((((mu / (Vef * KbT)) + (EDonor / (Vef * KbT))) + (2.0 / Vef)) - (Ec / (Vef * KbT))))));
	} else if (NaChar <= 2.7e-12) {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	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 = (Vef / KbT) + (mu / KbT)
	t_2 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	tmp = 0
	if NaChar <= -1.9e+86:
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))))
	elif NaChar <= -3.2e-15:
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0
	elif NaChar <= -3.5e-72:
		tmp = t_2 + (NdChar / (Vef * ((1.0 / KbT) + ((((mu / (Vef * KbT)) + (EDonor / (Vef * KbT))) + (2.0 / Vef)) - (Ec / (Vef * KbT))))))
	elif NaChar <= 2.7e-12:
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0
	else:
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))))
	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(Vef / KbT) + Float64(mu / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.9e+86)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + t_1)) / Ec) + Float64(-1.0 / KbT)))));
	elseif (NaChar <= -3.2e-15)
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 + Float64(Vef / KbT)) / NaChar)) - t_0);
	elseif (NaChar <= -3.5e-72)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(Float64(mu / Float64(Vef * KbT)) + Float64(EDonor / Float64(Vef * KbT))) + Float64(2.0 / Vef)) - Float64(Ec / Float64(Vef * KbT)))))));
	elseif (NaChar <= 2.7e-12)
		tmp = Float64(Float64(-1.0 / Float64(Vef * Float64(Float64(-1.0 / Float64(KbT * NaChar)) - Float64(2.0 / Float64(Vef * NaChar))))) - t_0);
	else
		tmp = Float64(t_2 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + t_1) - Float64(Ec / KbT)) / EDonor)))));
	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 = (Vef / KbT) + (mu / KbT);
	t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.9e+86)
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	elseif (NaChar <= -3.2e-15)
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	elseif (NaChar <= -3.5e-72)
		tmp = t_2 + (NdChar / (Vef * ((1.0 / KbT) + ((((mu / (Vef * KbT)) + (EDonor / (Vef * KbT))) + (2.0 / Vef)) - (Ec / (Vef * KbT))))));
	elseif (NaChar <= 2.7e-12)
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	else
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	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[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.9e+86], N[(t$95$2 + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -3.2e-15], N[(N[(1.0 / N[(N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, -3.5e-72], N[(t$95$2 + N[(NdChar / N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(N[(mu / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 / Vef), $MachinePrecision]), $MachinePrecision] - N[(Ec / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.7e-12], N[(N[(-1.0 / N[(Vef * N[(N[(-1.0 / N[(KbT * NaChar), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(Vef * NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(t$95$2 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + t$95$1), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -1.89999999999999989e86

   1. Initial program 100.0%

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

   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 75.0%

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

   6. Taylor expanded in Ec around -inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. *-commutative 77.2%

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

      3. distribute-rgt-neg-in 77.2%

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

      4. +-commutative 77.2%

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

      5. mul-1-neg 77.2%

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

      6. unsub-neg 77.2%

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

   8. Simplified 77.2%

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

   if -1.89999999999999989e86 < NaChar < -3.1999999999999999e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.4%

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

   6. Taylor expanded in Vef around 0 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. associate-+r+ 82.9%

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

      4. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   10. Simplified 82.9%

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

   if -3.1999999999999999e-15 < NaChar < -3.5e-72

   1. Initial program 100.0%

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

   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 56.1%

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

   6. Taylor expanded in Vef around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. +-commutative 62.3%

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

      3. *-commutative 62.3%

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

      4. *-commutative 62.3%

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

      5. associate-*r/ 62.3%

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

      6. metadata-eval 62.3%

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

      7. *-commutative 62.3%

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

   8. Simplified 62.3%

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

   if -3.5e-72 < NaChar < 2.6999999999999998e-12

   1. Initial program 100.0%

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

   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 72.5%

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

   6. Taylor expanded in Vef around 0 69.4%

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

      1. clear-num 69.4%

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

      2. inv-pow 69.4%

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

      3. associate-+r+ 69.4%

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

      4. metadata-eval 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. unpow-1 69.4%

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

   10. Simplified 69.4%

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

   11. Taylor expanded in Vef around inf 71.6%

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

       1. associate-*r/ 71.6%

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

       2. metadata-eval 71.6%

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

   13. Simplified 71.6%

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

   if 2.6999999999999998e-12 < 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 KbT around inf 71.2%

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

   6. Taylor expanded in EDonor around -inf 83.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -3.5 \cdot 10^{-72}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{Vef \cdot \left(\frac{1}{KbT} + \left(\left(\left(\frac{mu}{Vef \cdot KbT} + \frac{EDonor}{Vef \cdot KbT}\right) + \frac{2}{Vef}\right) - \frac{Ec}{Vef \cdot KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq 2.7 \cdot 10^{-12}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{Vef}{KbT} + \frac{mu}{KbT}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+87}:\\ \;\;\;\;t\_2 + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + t\_1\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - t\_0\\ \mathbf{elif}\;NaChar \leq -1.85 \cdot 10^{-75}:\\ \;\;\;\;t\_2 + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.26 \cdot 10^{-11}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + t\_1\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (+ (/ Vef KbT) (/ mu KbT)))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
   (if (<= NaChar -6.8e+87)
     (+
      t_2
      (/ NdChar (* Ec (+ (/ (+ 2.0 (+ (/ EDonor KbT) t_1)) Ec) (/ -1.0 KbT)))))
     (if (<= NaChar -3.2e-15)
       (- (/ 1.0 (/ (+ 2.0 (/ Vef KbT)) NaChar)) t_0)
       (if (<= NaChar -1.85e-75)
         (+ t_2 (/ NdChar (+ 2.0 (/ (- (+ EDonor (+ mu Vef)) Ec) KbT))))
         (if (<= NaChar 1.26e-11)
           (-
            (/ -1.0 (* Vef (- (/ -1.0 (* KbT NaChar)) (/ 2.0 (* Vef NaChar)))))
            t_0)
           (+
            t_2
            (/
             NdChar
             (*
              EDonor
              (+ (/ 1.0 KbT) (/ (- (+ 2.0 t_1) (/ Ec KbT)) EDonor)))))))))))

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 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -6.8e+87) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -3.2e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if (NaChar <= -1.85e-75) {
		tmp = t_2 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	} else if (NaChar <= 1.26e-11) {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	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 = (vef / kbt) + (mu / kbt)
    t_2 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    if (nachar <= (-6.8d+87)) then
        tmp = t_2 + (ndchar / (ec * (((2.0d0 + ((edonor / kbt) + t_1)) / ec) + ((-1.0d0) / kbt))))
    else if (nachar <= (-3.2d-15)) then
        tmp = (1.0d0 / ((2.0d0 + (vef / kbt)) / nachar)) - t_0
    else if (nachar <= (-1.85d-75)) then
        tmp = t_2 + (ndchar / (2.0d0 + (((edonor + (mu + vef)) - ec) / kbt)))
    else if (nachar <= 1.26d-11) then
        tmp = ((-1.0d0) / (vef * (((-1.0d0) / (kbt * nachar)) - (2.0d0 / (vef * nachar))))) - t_0
    else
        tmp = t_2 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + t_1) - (ec / kbt)) / edonor))))
    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 = (Vef / KbT) + (mu / KbT);
	double t_2 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -6.8e+87) {
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -3.2e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if (NaChar <= -1.85e-75) {
		tmp = t_2 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	} else if (NaChar <= 1.26e-11) {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	} else {
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	}
	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 = (Vef / KbT) + (mu / KbT)
	t_2 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	tmp = 0
	if NaChar <= -6.8e+87:
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))))
	elif NaChar <= -3.2e-15:
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0
	elif NaChar <= -1.85e-75:
		tmp = t_2 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)))
	elif NaChar <= 1.26e-11:
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0
	else:
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))))
	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(Vef / KbT) + Float64(mu / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	tmp = 0.0
	if (NaChar <= -6.8e+87)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + t_1)) / Ec) + Float64(-1.0 / KbT)))));
	elseif (NaChar <= -3.2e-15)
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 + Float64(Vef / KbT)) / NaChar)) - t_0);
	elseif (NaChar <= -1.85e-75)
		tmp = Float64(t_2 + Float64(NdChar / Float64(2.0 + Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT))));
	elseif (NaChar <= 1.26e-11)
		tmp = Float64(Float64(-1.0 / Float64(Vef * Float64(Float64(-1.0 / Float64(KbT * NaChar)) - Float64(2.0 / Float64(Vef * NaChar))))) - t_0);
	else
		tmp = Float64(t_2 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + t_1) - Float64(Ec / KbT)) / EDonor)))));
	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 = (Vef / KbT) + (mu / KbT);
	t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -6.8e+87)
		tmp = t_2 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + t_1)) / Ec) + (-1.0 / KbT))));
	elseif (NaChar <= -3.2e-15)
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	elseif (NaChar <= -1.85e-75)
		tmp = t_2 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	elseif (NaChar <= 1.26e-11)
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	else
		tmp = t_2 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + t_1) - (Ec / KbT)) / EDonor))));
	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[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.8e+87], N[(t$95$2 + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -3.2e-15], N[(N[(1.0 / N[(N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NaChar, -1.85e-75], N[(t$95$2 + N[(NdChar / N[(2.0 + N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.26e-11], N[(N[(-1.0 / N[(Vef * N[(N[(-1.0 / N[(KbT * NaChar), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(Vef * NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(t$95$2 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + t$95$1), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -6.8000000000000004e87

