Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 35.6s

Alternatives: 29

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -1.0170749814681026e-249
  2. Ec = 1.6773835104314048e+68
  3. Vef = -5.375116444870854e-28
  4. EDonor = -5.265582932935344e-240
  5. mu = 1.5880340737089262e+32
  6. KbT = 2.7727150743152974e-210
  7. NaChar = 2.0300169089446457e-250
  8. Ev = -5.388870564667336e+49
  9. EAccept = -2.0021271710179093e-127

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

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

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 (- (- mu EAccept) Ev)) KbT))))))

C

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

Fortran

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

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / 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 - ((mu - EAccept) - Ev)) / 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(Float64(mu - EAccept) - Ev)) / 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 - ((mu - EAccept) - Ev)) / 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[(N[(mu - EAccept), $MachinePrecision] - Ev), $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%

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

Alternative 2: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ t_3 := e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}\\ \mathbf{if}\;mu \leq -1.1 \cdot 10^{+240}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -1.6 \cdot 10^{+195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -1.05 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -2.2 \cdot 10^{-189}:\\ \;\;\;\;t\_0 - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -4.2 \cdot 10^{-265}:\\ \;\;\;\;\frac{NdChar}{1 + t\_3} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 4.8 \cdot 10^{-211}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{mu \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.7 \cdot 10^{-148}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - t\_3}\\ \mathbf{elif}\;mu \leq 8.2 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))))
        (t_3 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
   (if (<= mu -1.1e+240)
     t_2
     (if (<= mu -1.6e+195)
       t_1
       (if (<= mu -1.05e+133)
         t_2
         (if (<= mu -2.2e-189)
           (-
            t_0
            (/
             NdChar
             (+
              -1.0
              (*
               EDonor
               (+
                (/ (+ (/ Ec KbT) (- -1.0 (+ (/ Vef KbT) (/ mu KbT)))) EDonor)
                (/ -1.0 KbT))))))
           (if (<= mu -4.2e-265)
             (+
              (/ NdChar (+ 1.0 t_3))
              (/
               NaChar
               (+
                1.0
                (-
                 (+ 1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
                 (/ mu KbT)))))
             (if (<= mu 4.8e-211)
               (+
                t_0
                (/
                 NdChar
                 (+
                  1.0
                  (-
                   (+
                    1.0
                    (+
                     (/ EDonor KbT)
                     (* mu (+ (/ 1.0 KbT) (/ Vef (* mu KbT))))))
                   (/ Ec KbT)))))
               (if (<= mu 1.7e-148)
                 (- (/ NaChar (+ (/ EAccept KbT) 2.0)) (/ NdChar (- -1.0 t_3)))
                 (if (<= mu 8.2e+141) t_1 t_2))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	double t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	double t_3 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double tmp;
	if (mu <= -1.1e+240) {
		tmp = t_2;
	} else if (mu <= -1.6e+195) {
		tmp = t_1;
	} else if (mu <= -1.05e+133) {
		tmp = t_2;
	} else if (mu <= -2.2e-189) {
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (mu <= -4.2e-265) {
		tmp = (NdChar / (1.0 + t_3)) + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))));
	} else if (mu <= 4.8e-211) {
		tmp = t_0 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))));
	} else if (mu <= 1.7e-148) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - t_3));
	} else if (mu <= 8.2e+141) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    t_2 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    t_3 = exp(((edonor + (mu + (vef - ec))) / kbt))
    if (mu <= (-1.1d+240)) then
        tmp = t_2
    else if (mu <= (-1.6d+195)) then
        tmp = t_1
    else if (mu <= (-1.05d+133)) then
        tmp = t_2
    else if (mu <= (-2.2d-189)) then
        tmp = t_0 - (ndchar / ((-1.0d0) + (edonor * ((((ec / kbt) + ((-1.0d0) - ((vef / kbt) + (mu / kbt)))) / edonor) + ((-1.0d0) / kbt)))))
    else if (mu <= (-4.2d-265)) then
        tmp = (ndchar / (1.0d0 + t_3)) + (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt))))
    else if (mu <= 4.8d-211) then
        tmp = t_0 + (ndchar / (1.0d0 + ((1.0d0 + ((edonor / kbt) + (mu * ((1.0d0 / kbt) + (vef / (mu * kbt)))))) - (ec / kbt))))
    else if (mu <= 1.7d-148) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - t_3))
    else if (mu <= 8.2d+141) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	double t_2 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	double t_3 = Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double tmp;
	if (mu <= -1.1e+240) {
		tmp = t_2;
	} else if (mu <= -1.6e+195) {
		tmp = t_1;
	} else if (mu <= -1.05e+133) {
		tmp = t_2;
	} else if (mu <= -2.2e-189) {
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (mu <= -4.2e-265) {
		tmp = (NdChar / (1.0 + t_3)) + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))));
	} else if (mu <= 4.8e-211) {
		tmp = t_0 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))));
	} else if (mu <= 1.7e-148) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - t_3));
	} else if (mu <= 8.2e+141) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	t_2 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	t_3 = math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))
	tmp = 0
	if mu <= -1.1e+240:
		tmp = t_2
	elif mu <= -1.6e+195:
		tmp = t_1
	elif mu <= -1.05e+133:
		tmp = t_2
	elif mu <= -2.2e-189:
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))))
	elif mu <= -4.2e-265:
		tmp = (NdChar / (1.0 + t_3)) + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))))
	elif mu <= 4.8e-211:
		tmp = t_0 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))))
	elif mu <= 1.7e-148:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - t_3))
	elif mu <= 8.2e+141:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))))
	t_3 = exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))
	tmp = 0.0
	if (mu <= -1.1e+240)
		tmp = t_2;
	elseif (mu <= -1.6e+195)
		tmp = t_1;
	elseif (mu <= -1.05e+133)
		tmp = t_2;
	elseif (mu <= -2.2e-189)
		tmp = Float64(t_0 - Float64(NdChar / Float64(-1.0 + Float64(EDonor * Float64(Float64(Float64(Float64(Ec / KbT) + Float64(-1.0 - Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / EDonor) + Float64(-1.0 / KbT))))));
	elseif (mu <= -4.2e-265)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_3)) + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT)))));
	elseif (mu <= 4.8e-211)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Vef / Float64(mu * KbT)))))) - Float64(Ec / KbT)))));
	elseif (mu <= 1.7e-148)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - t_3)));
	elseif (mu <= 8.2e+141)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	t_3 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	tmp = 0.0;
	if (mu <= -1.1e+240)
		tmp = t_2;
	elseif (mu <= -1.6e+195)
		tmp = t_1;
	elseif (mu <= -1.05e+133)
		tmp = t_2;
	elseif (mu <= -2.2e-189)
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	elseif (mu <= -4.2e-265)
		tmp = (NdChar / (1.0 + t_3)) + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))));
	elseif (mu <= 4.8e-211)
		tmp = t_0 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))));
	elseif (mu <= 1.7e-148)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - t_3));
	elseif (mu <= 8.2e+141)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[mu, -1.1e+240], t$95$2, If[LessEqual[mu, -1.6e+195], t$95$1, If[LessEqual[mu, -1.05e+133], t$95$2, If[LessEqual[mu, -2.2e-189], N[(t$95$0 - N[(NdChar / N[(-1.0 + N[(EDonor * N[(N[(N[(N[(Ec / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -4.2e-265], N[(N[(NdChar / N[(1.0 + t$95$3), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 4.8e-211], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(Vef / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.7e-148], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 8.2e+141], t$95$1, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if mu < -1.1000000000000001e240 or -1.59999999999999991e195 < mu < -1.05e133 or 8.20000000000000044e141 < 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 95.2%