   1. Initial program 100.0%

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

   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 75.0%

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

   6. Taylor expanded in Ec around -inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. *-commutative 77.2%

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

      3. distribute-rgt-neg-in 77.2%

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

      4. +-commutative 77.2%

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

      5. mul-1-neg 77.2%

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

      6. unsub-neg 77.2%

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

   8. Simplified 77.2%

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

   if -6.8000000000000004e87 < NaChar < -3.1999999999999999e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.4%

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

   6. Taylor expanded in Vef around 0 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. associate-+r+ 82.9%

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

      4. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   10. Simplified 82.9%

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

   if -3.1999999999999999e-15 < NaChar < -1.85000000000000012e-75

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.1%

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

   6. Taylor expanded in KbT around -inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   8. Simplified 61.6%

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

   if -1.85000000000000012e-75 < NaChar < 1.26e-11

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.5%

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

   6. Taylor expanded in Vef around 0 69.4%

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

      1. clear-num 69.4%

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

      2. inv-pow 69.4%

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

      3. associate-+r+ 69.4%

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

      4. metadata-eval 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. unpow-1 69.4%

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

   10. Simplified 69.4%

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

   11. Taylor expanded in Vef around inf 71.6%

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

       1. associate-*r/ 71.6%

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

       2. metadata-eval 71.6%

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

   13. Simplified 71.6%

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

   if 1.26e-11 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.2%

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

   6. Taylor expanded in EDonor around -inf 83.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.85 \cdot 10^{-75}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.26 \cdot 10^{-11}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ t_1 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := NaChar \cdot 0.5 - t\_1\\ t_3 := KbT \cdot \frac{NaChar}{Vef} - t\_1\\ \mathbf{if}\;NaChar \leq -1.38 \cdot 10^{+163}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -2.1 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -3 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -1.16 \cdot 10^{-205}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;NaChar \leq -5.8 \cdot 10^{-290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 1.02 \cdot 10^{-218}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
          (/ NdChar 2.0)))
        (t_1 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_2 (- (* NaChar 0.5) t_1))
        (t_3 (- (* KbT (/ NaChar Vef)) t_1)))
   (if (<= NaChar -1.38e+163)
     t_0
     (if (<= NaChar -2.1e-21)
       t_2
       (if (<= NaChar -3e-38)
         t_0
         (if (<= NaChar -1.16e-205)
           t_3
           (if (<= NaChar -5.8e-290)
             t_2
             (if (<= NaChar 1.02e-218)
               t_3
               (if (<= NaChar 8e-38) t_2 t_0)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	double t_1 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = (NaChar * 0.5) - t_1;
	double t_3 = (KbT * (NaChar / Vef)) - t_1;
	double tmp;
	if (NaChar <= -1.38e+163) {
		tmp = t_0;
	} else if (NaChar <= -2.1e-21) {
		tmp = t_2;
	} else if (NaChar <= -3e-38) {
		tmp = t_0;
	} else if (NaChar <= -1.16e-205) {
		tmp = t_3;
	} else if (NaChar <= -5.8e-290) {
		tmp = t_2;
	} else if (NaChar <= 1.02e-218) {
		tmp = t_3;
	} else if (NaChar <= 8e-38) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / 2.0d0)
    t_1 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_2 = (nachar * 0.5d0) - t_1
    t_3 = (kbt * (nachar / vef)) - t_1
    if (nachar <= (-1.38d+163)) then
        tmp = t_0
    else if (nachar <= (-2.1d-21)) then
        tmp = t_2
    else if (nachar <= (-3d-38)) then
        tmp = t_0
    else if (nachar <= (-1.16d-205)) then
        tmp = t_3
    else if (nachar <= (-5.8d-290)) then
        tmp = t_2
    else if (nachar <= 1.02d-218) then
        tmp = t_3
    else if (nachar <= 8d-38) then
        tmp = t_2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	double t_1 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = (NaChar * 0.5) - t_1;
	double t_3 = (KbT * (NaChar / Vef)) - t_1;
	double tmp;
	if (NaChar <= -1.38e+163) {
		tmp = t_0;
	} else if (NaChar <= -2.1e-21) {
		tmp = t_2;
	} else if (NaChar <= -3e-38) {
		tmp = t_0;
	} else if (NaChar <= -1.16e-205) {
		tmp = t_3;
	} else if (NaChar <= -5.8e-290) {
		tmp = t_2;
	} else if (NaChar <= 1.02e-218) {
		tmp = t_3;
	} else if (NaChar <= 8e-38) {
		tmp = t_2;
	} 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 + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0)
	t_1 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_2 = (NaChar * 0.5) - t_1
	t_3 = (KbT * (NaChar / Vef)) - t_1
	tmp = 0
	if NaChar <= -1.38e+163:
		tmp = t_0
	elif NaChar <= -2.1e-21:
		tmp = t_2
	elif NaChar <= -3e-38:
		tmp = t_0
	elif NaChar <= -1.16e-205:
		tmp = t_3
	elif NaChar <= -5.8e-290:
		tmp = t_2
	elif NaChar <= 1.02e-218:
		tmp = t_3
	elif NaChar <= 8e-38:
		tmp = t_2
	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(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / 2.0))
	t_1 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(Float64(NaChar * 0.5) - t_1)
	t_3 = Float64(Float64(KbT * Float64(NaChar / Vef)) - t_1)
	tmp = 0.0
	if (NaChar <= -1.38e+163)
		tmp = t_0;
	elseif (NaChar <= -2.1e-21)
		tmp = t_2;
	elseif (NaChar <= -3e-38)
		tmp = t_0;
	elseif (NaChar <= -1.16e-205)
		tmp = t_3;
	elseif (NaChar <= -5.8e-290)
		tmp = t_2;
	elseif (NaChar <= 1.02e-218)
		tmp = t_3;
	elseif (NaChar <= 8e-38)
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	t_1 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_2 = (NaChar * 0.5) - t_1;
	t_3 = (KbT * (NaChar / Vef)) - t_1;
	tmp = 0.0;
	if (NaChar <= -1.38e+163)
		tmp = t_0;
	elseif (NaChar <= -2.1e-21)
		tmp = t_2;
	elseif (NaChar <= -3e-38)
		tmp = t_0;
	elseif (NaChar <= -1.16e-205)
		tmp = t_3;
	elseif (NaChar <= -5.8e-290)
		tmp = t_2;
	elseif (NaChar <= 1.02e-218)
		tmp = t_3;
	elseif (NaChar <= 8e-38)
		tmp = t_2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar * 0.5), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(KbT * N[(NaChar / Vef), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[NaChar, -1.38e+163], t$95$0, If[LessEqual[NaChar, -2.1e-21], t$95$2, If[LessEqual[NaChar, -3e-38], t$95$0, If[LessEqual[NaChar, -1.16e-205], t$95$3, If[LessEqual[NaChar, -5.8e-290], t$95$2, If[LessEqual[NaChar, 1.02e-218], t$95$3, If[LessEqual[NaChar, 8e-38], t$95$2, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.38000000000000004e163 or -2.10000000000000013e-21 < NaChar < -2.99999999999999989e-38 or 7.9999999999999997e-38 < 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 KbT around inf 66.0%

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

   if -1.38000000000000004e163 < NaChar < -2.10000000000000013e-21 or -1.1600000000000001e-205 < NaChar < -5.79999999999999989e-290 or 1.02e-218 < NaChar < 7.9999999999999997e-38

   1. Initial program 100.0%

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

   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 63.5%

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

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   if -2.99999999999999989e-38 < NaChar < -1.1600000000000001e-205 or -5.79999999999999989e-290 < NaChar < 1.02e-218