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

   6. Taylor expanded in mu around inf 89.1%

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

      1. associate-*r/ 89.1%

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

      2. mul-1-neg 89.1%

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

   8. Simplified 89.1%

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

   if -1.1000000000000001e240 < mu < -1.59999999999999991e195 or 1.7000000000000001e-148 < mu < 8.20000000000000044e141

   1. Initial program 100.0%

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

   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 72.7%

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

   6. Taylor expanded in EAccept around 0 66.0%

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

   if -1.05e133 < mu < -2.20000000000000019e-189

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.3%

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

   6. Taylor expanded in EDonor around -inf 78.2%

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

   if -2.20000000000000019e-189 < mu < -4.20000000000000007e-265

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 100.0%

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

   if -4.20000000000000007e-265 < mu < 4.8000000000000004e-211

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 69.6%

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

   6. Taylor expanded in mu around inf 76.4%

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

   if 4.8000000000000004e-211 < mu < 1.7000000000000001e-148

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 92.9%

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

   6. Taylor expanded in EAccept around 0 81.7%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -1.1 \cdot 10^{+240}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -1.6 \cdot 10^{+195}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.05 \cdot 10^{+133}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -2.2 \cdot 10^{-189}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -4.2 \cdot 10^{-265}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 4.8 \cdot 10^{-211}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{mu \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.7 \cdot 10^{-148}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 8.2 \cdot 10^{+141}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -3.5 \cdot 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -3.6 \cdot 10^{+195}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;mu \leq -1.2 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -1.15 \cdot 10^{-185}:\\ \;\;\;\;t\_2 - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -7.5 \cdot 10^{-292}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.32 \cdot 10^{-210}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{mu \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.9 \cdot 10^{-144}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - t\_0}\\ \mathbf{elif}\;mu \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 + Vef \cdot \left(\frac{1}{KbT} + EDonor \cdot \frac{\frac{1}{KbT} + \left(\frac{1}{EDonor} + \left(\frac{mu}{EDonor \cdot KbT} - \frac{\frac{Ec}{KbT}}{EDonor}\right)\right)}{Vef}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= mu -3.5e+241)
     t_1
     (if (<= mu -3.6e+195)
       (+ t_2 (/ NdChar (+ 1.0 (/ EDonor KbT))))
       (if (<= mu -1.2e+130)
         t_1
         (if (<= mu -1.15e-185)
           (-
            t_2
            (/
             NdChar
             (+
              -1.0
              (*
               EDonor
               (+
                (/ (+ (/ Ec KbT) (- -1.0 (+ (/ Vef KbT) (/ mu KbT)))) EDonor)
                (/ -1.0 KbT))))))
           (if (<= mu -7.5e-292)
             (+
              (/ NdChar (+ 1.0 t_0))
              (/
               NaChar
               (+
                1.0
                (-
                 (+ 1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
                 (/ mu KbT)))))
             (if (<= mu 1.32e-210)
               (+
                t_2
                (/
                 NdChar
                 (+
                  1.0
                  (-
                   (+
                    1.0
                    (+
                     (/ EDonor KbT)
                     (* mu (+ (/ 1.0 KbT) (/ Vef (* mu KbT))))))
                   (/ Ec KbT)))))
               (if (<= mu 1.9e-144)
                 (- (/ NaChar (+ (/ EAccept KbT) 2.0)) (/ NdChar (- -1.0 t_0)))
                 (if (<= mu 5.2e+41)
                   (+
                    t_2
                    (/
                     NdChar
                     (+
                      1.0
                      (*
                       Vef
                       (+
                        (/ 1.0 KbT)
                        (*
                         EDonor
                         (/
                          (+
                           (/ 1.0 KbT)
                           (+
                            (/ 1.0 EDonor)
                            (- (/ mu (* EDonor KbT)) (/ (/ Ec KbT) EDonor))))
                          Vef)))))))
                   t_1))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	double t_2 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (mu <= -3.5e+241) {
		tmp = t_1;
	} else if (mu <= -3.6e+195) {
		tmp = t_2 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (mu <= -1.2e+130) {
		tmp = t_1;
	} else if (mu <= -1.15e-185) {
		tmp = t_2 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (mu <= -7.5e-292) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))));
	} else if (mu <= 1.32e-210) {
		tmp = t_2 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))));
	} else if (mu <= 1.9e-144) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - t_0));
	} else if (mu <= 5.2e+41) {