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.8%

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

   6. Taylor expanded in Vef around 0 66.4%

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

   7. Taylor expanded in Vef around inf 65.3%

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

      1. associate-/l* 61.5%

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

   9. Simplified 61.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.38 \cdot 10^{+163}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq -2.1 \cdot 10^{-21}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -3 \cdot 10^{-38}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq -1.16 \cdot 10^{-205}:\\ \;\;\;\;KbT \cdot \frac{NaChar}{Vef} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -5.8 \cdot 10^{-290}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.02 \cdot 10^{-218}:\\ \;\;\;\;KbT \cdot \frac{NaChar}{Vef} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{-38}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}\\ t_1 := \frac{NdChar}{-1 - t\_0}\\ t_2 := 2 + \frac{Vef}{KbT}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{t\_2 - \frac{Ec}{KbT}}\\ \mathbf{if}\;NaChar \leq -1.65 \cdot 10^{+87}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;NaChar \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{t\_2}{NaChar}} - t\_1\\ \mathbf{elif}\;NaChar \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;NaChar \leq -2.65 \cdot 10^{-102}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NaChar \leq 3.35 \cdot 10^{-12}:\\ \;\;\;\;\frac{NaChar}{1 + \left(1 + \frac{Vef}{KbT}\right)} - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))
        (t_1 (/ NdChar (- -1.0 t_0)))
        (t_2 (+ 2.0 (/ Vef KbT)))
        (t_3
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
          (/ NdChar (- t_2 (/ Ec KbT))))))
   (if (<= NaChar -1.65e+87)
     t_3
     (if (<= NaChar -3.8e-15)
       (- (/ 1.0 (/ t_2 NaChar)) t_1)
       (if (<= NaChar -2.8e-38)
         t_3
         (if (<= NaChar -2.65e-102)
           (+ (/ NdChar (+ 1.0 t_0)) (/ (* KbT NaChar) Vef))
           (if (<= NaChar 3.35e-12)
             (- (/ NaChar (+ 1.0 (+ 1.0 (/ Vef KbT)))) t_1)
             t_3)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = NdChar / (-1.0 - t_0);
	double t_2 = 2.0 + (Vef / KbT);
	double t_3 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (t_2 - (Ec / KbT)));
	double tmp;
	if (NaChar <= -1.65e+87) {
		tmp = t_3;
	} else if (NaChar <= -3.8e-15) {
		tmp = (1.0 / (t_2 / NaChar)) - t_1;
	} else if (NaChar <= -2.8e-38) {
		tmp = t_3;
	} else if (NaChar <= -2.65e-102) {
		tmp = (NdChar / (1.0 + t_0)) + ((KbT * NaChar) / Vef);
	} else if (NaChar <= 3.35e-12) {
		tmp = (NaChar / (1.0 + (1.0 + (Vef / KbT)))) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = exp(((edonor + (mu + (vef - ec))) / kbt))
    t_1 = ndchar / ((-1.0d0) - t_0)
    t_2 = 2.0d0 + (vef / kbt)
    t_3 = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (t_2 - (ec / kbt)))
    if (nachar <= (-1.65d+87)) then
        tmp = t_3
    else if (nachar <= (-3.8d-15)) then
        tmp = (1.0d0 / (t_2 / nachar)) - t_1
    else if (nachar <= (-2.8d-38)) then
        tmp = t_3
    else if (nachar <= (-2.65d-102)) then
        tmp = (ndchar / (1.0d0 + t_0)) + ((kbt * nachar) / vef)
    else if (nachar <= 3.35d-12) then
        tmp = (nachar / (1.0d0 + (1.0d0 + (vef / kbt)))) - t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = NdChar / (-1.0 - t_0);
	double t_2 = 2.0 + (Vef / KbT);
	double t_3 = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (t_2 - (Ec / KbT)));
	double tmp;
	if (NaChar <= -1.65e+87) {
		tmp = t_3;
	} else if (NaChar <= -3.8e-15) {
		tmp = (1.0 / (t_2 / NaChar)) - t_1;
	} else if (NaChar <= -2.8e-38) {
		tmp = t_3;
	} else if (NaChar <= -2.65e-102) {
		tmp = (NdChar / (1.0 + t_0)) + ((KbT * NaChar) / Vef);
	} else if (NaChar <= 3.35e-12) {
		tmp = (NaChar / (1.0 + (1.0 + (Vef / KbT)))) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))
	t_1 = NdChar / (-1.0 - t_0)
	t_2 = 2.0 + (Vef / KbT)
	t_3 = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (t_2 - (Ec / KbT)))
	tmp = 0
	if NaChar <= -1.65e+87:
		tmp = t_3
	elif NaChar <= -3.8e-15:
		tmp = (1.0 / (t_2 / NaChar)) - t_1
	elif NaChar <= -2.8e-38:
		tmp = t_3
	elif NaChar <= -2.65e-102:
		tmp = (NdChar / (1.0 + t_0)) + ((KbT * NaChar) / Vef)
	elif NaChar <= 3.35e-12:
		tmp = (NaChar / (1.0 + (1.0 + (Vef / KbT)))) - t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))
	t_1 = Float64(NdChar / Float64(-1.0 - t_0))
	t_2 = Float64(2.0 + Float64(Vef / KbT))
	t_3 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(t_2 - Float64(Ec / KbT))))
	tmp = 0.0
	if (NaChar <= -1.65e+87)
		tmp = t_3;
	elseif (NaChar <= -3.8e-15)
		tmp = Float64(Float64(1.0 / Float64(t_2 / NaChar)) - t_1);
	elseif (NaChar <= -2.8e-38)
		tmp = t_3;
	elseif (NaChar <= -2.65e-102)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) + Float64(Float64(KbT * NaChar) / Vef));
	elseif (NaChar <= 3.35e-12)
		tmp = Float64(Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Vef / KbT)))) - t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	t_1 = NdChar / (-1.0 - t_0);
	t_2 = 2.0 + (Vef / KbT);
	t_3 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (t_2 - (Ec / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.65e+87)
		tmp = t_3;
	elseif (NaChar <= -3.8e-15)
		tmp = (1.0 / (t_2 / NaChar)) - t_1;
	elseif (NaChar <= -2.8e-38)
		tmp = t_3;
	elseif (NaChar <= -2.65e-102)
		tmp = (NdChar / (1.0 + t_0)) + ((KbT * NaChar) / Vef);
	elseif (NaChar <= 3.35e-12)
		tmp = (NaChar / (1.0 + (1.0 + (Vef / KbT)))) - t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(t$95$2 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.65e+87], t$95$3, If[LessEqual[NaChar, -3.8e-15], N[(N[(1.0 / N[(t$95$2 / NaChar), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[NaChar, -2.8e-38], t$95$3, If[LessEqual[NaChar, -2.65e-102], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.35e-12], N[(N[(NaChar / N[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.6500000000000001e87 or -3.8000000000000002e-15 < NaChar < -2.8e-38 or 3.3500000000000001e-12 < 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 KbT around inf 73.4%

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

   6. Taylor expanded in EDonor around inf 75.9%

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

      1. associate-/r* 76.3%

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

      2. associate-/r* 76.2%

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

   8. Simplified 76.2%

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

   9. Taylor expanded in Vef around inf 75.3%

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

   if -1.6500000000000001e87 < NaChar < -3.8000000000000002e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.4%

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

   6. Taylor expanded in Vef around 0 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. associate-+r+ 82.9%

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

      4. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   10. Simplified 82.9%

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

   if -2.8e-38 < NaChar < -2.6500000000000001e-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. Taylor expanded in Vef around inf 73.8%

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

   6. Taylor expanded in Vef around 0 51.3%

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

   7. Taylor expanded in Vef around inf 55.1%

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

   if -2.6500000000000001e-102 < NaChar < 3.3500000000000001e-12

   1. Initial program 100.0%

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

   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 72.5%

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

   6. Taylor expanded in Vef around 0 70.0%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.65 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{Vef}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{Vef}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2.65 \cdot 10^{-102}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NaChar \leq 3.35 \cdot 10^{-12}:\\ \;\;\;\;\frac{NaChar}{1 + \left(1 + \frac{Vef}{KbT}\right)} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{Vef}{KbT}\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ t_1 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - t\_1\\ \mathbf{elif}\;NaChar \leq -3.9 \cdot 10^{-73} \lor \neg \left(NaChar \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
          (/ NdChar (+ 2.0 (/ (- (+ EDonor (+ mu Vef)) Ec) KbT)))))
        (t_1 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NaChar -1.9e+86)
     t_0
     (if (<= NaChar -2e-15)
       (- (/ 1.0 (/ (+ 2.0 (/ Vef KbT)) NaChar)) t_1)
       (if (or (<= NaChar -3.9e-73) (not (<= NaChar 5e-9)))
         t_0
         (-
          (/ -1.0 (* Vef (- (/ -1.0 (* KbT NaChar)) (/ 2.0 (* Vef NaChar)))))
          t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	double t_1 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NaChar <= -1.9e+86) {
		tmp = t_0;
	} else if (NaChar <= -2e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_1;
	} else if ((NaChar <= -3.9e-73) || !(NaChar <= 5e-9)) {
		tmp = t_0;
	} else {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (2.0d0 + (((edonor + (mu + vef)) - ec) / kbt)))
    t_1 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (nachar <= (-1.9d+86)) then
        tmp = t_0
    else if (nachar <= (-2d-15)) then
        tmp = (1.0d0 / ((2.0d0 + (vef / kbt)) / nachar)) - t_1
    else if ((nachar <= (-3.9d-73)) .or. (.not. (nachar <= 5d-9))) then
        tmp = t_0
    else
        tmp = ((-1.0d0) / (vef * (((-1.0d0) / (kbt * nachar)) - (2.0d0 / (vef * nachar))))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	double t_1 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NaChar <= -1.9e+86) {
		tmp = t_0;
	} else if (NaChar <= -2e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_1;
	} else if ((NaChar <= -3.9e-73) || !(NaChar <= 5e-9)) {
		tmp = t_0;
	} else {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)))
	t_1 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NaChar <= -1.9e+86:
		tmp = t_0
	elif NaChar <= -2e-15:
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_1
	elif (NaChar <= -3.9e-73) or not (NaChar <= 5e-9):
		tmp = t_0
	else:
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(2.0 + Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT))))
	t_1 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.9e+86)
		tmp = t_0;
	elseif (NaChar <= -2e-15)
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 + Float64(Vef / KbT)) / NaChar)) - t_1);
	elseif ((NaChar <= -3.9e-73) || !(NaChar <= 5e-9))
		tmp = t_0;
	else
		tmp = Float64(Float64(-1.0 / Float64(Vef * Float64(Float64(-1.0 / Float64(KbT * NaChar)) - Float64(2.0 / Float64(Vef * NaChar))))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	t_1 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.9e+86)
		tmp = t_0;
	elseif (NaChar <= -2e-15)
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_1;
	elseif ((NaChar <= -3.9e-73) || ~((NaChar <= 5e-9)))
		tmp = t_0;
	else
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_1;
	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[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.9e+86], t$95$0, If[LessEqual[NaChar, -2e-15], N[(N[(1.0 / N[(N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[Or[LessEqual[NaChar, -3.9e-73], N[Not[LessEqual[NaChar, 5e-9]], $MachinePrecision]], t$95$0, N[(N[(-1.0 / N[(Vef * N[(N[(-1.0 / N[(KbT * NaChar), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(Vef * NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.89999999999999989e86 or -2.0000000000000002e-15 < NaChar < -3.89999999999999982e-73 or 5.0000000000000001e-9 < 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 KbT around inf 70.1%

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

   6. Taylor expanded in KbT around -inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. unsub-neg 74.2%

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

   8. Simplified 74.2%

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

   if -1.89999999999999989e86 < NaChar < -2.0000000000000002e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.4%

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

   6. Taylor expanded in Vef around 0 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. associate-+r+ 82.9%

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

      4. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   10. Simplified 82.9%

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

   if -3.89999999999999982e-73 < NaChar < 5.0000000000000001e-9

   1. Initial program 100.0%

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

   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 72.5%

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

   6. Taylor expanded in Vef around 0 69.4%

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

      1. clear-num 69.4%

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

      2. inv-pow 69.4%

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

      3. associate-+r+ 69.4%

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

      4. metadata-eval 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. unpow-1 69.4%

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

   10. Simplified 69.4%

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

   11. Taylor expanded in Vef around inf 71.6%

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

       1. associate-*r/ 71.6%

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

       2. metadata-eval 71.6%

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

   13. Simplified 71.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -3.9 \cdot 10^{-73} \lor \neg \left(NaChar \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{+86}:\\ \;\;\;\;t\_1 + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.9 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - t\_0\\ \mathbf{elif}\;NaChar \leq -1 \cdot 10^{-78} \lor \neg \left(NaChar \leq 2.2 \cdot 10^{-13}\right):\\ \;\;\;\;t\_1 + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
   (if (<= NaChar -2.7e+86)
     (+
      t_1
      (/
       NdChar
       (*
        Ec
        (+
         (/ (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) Ec)
         (/ -1.0 KbT)))))
     (if (<= NaChar -2.9e-15)
       (- (/ 1.0 (/ (+ 2.0 (/ Vef KbT)) NaChar)) t_0)
       (if (or (<= NaChar -1e-78) (not (<= NaChar 2.2e-13)))
         (+ t_1 (/ NdChar (+ 2.0 (/ (- (+ EDonor (+ mu Vef)) Ec) KbT))))
         (-
          (/ -1.0 (* Vef (- (/ -1.0 (* KbT NaChar)) (/ 2.0 (* Vef NaChar)))))
          t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -2.7e+86) {
		tmp = t_1 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -2.9e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if ((NaChar <= -1e-78) || !(NaChar <= 2.2e-13)) {
		tmp = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	} else {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    if (nachar <= (-2.7d+86)) then
        tmp = t_1 + (ndchar / (ec * (((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) / ec) + ((-1.0d0) / kbt))))
    else if (nachar <= (-2.9d-15)) then
        tmp = (1.0d0 / ((2.0d0 + (vef / kbt)) / nachar)) - t_0
    else if ((nachar <= (-1d-78)) .or. (.not. (nachar <= 2.2d-13))) then
        tmp = t_1 + (ndchar / (2.0d0 + (((edonor + (mu + vef)) - ec) / kbt)))
    else
        tmp = ((-1.0d0) / (vef * (((-1.0d0) / (kbt * nachar)) - (2.0d0 / (vef * nachar))))) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NaChar <= -2.7e+86) {
		tmp = t_1 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))));
	} else if (NaChar <= -2.9e-15) {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	} else if ((NaChar <= -1e-78) || !(NaChar <= 2.2e-13)) {
		tmp = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	} else {
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_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)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	tmp = 0
	if NaChar <= -2.7e+86:
		tmp = t_1 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))))
	elif NaChar <= -2.9e-15:
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0
	elif (NaChar <= -1e-78) or not (NaChar <= 2.2e-13):
		tmp = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)))
	else:
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.7e+86)
		tmp = Float64(t_1 + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / KbT)))));
	elseif (NaChar <= -2.9e-15)
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 + Float64(Vef / KbT)) / NaChar)) - t_0);
	elseif ((NaChar <= -1e-78) || !(NaChar <= 2.2e-13))
		tmp = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT))));
	else
		tmp = Float64(Float64(-1.0 / Float64(Vef * Float64(Float64(-1.0 / Float64(KbT * NaChar)) - Float64(2.0 / Float64(Vef * NaChar))))) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.7e+86)
		tmp = t_1 + (NdChar / (Ec * (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))));
	elseif (NaChar <= -2.9e-15)
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - t_0;
	elseif ((NaChar <= -1e-78) || ~((NaChar <= 2.2e-13)))
		tmp = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	else
		tmp = (-1.0 / (Vef * ((-1.0 / (KbT * NaChar)) - (2.0 / (Vef * NaChar))))) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.7e+86], N[(t$95$1 + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2.9e-15], N[(N[(1.0 / N[(N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[Or[LessEqual[NaChar, -1e-78], N[Not[LessEqual[NaChar, 2.2e-13]], $MachinePrecision]], N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(Vef * N[(N[(-1.0 / N[(KbT * NaChar), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(Vef * NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.70000000000000018e86

   1. Initial program 100.0%

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

   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 75.0%

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

   6. Taylor expanded in Ec around -inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. *-commutative 77.2%

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

      3. distribute-rgt-neg-in 77.2%

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

      4. +-commutative 77.2%

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

      5. mul-1-neg 77.2%

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

      6. unsub-neg 77.2%

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

   8. Simplified 77.2%

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

   if -2.70000000000000018e86 < NaChar < -2.90000000000000019e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.4%

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

   6. Taylor expanded in Vef around 0 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. associate-+r+ 82.9%

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

      4. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   10. Simplified 82.9%

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

   if -2.90000000000000019e-15 < NaChar < -9.99999999999999999e-79 or 2.19999999999999997e-13 < 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 KbT around inf 67.6%

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

   6. Taylor expanded in KbT around -inf 73.7%

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

      1. mul-1-neg 73.7%

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

      2. unsub-neg 73.7%

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

   8. Simplified 73.7%

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

   if -9.99999999999999999e-79 < NaChar < 2.19999999999999997e-13

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.5%

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

   6. Taylor expanded in Vef around 0 69.4%

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

      1. clear-num 69.4%

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

      2. inv-pow 69.4%

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

      3. associate-+r+ 69.4%

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

      4. metadata-eval 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. unpow-1 69.4%