		tmp = t_2 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + ((mu / (EDonor * KbT)) - ((Ec / KbT) / EDonor)))) / Vef))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = exp(((edonor + (mu + (vef - ec))) / kbt))
    t_1 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    t_2 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (mu <= (-3.5d+241)) then
        tmp = t_1
    else if (mu <= (-3.6d+195)) then
        tmp = t_2 + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (mu <= (-1.2d+130)) then
        tmp = t_1
    else if (mu <= (-1.15d-185)) then
        tmp = t_2 - (ndchar / ((-1.0d0) + (edonor * ((((ec / kbt) + ((-1.0d0) - ((vef / kbt) + (mu / kbt)))) / edonor) + ((-1.0d0) / kbt)))))
    else if (mu <= (-7.5d-292)) then
        tmp = (ndchar / (1.0d0 + t_0)) + (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt))))
    else if (mu <= 1.32d-210) then
        tmp = t_2 + (ndchar / (1.0d0 + ((1.0d0 + ((edonor / kbt) + (mu * ((1.0d0 / kbt) + (vef / (mu * kbt)))))) - (ec / kbt))))
    else if (mu <= 1.9d-144) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - t_0))
    else if (mu <= 5.2d+41) then
        tmp = t_2 + (ndchar / (1.0d0 + (vef * ((1.0d0 / kbt) + (edonor * (((1.0d0 / kbt) + ((1.0d0 / edonor) + ((mu / (edonor * kbt)) - ((ec / kbt) / edonor)))) / vef))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	double t_2 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (mu <= -3.5e+241) {
		tmp = t_1;
	} else if (mu <= -3.6e+195) {
		tmp = t_2 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (mu <= -1.2e+130) {
		tmp = t_1;
	} else if (mu <= -1.15e-185) {
		tmp = t_2 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (mu <= -7.5e-292) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))));
	} else if (mu <= 1.32e-210) {
		tmp = t_2 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))));
	} else if (mu <= 1.9e-144) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - t_0));
	} else if (mu <= 5.2e+41) {
		tmp = t_2 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + ((mu / (EDonor * KbT)) - ((Ec / KbT) / EDonor)))) / Vef))))));
	} else {
		tmp = t_1;
	}
	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 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	t_2 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if mu <= -3.5e+241:
		tmp = t_1
	elif mu <= -3.6e+195:
		tmp = t_2 + (NdChar / (1.0 + (EDonor / KbT)))
	elif mu <= -1.2e+130:
		tmp = t_1
	elif mu <= -1.15e-185:
		tmp = t_2 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))))
	elif mu <= -7.5e-292:
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))))
	elif mu <= 1.32e-210:
		tmp = t_2 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))))
	elif mu <= 1.9e-144:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - t_0))
	elif mu <= 5.2e+41:
		tmp = t_2 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + ((mu / (EDonor * KbT)) - ((Ec / KbT) / EDonor)))) / Vef))))))
	else:
		tmp = t_1
	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(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (mu <= -3.5e+241)
		tmp = t_1;
	elseif (mu <= -3.6e+195)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (mu <= -1.2e+130)
		tmp = t_1;
	elseif (mu <= -1.15e-185)
		tmp = Float64(t_2 - Float64(NdChar / Float64(-1.0 + Float64(EDonor * Float64(Float64(Float64(Float64(Ec / KbT) + Float64(-1.0 - Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / EDonor) + Float64(-1.0 / KbT))))));
	elseif (mu <= -7.5e-292)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT)))));
	elseif (mu <= 1.32e-210)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Vef / Float64(mu * KbT)))))) - Float64(Ec / KbT)))));
	elseif (mu <= 1.9e-144)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - t_0)));
	elseif (mu <= 5.2e+41)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(EDonor * Float64(Float64(Float64(1.0 / KbT) + Float64(Float64(1.0 / EDonor) + Float64(Float64(mu / Float64(EDonor * KbT)) - Float64(Float64(Ec / KbT) / EDonor)))) / Vef)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((EDonor + (mu + (Vef - Ec))) / KbT));
	t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	t_2 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (mu <= -3.5e+241)
		tmp = t_1;
	elseif (mu <= -3.6e+195)
		tmp = t_2 + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (mu <= -1.2e+130)
		tmp = t_1;
	elseif (mu <= -1.15e-185)
		tmp = t_2 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	elseif (mu <= -7.5e-292)
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))));
	elseif (mu <= 1.32e-210)
		tmp = t_2 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))));
	elseif (mu <= 1.9e-144)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - t_0));
	elseif (mu <= 5.2e+41)
		tmp = t_2 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + ((mu / (EDonor * KbT)) - ((Ec / KbT) / EDonor)))) / Vef))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -3.5e+241], t$95$1, If[LessEqual[mu, -3.6e+195], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -1.2e+130], t$95$1, If[LessEqual[mu, -1.15e-185], N[(t$95$2 - N[(NdChar / N[(-1.0 + N[(EDonor * N[(N[(N[(N[(Ec / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -7.5e-292], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.32e-210], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(Vef / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.9e-144], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 5.2e+41], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(EDonor * N[(N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(1.0 / EDonor), $MachinePrecision] + N[(N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision] - N[(N[(Ec / KbT), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if mu < -3.5e241 or -3.5999999999999999e195 < mu < -1.20000000000000012e130 or 5.2000000000000001e41 < 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 88.7%