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

   10. Simplified 69.4%

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

   11. Taylor expanded in Vef around inf 71.6%

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

       1. associate-*r/ 71.6%

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

       2. metadata-eval 71.6%

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

   13. Simplified 71.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.9 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1 \cdot 10^{-78} \lor \neg \left(NaChar \leq 2.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{Vef \cdot \left(\frac{-1}{KbT \cdot NaChar} - \frac{2}{Vef \cdot NaChar}\right)} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := 2 + \frac{Vef}{KbT}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{t\_1 - \frac{Ec}{KbT}}\\ \mathbf{if}\;NaChar \leq -4.8 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -2.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{NaChar}} - t\_0\\ \mathbf{elif}\;NaChar \leq -2.7 \cdot 10^{-37} \lor \neg \left(NaChar \leq 9.8 \cdot 10^{-11}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot \frac{KbT}{NaChar} + \frac{Vef}{NaChar}}{KbT}} - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (+ 2.0 (/ Vef KbT)))
        (t_2
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
          (/ NdChar (- t_1 (/ Ec KbT))))))
   (if (<= NaChar -4.8e+87)
     t_2
     (if (<= NaChar -2.2e-15)
       (- (/ 1.0 (/ t_1 NaChar)) t_0)
       (if (or (<= NaChar -2.7e-37) (not (<= NaChar 9.8e-11)))
         t_2
         (- (/ 1.0 (/ (+ (* 2.0 (/ KbT NaChar)) (/ Vef NaChar)) KbT)) t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = 2.0 + (Vef / KbT);
	double t_2 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (t_1 - (Ec / KbT)));
	double tmp;
	if (NaChar <= -4.8e+87) {
		tmp = t_2;
	} else if (NaChar <= -2.2e-15) {
		tmp = (1.0 / (t_1 / NaChar)) - t_0;
	} else if ((NaChar <= -2.7e-37) || !(NaChar <= 9.8e-11)) {
		tmp = t_2;
	} else {
		tmp = (1.0 / (((2.0 * (KbT / NaChar)) + (Vef / NaChar)) / KbT)) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = 2.0d0 + (vef / kbt)
    t_2 = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / (t_1 - (ec / kbt)))
    if (nachar <= (-4.8d+87)) then
        tmp = t_2
    else if (nachar <= (-2.2d-15)) then
        tmp = (1.0d0 / (t_1 / nachar)) - t_0
    else if ((nachar <= (-2.7d-37)) .or. (.not. (nachar <= 9.8d-11))) then
        tmp = t_2
    else
        tmp = (1.0d0 / (((2.0d0 * (kbt / nachar)) + (vef / nachar)) / kbt)) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = 2.0 + (Vef / KbT);
	double t_2 = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (t_1 - (Ec / KbT)));
	double tmp;
	if (NaChar <= -4.8e+87) {
		tmp = t_2;
	} else if (NaChar <= -2.2e-15) {
		tmp = (1.0 / (t_1 / NaChar)) - t_0;
	} else if ((NaChar <= -2.7e-37) || !(NaChar <= 9.8e-11)) {
		tmp = t_2;
	} else {
		tmp = (1.0 / (((2.0 * (KbT / NaChar)) + (Vef / NaChar)) / KbT)) - t_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)))
	t_1 = 2.0 + (Vef / KbT)
	t_2 = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (t_1 - (Ec / KbT)))
	tmp = 0
	if NaChar <= -4.8e+87:
		tmp = t_2
	elif NaChar <= -2.2e-15:
		tmp = (1.0 / (t_1 / NaChar)) - t_0
	elif (NaChar <= -2.7e-37) or not (NaChar <= 9.8e-11):
		tmp = t_2
	else:
		tmp = (1.0 / (((2.0 * (KbT / NaChar)) + (Vef / NaChar)) / KbT)) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(2.0 + Float64(Vef / KbT))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / Float64(t_1 - Float64(Ec / KbT))))
	tmp = 0.0
	if (NaChar <= -4.8e+87)
		tmp = t_2;
	elseif (NaChar <= -2.2e-15)
		tmp = Float64(Float64(1.0 / Float64(t_1 / NaChar)) - t_0);
	elseif ((NaChar <= -2.7e-37) || !(NaChar <= 9.8e-11))
		tmp = t_2;
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(Float64(2.0 * Float64(KbT / NaChar)) + Float64(Vef / NaChar)) / KbT)) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = 2.0 + (Vef / KbT);
	t_2 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / (t_1 - (Ec / KbT)));
	tmp = 0.0;
	if (NaChar <= -4.8e+87)
		tmp = t_2;
	elseif (NaChar <= -2.2e-15)
		tmp = (1.0 / (t_1 / NaChar)) - t_0;
	elseif ((NaChar <= -2.7e-37) || ~((NaChar <= 9.8e-11)))
		tmp = t_2;
	else
		tmp = (1.0 / (((2.0 * (KbT / NaChar)) + (Vef / NaChar)) / KbT)) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(t$95$1 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.8e+87], t$95$2, If[LessEqual[NaChar, -2.2e-15], N[(N[(1.0 / N[(t$95$1 / NaChar), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[Or[LessEqual[NaChar, -2.7e-37], N[Not[LessEqual[NaChar, 9.8e-11]], $MachinePrecision]], t$95$2, N[(N[(1.0 / N[(N[(N[(2.0 * N[(KbT / NaChar), $MachinePrecision]), $MachinePrecision] + N[(Vef / NaChar), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -4.79999999999999963e87 or -2.19999999999999986e-15 < NaChar < -2.70000000000000016e-37 or 9.7999999999999998e-11 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 74.0%

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

   6. Taylor expanded in EDonor around inf 76.5%

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

      1. associate-/r* 76.9%

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

      2. associate-/r* 76.8%

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

   8. Simplified 76.8%

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

   9. Taylor expanded in Vef around inf 75.8%

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

   if -4.79999999999999963e87 < NaChar < -2.19999999999999986e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.4%

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

   6. Taylor expanded in Vef around 0 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. associate-+r+ 82.9%

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

      4. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   10. Simplified 82.9%

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

   if -2.70000000000000016e-37 < NaChar < 9.7999999999999998e-11

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.2%

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

   6. Taylor expanded in Vef around 0 66.6%

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

      1. clear-num 66.5%

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

      2. inv-pow 66.5%

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

      3. associate-+r+ 66.5%

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

      4. metadata-eval 66.5%

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

   8. Applied egg-rr 66.5%

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

      1. unpow-1 66.5%

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

   10. Simplified 66.5%

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

   11. Taylor expanded in KbT around 0 68.8%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{Vef}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.7 \cdot 10^{-37} \lor \neg \left(NaChar \leq 9.8 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{Vef}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot \frac{KbT}{NaChar} + \frac{Vef}{NaChar}}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 + \frac{Vef}{KbT}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ t_3 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.25 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{t\_0}{NaChar}} - t\_3\\ \mathbf{elif}\;NaChar \leq -2.4 \cdot 10^{-36}:\\ \;\;\;\;t\_1 + \frac{NdChar}{t\_0 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 10^{-10}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot \frac{KbT}{NaChar} + \frac{Vef}{NaChar}}{KbT}} - t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 2.0 (/ Vef KbT)))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_2 (+ t_1 (/ NdChar (+ 2.0 (/ (- (+ EDonor (+ mu Vef)) Ec) KbT)))))
        (t_3 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NaChar -2.25e+86)
     t_2
     (if (<= NaChar -2e-15)
       (- (/ 1.0 (/ t_0 NaChar)) t_3)
       (if (<= NaChar -2.4e-36)
         (+ t_1 (/ NdChar (- t_0 (/ Ec KbT))))
         (if (<= NaChar 1e-10)
           (- (/ 1.0 (/ (+ (* 2.0 (/ KbT NaChar)) (/ Vef NaChar)) KbT)) t_3)
           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 = 2.0 + (Vef / KbT);
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	double t_3 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NaChar <= -2.25e+86) {
		tmp = t_2;
	} else if (NaChar <= -2e-15) {
		tmp = (1.0 / (t_0 / NaChar)) - t_3;
	} else if (NaChar <= -2.4e-36) {
		tmp = t_1 + (NdChar / (t_0 - (Ec / KbT)));
	} else if (NaChar <= 1e-10) {
		tmp = (1.0 / (((2.0 * (KbT / NaChar)) + (Vef / NaChar)) / KbT)) - t_3;
	} 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 = 2.0d0 + (vef / kbt)
    t_1 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    t_2 = t_1 + (ndchar / (2.0d0 + (((edonor + (mu + vef)) - ec) / kbt)))
    t_3 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (nachar <= (-2.25d+86)) then
        tmp = t_2
    else if (nachar <= (-2d-15)) then
        tmp = (1.0d0 / (t_0 / nachar)) - t_3
    else if (nachar <= (-2.4d-36)) then
        tmp = t_1 + (ndchar / (t_0 - (ec / kbt)))
    else if (nachar <= 1d-10) then
        tmp = (1.0d0 / (((2.0d0 * (kbt / nachar)) + (vef / nachar)) / kbt)) - t_3
    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 = 2.0 + (Vef / KbT);
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_2 = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	double t_3 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NaChar <= -2.25e+86) {
		tmp = t_2;
	} else if (NaChar <= -2e-15) {
		tmp = (1.0 / (t_0 / NaChar)) - t_3;
	} else if (NaChar <= -2.4e-36) {
		tmp = t_1 + (NdChar / (t_0 - (Ec / KbT)));
	} else if (NaChar <= 1e-10) {
		tmp = (1.0 / (((2.0 * (KbT / NaChar)) + (Vef / NaChar)) / KbT)) - t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 2.0 + (Vef / KbT)
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	t_2 = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)))
	t_3 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NaChar <= -2.25e+86:
		tmp = t_2
	elif NaChar <= -2e-15:
		tmp = (1.0 / (t_0 / NaChar)) - t_3
	elif NaChar <= -2.4e-36:
		tmp = t_1 + (NdChar / (t_0 - (Ec / KbT)))
	elif NaChar <= 1e-10:
		tmp = (1.0 / (((2.0 * (KbT / NaChar)) + (Vef / NaChar)) / KbT)) - t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(2.0 + Float64(Vef / KbT))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(2.0 + Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT))))
	t_3 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.25e+86)
		tmp = t_2;
	elseif (NaChar <= -2e-15)
		tmp = Float64(Float64(1.0 / Float64(t_0 / NaChar)) - t_3);
	elseif (NaChar <= -2.4e-36)
		tmp = Float64(t_1 + Float64(NdChar / Float64(t_0 - Float64(Ec / KbT))));
	elseif (NaChar <= 1e-10)
		tmp = Float64(Float64(1.0 / Float64(Float64(Float64(2.0 * Float64(KbT / NaChar)) + Float64(Vef / NaChar)) / KbT)) - t_3);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 2.0 + (Vef / KbT);
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	t_2 = t_1 + (NdChar / (2.0 + (((EDonor + (mu + Vef)) - Ec) / KbT)));
	t_3 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.25e+86)
		tmp = t_2;
	elseif (NaChar <= -2e-15)
		tmp = (1.0 / (t_0 / NaChar)) - t_3;
	elseif (NaChar <= -2.4e-36)
		tmp = t_1 + (NdChar / (t_0 - (Ec / KbT)));
	elseif (NaChar <= 1e-10)
		tmp = (1.0 / (((2.0 * (KbT / NaChar)) + (Vef / NaChar)) / KbT)) - t_3;
	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[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(2.0 + N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.25e+86], t$95$2, If[LessEqual[NaChar, -2e-15], N[(N[(1.0 / N[(t$95$0 / NaChar), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[NaChar, -2.4e-36], N[(t$95$1 + N[(NdChar / N[(t$95$0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1e-10], N[(N[(1.0 / N[(N[(N[(2.0 * N[(KbT / NaChar), $MachinePrecision]), $MachinePrecision] + N[(Vef / NaChar), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.24999999999999996e86 or 1.00000000000000004e-10 < 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 KbT around inf 72.8%

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

   6. Taylor expanded in KbT around -inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

   8. Simplified 76.5%

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

   if -2.24999999999999996e86 < NaChar < -2.0000000000000002e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.4%

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

   6. Taylor expanded in Vef around 0 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. associate-+r+ 82.9%

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

      4. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   10. Simplified 82.9%

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

   if -2.0000000000000002e-15 < NaChar < -2.4e-36

   1. Initial program 100.0%

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

   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 100.0%

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

   6. Taylor expanded in EDonor around inf 100.0%

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

      1. associate-/r* 100.0%

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

      2. associate-/r* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in Vef around inf 100.0%

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

   if -2.4e-36 < NaChar < 1.00000000000000004e-10

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.2%

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

   6. Taylor expanded in Vef around 0 66.6%

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

      1. clear-num 66.5%

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

      2. inv-pow 66.5%

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

      3. associate-+r+ 66.5%

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

      4. metadata-eval 66.5%

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

   8. Applied egg-rr 66.5%

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

      1. unpow-1 66.5%

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

   10. Simplified 66.5%

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

   11. Taylor expanded in KbT around 0 68.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.25 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.4 \cdot 10^{-36}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{Vef}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 10^{-10}:\\ \;\;\;\;\frac{1}{\frac{2 \cdot \frac{KbT}{NaChar} + \frac{Vef}{NaChar}}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2 + \frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}\\ t_1 := NaChar \cdot 0.5 - \frac{NdChar}{-1 - t\_0}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -3.2 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -1.46 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 1.05 \cdot 10^{-218}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NaChar \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))
        (t_1 (- (* NaChar 0.5) (/ NdChar (- -1.0 t_0))))
        (t_2
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
          (/ NdChar 2.0))))
   (if (<= NaChar -3.2e+162)
     t_2
     (if (<= NaChar -1.46e-22)
       t_1
       (if (<= NaChar -2.8e-38)
         t_2
         (if (<= NaChar 1.05e-218)
           (+ (/ NdChar (+ 1.0 t_0)) (/ (* KbT NaChar) Vef))
           (if (<= NaChar 4.5e-43) 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 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = (NaChar * 0.5) - (NdChar / (-1.0 - t_0));
	double t_2 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -3.2e+162) {
		tmp = t_2;
	} else if (NaChar <= -1.46e-22) {
		tmp = t_1;
	} else if (NaChar <= -2.8e-38) {
		tmp = t_2;
	} else if (NaChar <= 1.05e-218) {
		tmp = (NdChar / (1.0 + t_0)) + ((KbT * NaChar) / Vef);
	} else if (NaChar <= 4.5e-43) {
		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 = exp(((edonor + (mu + (vef - ec))) / kbt))
    t_1 = (nachar * 0.5d0) - (ndchar / ((-1.0d0) - t_0))
    t_2 = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / 2.0d0)
    if (nachar <= (-3.2d+162)) then
        tmp = t_2
    else if (nachar <= (-1.46d-22)) then
        tmp = t_1
    else if (nachar <= (-2.8d-38)) then
        tmp = t_2
    else if (nachar <= 1.05d-218) then
        tmp = (ndchar / (1.0d0 + t_0)) + ((kbt * nachar) / vef)
    else if (nachar <= 4.5d-43) 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 = Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = (NaChar * 0.5) - (NdChar / (-1.0 - t_0));
	double t_2 = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -3.2e+162) {
		tmp = t_2;
	} else if (NaChar <= -1.46e-22) {
		tmp = t_1;
	} else if (NaChar <= -2.8e-38) {
		tmp = t_2;
	} else if (NaChar <= 1.05e-218) {
		tmp = (NdChar / (1.0 + t_0)) + ((KbT * NaChar) / Vef);
	} else if (NaChar <= 4.5e-43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))
	t_1 = (NaChar * 0.5) - (NdChar / (-1.0 - t_0))
	t_2 = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -3.2e+162:
		tmp = t_2
	elif NaChar <= -1.46e-22:
		tmp = t_1
	elif NaChar <= -2.8e-38:
		tmp = t_2
	elif NaChar <= 1.05e-218:
		tmp = (NdChar / (1.0 + t_0)) + ((KbT * NaChar) / Vef)
	elif NaChar <= 4.5e-43:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))
	t_1 = Float64(Float64(NaChar * 0.5) - Float64(NdChar / Float64(-1.0 - t_0)))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -3.2e+162)
		tmp = t_2;
	elseif (NaChar <= -1.46e-22)
		tmp = t_1;
	elseif (NaChar <= -2.8e-38)
		tmp = t_2;
	elseif (NaChar <= 1.05e-218)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) + Float64(Float64(KbT * NaChar) / Vef));
	elseif (NaChar <= 4.5e-43)
		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 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	t_1 = (NaChar * 0.5) - (NdChar / (-1.0 - t_0));
	t_2 = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -3.2e+162)
		tmp = t_2;
	elseif (NaChar <= -1.46e-22)
		tmp = t_1;
	elseif (NaChar <= -2.8e-38)
		tmp = t_2;
	elseif (NaChar <= 1.05e-218)
		tmp = (NdChar / (1.0 + t_0)) + ((KbT * NaChar) / Vef);
	elseif (NaChar <= 4.5e-43)
		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[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar * 0.5), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -3.2e+162], t$95$2, If[LessEqual[NaChar, -1.46e-22], t$95$1, If[LessEqual[NaChar, -2.8e-38], t$95$2, If[LessEqual[NaChar, 1.05e-218], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.5e-43], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -3.2000000000000001e162 or -1.46000000000000001e-22 < NaChar < -2.8e-38 or 4.50000000000000025e-43 < 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 KbT around inf 66.0%