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

   6. Taylor expanded in mu around inf 81.9%

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

      1. associate-*r/ 81.9%

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

      2. mul-1-neg 81.9%

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

   8. Simplified 81.9%

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

   if -3.5e241 < mu < -3.5999999999999999e195

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.9%

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

   6. Taylor expanded in EDonor around inf 82.4%

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

   if -1.20000000000000012e130 < mu < -1.15e-185

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.3%

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

   6. Taylor expanded in EDonor around -inf 78.2%

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

   if -1.15e-185 < mu < -7.5000000000000002e-292

   1. Initial program 100.0%

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

   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%

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

   if -7.5000000000000002e-292 < mu < 1.3200000000000001e-210

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 69.6%

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

   6. Taylor expanded in mu around inf 76.4%

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

   if 1.3200000000000001e-210 < mu < 1.89999999999999996e-144

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 93.3%

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

   6. Taylor expanded in EAccept around 0 82.7%

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

   if 1.89999999999999996e-144 < mu < 5.2000000000000001e41

   1. Initial program 100.0%

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

   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 39.4%

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

   6. Taylor expanded in EDonor around -inf 56.6%

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

   7. Taylor expanded in Vef around inf 59.0%

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

      1. associate-/l* 59.0%

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

      2. mul-1-neg 59.0%

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

      3. associate--l+ 59.0%

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

      4. *-commutative 59.0%

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

      5. associate-/l/ 59.0%

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

   9. Simplified 59.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -3.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -3.6 \cdot 10^{+195}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;mu \leq -1.2 \cdot 10^{+130}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -7.5 \cdot 10^{-292}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.32 \cdot 10^{-210}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{mu \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.9 \cdot 10^{-144}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + Vef \cdot \left(\frac{1}{KbT} + EDonor \cdot \frac{\frac{1}{KbT} + \left(\frac{1}{EDonor} + \left(\frac{mu}{EDonor \cdot KbT} - \frac{\frac{Ec}{KbT}}{EDonor}\right)\right)}{Vef}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{mu}{EDonor \cdot KbT}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -9.4 \cdot 10^{+139}:\\ \;\;\;\;t\_1 - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.16 \cdot 10^{-54}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + EDonor \cdot \left(\frac{1}{EDonor} - \left(\frac{\frac{Ec}{EDonor}}{KbT} + \left(\left(\frac{-1}{KbT} - \frac{\frac{Vef}{EDonor}}{KbT}\right) - t\_0\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 1.08 \cdot 10^{-128}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{+44}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + Vef \cdot \left(\frac{1}{KbT} + EDonor \cdot \frac{\frac{1}{KbT} + \left(\frac{1}{EDonor} + \left(t\_0 - \frac{\frac{Ec}{KbT}}{EDonor}\right)\right)}{Vef}\right)}\\ \mathbf{elif}\;NaChar \leq 2.6 \cdot 10^{+144}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ mu (* EDonor KbT)))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -9.4e+139)
     (-
      t_1
      (/
       NdChar
       (+
        -1.0
        (*
         EDonor
         (+
          (/ (+ (/ Ec KbT) (- -1.0 (+ (/ Vef KbT) (/ mu KbT)))) EDonor)
          (/ -1.0 KbT))))))
     (if (<= NaChar -2.4e+61)
       (+
        (/ NdChar (+ 1.0 (exp (/ mu KbT))))
        (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))
       (if (<= NaChar -1.16e-54)
         (+
          t_1
          (/
           NdChar
           (+
            1.0
            (*
             EDonor
             (-
              (/ 1.0 EDonor)
              (+
               (/ (/ Ec EDonor) KbT)
               (- (- (/ -1.0 KbT) (/ (/ Vef EDonor) KbT)) t_0)))))))
         (if (<= NaChar 1.08e-128)
           (-
            (/ NaChar (+ (/ EAccept KbT) 2.0))
            (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
           (if (<= NaChar 8e+44)
             (+
              t_1
              (/
               NdChar
               (+
                1.0
                (*
                 Vef
                 (+
                  (/ 1.0 KbT)
                  (*
                   EDonor
                   (/
                    (+
                     (/ 1.0 KbT)
                     (+ (/ 1.0 EDonor) (- t_0 (/ (/ Ec KbT) EDonor))))
                    Vef)))))))
             (if (<= NaChar 2.6e+144)
               (+
                (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
                (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
               (+ t_1 (/ NdChar (+ 1.0 (/ Vef KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = mu / (EDonor * KbT);
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -9.4e+139) {
		tmp = t_1 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (NaChar <= -2.4e+61) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	} else if (NaChar <= -1.16e-54) {
		tmp = t_1 + (NdChar / (1.0 + (EDonor * ((1.0 / EDonor) - (((Ec / EDonor) / KbT) + (((-1.0 / KbT) - ((Vef / EDonor) / KbT)) - t_0))))));
	} else if (NaChar <= 1.08e-128) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 8e+44) {
		tmp = t_1 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + (t_0 - ((Ec / KbT) / EDonor)))) / Vef))))));
	} else if (NaChar <= 2.6e+144) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = mu / (edonor * kbt)
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-9.4d+139)) then
        tmp = t_1 - (ndchar / ((-1.0d0) + (edonor * ((((ec / kbt) + ((-1.0d0) - ((vef / kbt) + (mu / kbt)))) / edonor) + ((-1.0d0) / kbt)))))
    else if (nachar <= (-2.4d+61)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    else if (nachar <= (-1.16d-54)) then
        tmp = t_1 + (ndchar / (1.0d0 + (edonor * ((1.0d0 / edonor) - (((ec / edonor) / kbt) + ((((-1.0d0) / kbt) - ((vef / edonor) / kbt)) - t_0))))))
    else if (nachar <= 1.08d-128) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else if (nachar <= 8d+44) then
        tmp = t_1 + (ndchar / (1.0d0 + (vef * ((1.0d0 / kbt) + (edonor * (((1.0d0 / kbt) + ((1.0d0 / edonor) + (t_0 - ((ec / kbt) / edonor)))) / vef))))))
    else if (nachar <= 2.6d+144) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = t_1 + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = mu / (EDonor * KbT);
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -9.4e+139) {
		tmp = t_1 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (NaChar <= -2.4e+61) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	} else if (NaChar <= -1.16e-54) {
		tmp = t_1 + (NdChar / (1.0 + (EDonor * ((1.0 / EDonor) - (((Ec / EDonor) / KbT) + (((-1.0 / KbT) - ((Vef / EDonor) / KbT)) - t_0))))));
	} else if (NaChar <= 1.08e-128) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 8e+44) {
		tmp = t_1 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + (t_0 - ((Ec / KbT) / EDonor)))) / Vef))))));
	} else if (NaChar <= 2.6e+144) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = mu / (EDonor * KbT)
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -9.4e+139:
		tmp = t_1 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))))
	elif NaChar <= -2.4e+61:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	elif NaChar <= -1.16e-54:
		tmp = t_1 + (NdChar / (1.0 + (EDonor * ((1.0 / EDonor) - (((Ec / EDonor) / KbT) + (((-1.0 / KbT) - ((Vef / EDonor) / KbT)) - t_0))))))
	elif NaChar <= 1.08e-128:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	elif NaChar <= 8e+44:
		tmp = t_1 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + (t_0 - ((Ec / KbT) / EDonor)))) / Vef))))))
	elif NaChar <= 2.6e+144:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(mu / Float64(EDonor * KbT))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -9.4e+139)
		tmp = Float64(t_1 - Float64(NdChar / Float64(-1.0 + Float64(EDonor * Float64(Float64(Float64(Float64(Ec / KbT) + Float64(-1.0 - Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / EDonor) + Float64(-1.0 / KbT))))));
	elseif (NaChar <= -2.4e+61)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))));
	elseif (NaChar <= -1.16e-54)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(EDonor * Float64(Float64(1.0 / EDonor) - Float64(Float64(Float64(Ec / EDonor) / KbT) + Float64(Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / EDonor) / KbT)) - t_0)))))));
	elseif (NaChar <= 1.08e-128)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	elseif (NaChar <= 8e+44)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(EDonor * Float64(Float64(Float64(1.0 / KbT) + Float64(Float64(1.0 / EDonor) + Float64(t_0 - Float64(Float64(Ec / KbT) / EDonor)))) / Vef)))))));
	elseif (NaChar <= 2.6e+144)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = mu / (EDonor * KbT);
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -9.4e+139)
		tmp = t_1 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	elseif (NaChar <= -2.4e+61)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	elseif (NaChar <= -1.16e-54)
		tmp = t_1 + (NdChar / (1.0 + (EDonor * ((1.0 / EDonor) - (((Ec / EDonor) / KbT) + (((-1.0 / KbT) - ((Vef / EDonor) / KbT)) - t_0))))));
	elseif (NaChar <= 1.08e-128)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	elseif (NaChar <= 8e+44)
		tmp = t_1 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + (t_0 - ((Ec / KbT) / EDonor)))) / Vef))))));
	elseif (NaChar <= 2.6e+144)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -9.4e+139], N[(t$95$1 - N[(NdChar / N[(-1.0 + N[(EDonor * N[(N[(N[(N[(Ec / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2.4e+61], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.16e-54], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(EDonor * N[(N[(1.0 / EDonor), $MachinePrecision] - N[(N[(N[(Ec / EDonor), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(Vef / EDonor), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.08e-128], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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[NaChar, 8e+44], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(EDonor * N[(N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(1.0 / EDonor), $MachinePrecision] + N[(t$95$0 - N[(N[(Ec / KbT), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.6e+144], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if NaChar < -9.4000000000000002e139