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

   if -3.2000000000000001e162 < NaChar < -1.46000000000000001e-22 or 1.04999999999999997e-218 < NaChar < 4.50000000000000025e-43

   1. Initial program 100.0%

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

   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 65.2%

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

      1. *-commutative 65.2%

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

   7. Simplified 65.2%

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

   if -2.8e-38 < NaChar < 1.04999999999999997e-218

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 69.6%

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

   6. Taylor expanded in Vef around 0 64.5%

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

   7. Taylor expanded in Vef around inf 61.8%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.2 \cdot 10^{+162}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq -1.46 \cdot 10^{-22}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.05 \cdot 10^{-218}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{elif}\;NaChar \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 54.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{2 + \frac{Ev}{KbT}} - t\_0\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -2.85 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -1.55 \cdot 10^{-204}:\\ \;\;\;\;t\_2 + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NdChar \leq 5.8 \cdot 10^{-59}:\\ \;\;\;\;t\_2 - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{elif}\;NdChar \leq 8.2 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 0.00011:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (- (/ NaChar (+ 2.0 (/ Ev KbT))) t_0))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
   (if (<= NdChar -2.85e-39)
     t_1
     (if (<= NdChar -1.55e-204)
       (+ t_2 (* KbT (/ NdChar Vef)))
       (if (<= NdChar 5.8e-59)
         (- t_2 (* KbT (/ NdChar Ec)))
         (if (<= NdChar 8.2e-35)
           t_1
           (if (<= NdChar 0.00011)
             (/ NaChar (+ 2.0 (/ Vef KbT)))
             (- (* NaChar 0.5) t_0))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	double t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NdChar <= -2.85e-39) {
		tmp = t_1;
	} else if (NdChar <= -1.55e-204) {
		tmp = t_2 + (KbT * (NdChar / Vef));
	} else if (NdChar <= 5.8e-59) {
		tmp = t_2 - (KbT * (NdChar / Ec));
	} else if (NdChar <= 8.2e-35) {
		tmp = t_1;
	} else if (NdChar <= 0.00011) {
		tmp = NaChar / (2.0 + (Vef / KbT));
	} else {
		tmp = (NaChar * 0.5) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = (nachar / (2.0d0 + (ev / kbt))) - t_0
    t_2 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    if (ndchar <= (-2.85d-39)) then
        tmp = t_1
    else if (ndchar <= (-1.55d-204)) then
        tmp = t_2 + (kbt * (ndchar / vef))
    else if (ndchar <= 5.8d-59) then
        tmp = t_2 - (kbt * (ndchar / ec))
    else if (ndchar <= 8.2d-35) then
        tmp = t_1
    else if (ndchar <= 0.00011d0) then
        tmp = nachar / (2.0d0 + (vef / kbt))
    else
        tmp = (nachar * 0.5d0) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	double t_2 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double tmp;
	if (NdChar <= -2.85e-39) {
		tmp = t_1;
	} else if (NdChar <= -1.55e-204) {
		tmp = t_2 + (KbT * (NdChar / Vef));
	} else if (NdChar <= 5.8e-59) {
		tmp = t_2 - (KbT * (NdChar / Ec));
	} else if (NdChar <= 8.2e-35) {
		tmp = t_1;
	} else if (NdChar <= 0.00011) {
		tmp = NaChar / (2.0 + (Vef / KbT));
	} else {
		tmp = (NaChar * 0.5) - t_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)))
	t_1 = (NaChar / (2.0 + (Ev / KbT))) - t_0
	t_2 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	tmp = 0
	if NdChar <= -2.85e-39:
		tmp = t_1
	elif NdChar <= -1.55e-204:
		tmp = t_2 + (KbT * (NdChar / Vef))
	elif NdChar <= 5.8e-59:
		tmp = t_2 - (KbT * (NdChar / Ec))
	elif NdChar <= 8.2e-35:
		tmp = t_1
	elif NdChar <= 0.00011:
		tmp = NaChar / (2.0 + (Vef / KbT))
	else:
		tmp = (NaChar * 0.5) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - t_0)
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	tmp = 0.0
	if (NdChar <= -2.85e-39)
		tmp = t_1;
	elseif (NdChar <= -1.55e-204)
		tmp = Float64(t_2 + Float64(KbT * Float64(NdChar / Vef)));
	elseif (NdChar <= 5.8e-59)
		tmp = Float64(t_2 - Float64(KbT * Float64(NdChar / Ec)));
	elseif (NdChar <= 8.2e-35)
		tmp = t_1;
	elseif (NdChar <= 0.00011)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Vef / KbT)));
	else
		tmp = Float64(Float64(NaChar * 0.5) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	t_2 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -2.85e-39)
		tmp = t_1;
	elseif (NdChar <= -1.55e-204)
		tmp = t_2 + (KbT * (NdChar / Vef));
	elseif (NdChar <= 5.8e-59)
		tmp = t_2 - (KbT * (NdChar / Ec));
	elseif (NdChar <= 8.2e-35)
		tmp = t_1;
	elseif (NdChar <= 0.00011)
		tmp = NaChar / (2.0 + (Vef / KbT));
	else
		tmp = (NaChar * 0.5) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -2.85e-39], t$95$1, If[LessEqual[NdChar, -1.55e-204], N[(t$95$2 + N[(KbT * N[(NdChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 5.8e-59], N[(t$95$2 - N[(KbT * N[(NdChar / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 8.2e-35], t$95$1, If[LessEqual[NdChar, 0.00011], N[(NaChar / N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar * 0.5), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -2.8499999999999998e-39 or 5.80000000000000033e-59 < NdChar < 8.20000000000000052e-35

   1. Initial program 100.0%

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

   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 78.1%

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

   6. Taylor expanded in Ev around 0 68.0%

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

      1. +-commutative 68.0%

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

   8. Simplified 68.0%

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

   if -2.8499999999999998e-39 < NdChar < -1.55e-204

   1. Initial program 100.0%

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

   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 58.5%

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

   6. Taylor expanded in Vef around inf 48.8%

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

      1. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if -1.55e-204 < NdChar < 5.80000000000000033e-59

   1. Initial program 100.0%

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

   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 68.9%

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

   6. Taylor expanded in Ec around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-/l* 60.0%

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

      3. distribute-rgt-neg-in 60.0%

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

   8. Simplified 60.0%

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

   if 8.20000000000000052e-35 < NdChar < 1.10000000000000004e-4

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 29.2%

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

   6. Taylor expanded in Vef around inf 29.2%

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

   7. Taylor expanded in Vef around 0 29.2%

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

   8. Taylor expanded in NdChar around 0 65.2%

      \[\leadsto \color{blue}{\frac{NaChar}{2 + \frac{Vef}{KbT}}} \]

   if 1.10000000000000004e-4 < 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 57.2%

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

      1. *-commutative 57.2%

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

   7. Simplified 57.2%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.85 \cdot 10^{-39}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -1.55 \cdot 10^{-204}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NdChar \leq 5.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{elif}\;NdChar \leq 8.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 0.00011:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_1 := NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -1.1 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -5.5 \cdot 10^{-205}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NdChar \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;t\_0 - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
        (t_1
         (-
          (* NaChar 0.5)
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))
   (if (<= NdChar -1.1e-39)
     t_1
     (if (<= NdChar -5.5e-205)
       (+ t_0 (* KbT (/ NdChar Vef)))
       (if (<= NdChar 6.2e-59) (- t_0 (* KbT (/ NdChar Ec))) t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_1 = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NdChar <= -1.1e-39) {
		tmp = t_1;
	} else if (NdChar <= -5.5e-205) {
		tmp = t_0 + (KbT * (NdChar / Vef));
	} else if (NdChar <= 6.2e-59) {
		tmp = t_0 - (KbT * (NdChar / Ec));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))
    t_1 = (nachar * 0.5d0) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    if (ndchar <= (-1.1d-39)) then
        tmp = t_1
    else if (ndchar <= (-5.5d-205)) then
        tmp = t_0 + (kbt * (ndchar / vef))
    else if (ndchar <= 6.2d-59) then
        tmp = t_0 - (kbt * (ndchar / ec))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	double t_1 = (NaChar * 0.5) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NdChar <= -1.1e-39) {
		tmp = t_1;
	} else if (NdChar <= -5.5e-205) {
		tmp = t_0 + (KbT * (NdChar / Vef));
	} else if (NdChar <= 6.2e-59) {
		tmp = t_0 - (KbT * (NdChar / Ec));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))
	t_1 = (NaChar * 0.5) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	tmp = 0
	if NdChar <= -1.1e-39:
		tmp = t_1
	elif NdChar <= -5.5e-205:
		tmp = t_0 + (KbT * (NdChar / Vef))
	elif NdChar <= 6.2e-59:
		tmp = t_0 - (KbT * (NdChar / Ec))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))))
	t_1 = Float64(Float64(NaChar * 0.5) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	tmp = 0.0
	if (NdChar <= -1.1e-39)
		tmp = t_1;
	elseif (NdChar <= -5.5e-205)
		tmp = Float64(t_0 + Float64(KbT * Float64(NdChar / Vef)));
	elseif (NdChar <= 6.2e-59)
		tmp = Float64(t_0 - Float64(KbT * Float64(NdChar / Ec)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)));
	t_1 = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	tmp = 0.0;
	if (NdChar <= -1.1e-39)
		tmp = t_1;
	elseif (NdChar <= -5.5e-205)
		tmp = t_0 + (KbT * (NdChar / Vef));
	elseif (NdChar <= 6.2e-59)
		tmp = t_0 - (KbT * (NdChar / Ec));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar * 0.5), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.1e-39], t$95$1, If[LessEqual[NdChar, -5.5e-205], N[(t$95$0 + N[(KbT * N[(NdChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 6.2e-59], N[(t$95$0 - N[(KbT * N[(NdChar / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -1.1e-39 or 6.19999999999999998e-59 < 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 61.6%