   1. Initial program 100.0%

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

   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 74.3%

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

   6. Taylor expanded in EDonor around -inf 83.2%

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

   if -9.4000000000000002e139 < NaChar < -2.3999999999999999e61

   1. Initial program 100.0%

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

   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 83.8%

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

   6. Taylor expanded in mu around inf 82.6%

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

      1. associate-*r/ 82.6%

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

      2. mul-1-neg 82.6%

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

   8. Simplified 82.6%

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

   if -2.3999999999999999e61 < NaChar < -1.16e-54

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.7%

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

   6. Taylor expanded in EDonor around inf 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-+r+ 77.9%

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

      3. associate-/r* 77.9%

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

      4. *-commutative 77.9%

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

      5. associate-/r* 81.0%

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

   8. Simplified 81.0%

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

   if -1.16e-54 < NaChar < 1.08e-128

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 79.1%

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

   6. Taylor expanded in EAccept around 0 67.8%

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

   if 1.08e-128 < NaChar < 8.0000000000000007e44

   1. Initial program 100.0%

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

   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 62.2%

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

   6. Taylor expanded in EDonor around -inf 67.7%

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

   7. Taylor expanded in Vef around inf 67.7%

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

      1. associate-/l* 67.7%

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

      2. mul-1-neg 67.7%

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

      3. associate--l+ 67.7%

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

      4. *-commutative 67.7%

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

      5. associate-/l/ 70.5%

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

   9. Simplified 70.5%

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

   if 8.0000000000000007e44 < NaChar < 2.5999999999999999e144

   1. Initial program 100.0%

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

   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 Ec around inf 91.7%

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

      1. associate-*r/ 91.7%

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

      2. mul-1-neg 91.7%

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

   7. Simplified 91.7%

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

   8. Taylor expanded in Ev around inf 72.6%

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

   if 2.5999999999999999e144 < 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 59.6%

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

   6. Taylor expanded in Vef around inf 76.8%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -9.4 \cdot 10^{+139}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.16 \cdot 10^{-54}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + EDonor \cdot \left(\frac{1}{EDonor} - \left(\frac{\frac{Ec}{EDonor}}{KbT} + \left(\left(\frac{-1}{KbT} - \frac{\frac{Vef}{EDonor}}{KbT}\right) - \frac{mu}{EDonor \cdot KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 1.08 \cdot 10^{-128}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + Vef \cdot \left(\frac{1}{KbT} + EDonor \cdot \frac{\frac{1}{KbT} + \left(\frac{1}{EDonor} + \left(\frac{mu}{EDonor \cdot KbT} - \frac{\frac{Ec}{KbT}}{EDonor}\right)\right)}{Vef}\right)}\\ \mathbf{elif}\;NaChar \leq 2.6 \cdot 10^{+144}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{if}\;Ec \leq -2.4 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Ec \leq 1.85 \cdot 10^{-160}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ec \leq 1.95 \cdot 10^{+65}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ec \leq 8.8 \cdot 10^{+192}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))))))
   (if (<= Ec -2.4e-64)
     t_1
     (if (<= Ec 1.85e-160)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
       (if (<= Ec 1.95e+65)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         (if (<= Ec 8.8e+192)
           (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
           t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((Ec / -KbT))));
	double tmp;
	if (Ec <= -2.4e-64) {
		tmp = t_1;
	} else if (Ec <= 1.85e-160) {
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	} else if (Ec <= 1.95e+65) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Ec <= 8.8e+192) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((ec / -kbt))))
    if (ec <= (-2.4d-64)) then
        tmp = t_1
    else if (ec <= 1.85d-160) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    else if (ec <= 1.95d+65) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (ec <= 8.8d+192) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((Ec / -KbT))));
	double tmp;
	if (Ec <= -2.4e-64) {
		tmp = t_1;
	} else if (Ec <= 1.85e-160) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	} else if (Ec <= 1.95e+65) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Ec <= 8.8e+192) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((Ec / -KbT))))
	tmp = 0
	if Ec <= -2.4e-64:
		tmp = t_1
	elif Ec <= 1.85e-160:
		tmp = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	elif Ec <= 1.95e+65:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Ec <= 8.8e+192:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))))
	tmp = 0.0
	if (Ec <= -2.4e-64)
		tmp = t_1;
	elseif (Ec <= 1.85e-160)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	elseif (Ec <= 1.95e+65)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Ec <= 8.8e+192)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((Ec / -KbT))));
	tmp = 0.0;
	if (Ec <= -2.4e-64)
		tmp = t_1;
	elseif (Ec <= 1.85e-160)
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	elseif (Ec <= 1.95e+65)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Ec <= 8.8e+192)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ec, -2.4e-64], t$95$1, If[LessEqual[Ec, 1.85e-160], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 1.95e+65], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 8.8e+192], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ec < -2.39999999999999998e-64 or 8.8000000000000003e192 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 88.5%