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

      1. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   if -1.1e-39 < NdChar < -5.4999999999999996e-205

   1. Initial program 100.0%

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

   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 58.5%

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

   6. Taylor expanded in Vef around inf 48.8%

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

      1. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if -5.4999999999999996e-205 < NdChar < 6.19999999999999998e-59

   1. Initial program 100.0%

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

   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 68.9%

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

   6. Taylor expanded in Ec around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-/l* 60.0%

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

      3. distribute-rgt-neg-in 60.0%

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

   8. Simplified 60.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.1 \cdot 10^{-39}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -5.5 \cdot 10^{-205}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NdChar \leq 6.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} - KbT \cdot \frac{NdChar}{Ec}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 60.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -6.4 \cdot 10^{+162} \lor \neg \left(NaChar \leq 1.55 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -6.4e+162) (not (<= NaChar 1.55e-38)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
    (/ NdChar 2.0))
   (-
    (/ 1.0 (/ (+ 2.0 (/ Vef KbT)) NaChar))
    (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -6.4e+162) || !(NaChar <= 1.55e-38)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-6.4d+162)) .or. (.not. (nachar <= 1.55d-38))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (1.0d0 / ((2.0d0 + (vef / kbt)) / nachar)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -6.4e+162) || !(NaChar <= 1.55e-38)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -6.4e+162) or not (NaChar <= 1.55e-38):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -6.4e+162) || !(NaChar <= 1.55e-38))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 + Float64(Vef / KbT)) / NaChar)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -6.4e+162) || ~((NaChar <= 1.55e-38)))
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (1.0 / ((2.0 + (Vef / KbT)) / NaChar)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -6.4e+162], N[Not[LessEqual[NaChar, 1.55e-38]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -6.4000000000000002e162 or 1.54999999999999991e-38 < 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 KbT around inf 65.1%

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

   if -6.4000000000000002e162 < NaChar < 1.54999999999999991e-38

   1. Initial program 100.0%

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

   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 69.3%

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

   6. Taylor expanded in Vef around 0 64.6%

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

      1. clear-num 64.6%

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

      2. inv-pow 64.6%

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

      3. associate-+r+ 64.6%

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

      4. metadata-eval 64.6%

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

   8. Applied egg-rr 64.6%

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

      1. unpow-1 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.4 \cdot 10^{+162} \lor \neg \left(NaChar \leq 1.55 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2 + \frac{Vef}{KbT}}{NaChar}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 60.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -3 \cdot 10^{+162} \lor \neg \left(NaChar \leq 1.45 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + \left(1 + \frac{Vef}{KbT}\right)} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -3e+162) (not (<= NaChar 1.45e-38)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
    (/ NdChar 2.0))
   (-
    (/ NaChar (+ 1.0 (+ 1.0 (/ Vef KbT))))
    (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -3e+162) || !(NaChar <= 1.45e-38)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + (1.0 + (Vef / KbT)))) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-3d+162)) .or. (.not. (nachar <= 1.45d-38))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + (1.0d0 + (vef / kbt)))) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -3e+162) || !(NaChar <= 1.45e-38)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + (1.0 + (Vef / KbT)))) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -3e+162) or not (NaChar <= 1.45e-38):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + (1.0 + (Vef / KbT)))) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -3e+162) || !(NaChar <= 1.45e-38))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Vef / KbT)))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -3e+162) || ~((NaChar <= 1.45e-38)))
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / (1.0 + (1.0 + (Vef / KbT)))) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -3e+162], N[Not[LessEqual[NaChar, 1.45e-38]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.9999999999999998e162 or 1.44999999999999997e-38 < 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 KbT around inf 65.1%

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

   if -2.9999999999999998e162 < NaChar < 1.44999999999999997e-38

   1. Initial program 100.0%

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

   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 69.3%

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

   6. Taylor expanded in Vef around 0 64.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3 \cdot 10^{+162} \lor \neg \left(NaChar \leq 1.45 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + \left(1 + \frac{Vef}{KbT}\right)} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 55.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -3 \cdot 10^{+162} \lor \neg \left(NaChar \leq 3.7 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -3e+162) (not (<= NaChar 3.7e-40)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
    (/ NdChar 2.0))
   (-
    (* NaChar 0.5)
    (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -3e+162) || !(NaChar <= 3.7e-40)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-3d+162)) .or. (.not. (nachar <= 3.7d-40))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev - (mu - eaccept))) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar * 0.5d0) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -3e+162) || !(NaChar <= 3.7e-40)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -3e+162) or not (NaChar <= 3.7e-40):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -3e+162) || !(NaChar <= 3.7e-40))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar * 0.5) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -3e+162) || ~((NaChar <= 3.7e-40)))
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev - (mu - EAccept))) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -3e+162], N[Not[LessEqual[NaChar, 3.7e-40]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar * 0.5), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.9999999999999998e162 or 3.69999999999999998e-40 < 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 KbT around inf 65.1%

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

   if -2.9999999999999998e162 < NaChar < 3.69999999999999998e-40

   1. Initial program 100.0%

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

   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 56.7%

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

      1. *-commutative 56.7%

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

   7. Simplified 56.7%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3 \cdot 10^{+162} \lor \neg \left(NaChar \leq 3.7 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 46.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 45.6%

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

6. Final simplification 45.6%

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

Alternative 24: 36.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -3.7 \cdot 10^{+142}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -3.7e+142)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -3.7e+142) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-3.7d+142)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -3.7e+142) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -3.7e+142:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -3.7e+142)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -3.7e+142)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -3.7e+142], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -3.6999999999999997e142

   1. Initial program 100.0%

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

   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 48.9%

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

   6. Taylor expanded in Ev around inf 45.3%

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

   if -3.6999999999999997e142 < 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 KbT around inf 45.2%

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

   6. Taylor expanded in EAccept around inf 32.6%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -3.7 \cdot 10^{+142}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 35.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -4.1 \cdot 10^{+145}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -4.1e+145)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -4.1e+145) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-4.1d+145)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -4.1e+145) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -4.1e+145:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -4.1e+145)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -4.1e+145)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -4.1e+145], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -4.1000000000000001e145

   1. Initial program 100.0%

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

   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 48.9%

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

   6. Taylor expanded in Ev around inf 45.3%

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

   if -4.1000000000000001e145 < 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 KbT around inf 45.2%

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

   6. Taylor expanded in Vef around inf 35.1%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -4.1 \cdot 10^{+145}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 35.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 45.6%

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

6. Taylor expanded in EAccept around inf 32.5%

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

7. Final simplification 32.5%

   \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2} \]
8. Add Preprocessing

Alternative 27: 27.3% 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 45.6%

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

6. Taylor expanded in Vef around inf 33.9%

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

7. Taylor expanded in Vef around 0 23.7%

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

8. Taylor expanded in Vef around 0 25.4%

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

   1. distribute-lft-out 25.4%

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

10. Simplified 25.4%

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

11. Final simplification 25.4%

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

Alternative 28: 18.0% accurate, 76.3× speedup

Math

\[\begin{array}{l} \\ NdChar \cdot 0.5 \end{array} \]

FPCore

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

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;
}

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
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;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 45.6%

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

6. Taylor expanded in Vef around inf 33.9%

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

7. Taylor expanded in Vef around 0 23.7%

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

8. Taylor expanded in NdChar around inf 19.6%

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

9. Final simplification 19.6%

   \[\leadsto NdChar \cdot 0.5 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024112 
(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))))))