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

      1. associate-*r/ 88.5%

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

      2. mul-1-neg 88.5%

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

   7. Simplified 88.5%

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

   if -2.39999999999999998e-64 < Ec < 1.84999999999999988e-160

   1. Initial program 100.0%

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

   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 83.2%

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

   if 1.84999999999999988e-160 < Ec < 1.9499999999999999e65

   1. Initial program 100.0%

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

   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 79.9%

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

   if 1.9499999999999999e65 < Ec < 8.8000000000000003e192

   1. Initial program 100.0%

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

   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 EDonor around inf 85.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -2.4 \cdot 10^{-64}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;Ec \leq 1.85 \cdot 10^{-160}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ec \leq 1.95 \cdot 10^{+65}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ec \leq 8.8 \cdot 10^{+192}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_2 := t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -8.2 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -6.4 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq 1.25 \cdot 10^{-248}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;mu \leq 2.8 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_2 (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))))
   (if (<= mu -8.2e-25)
     t_2
     (if (<= mu -6.4e-237)
       t_1
       (if (<= mu 1.25e-248)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
         (if (<= mu 2.8e+96) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	double tmp;
	if (mu <= -8.2e-25) {
		tmp = t_2;
	} else if (mu <= -6.4e-237) {
		tmp = t_1;
	} else if (mu <= 1.25e-248) {
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	} else if (mu <= 2.8e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_2 = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    if (mu <= (-8.2d-25)) then
        tmp = t_2
    else if (mu <= (-6.4d-237)) then
        tmp = t_1
    else if (mu <= 1.25d-248) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    else if (mu <= 2.8d+96) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double tmp;
	if (mu <= -8.2e-25) {
		tmp = t_2;
	} else if (mu <= -6.4e-237) {
		tmp = t_1;
	} else if (mu <= 1.25e-248) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	} else if (mu <= 2.8e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_2 = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	tmp = 0
	if mu <= -8.2e-25:
		tmp = t_2
	elif mu <= -6.4e-237:
		tmp = t_1
	elif mu <= 1.25e-248:
		tmp = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	elif mu <= 2.8e+96:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_2 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	tmp = 0.0
	if (mu <= -8.2e-25)
		tmp = t_2;
	elseif (mu <= -6.4e-237)
		tmp = t_1;
	elseif (mu <= 1.25e-248)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	elseif (mu <= 2.8e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_2 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	tmp = 0.0;
	if (mu <= -8.2e-25)
		tmp = t_2;
	elseif (mu <= -6.4e-237)
		tmp = t_1;
	elseif (mu <= 1.25e-248)
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	elseif (mu <= 2.8e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -8.2e-25], t$95$2, If[LessEqual[mu, -6.4e-237], t$95$1, If[LessEqual[mu, 1.25e-248], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 2.8e+96], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -8.19999999999999974e-25 or 2.8e96 < 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 89.1%

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

   if -8.19999999999999974e-25 < mu < -6.3999999999999999e-237 or 1.25e-248 < mu < 2.8e96

   1. Initial program 100.0%

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

   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 EDonor around inf 75.3%

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

   if -6.3999999999999999e-237 < mu < 1.25e-248

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 79.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -8.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -6.4 \cdot 10^{-237}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.25 \cdot 10^{-248}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;mu \leq 2.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-226}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 9.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - t\_0}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
          (/ NdChar (+ 1.0 (exp (/ mu KbT)))))))
   (if (<= NaChar -4.2e+15)
     t_1
     (if (<= NaChar 1.45e-226)
       (+ (/ NdChar (+ 1.0 t_0)) (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
       (if (<= NaChar 9.6e-44)
         (- (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar (- -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(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	double tmp;
	if (NaChar <= -4.2e+15) {
		tmp = t_1;
	} else if (NaChar <= 1.45e-226) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (NaChar <= 9.6e-44) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - (NdChar / (-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(((edonor + (mu + (vef - ec))) / kbt))
    t_1 = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    if (nachar <= (-4.2d+15)) then
        tmp = t_1
    else if (nachar <= 1.45d-226) then
        tmp = (ndchar / (1.0d0 + t_0)) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (nachar <= 9.6d-44) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) - (ndchar / ((-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(((EDonor + (mu + (Vef - Ec))) / KbT));
	double t_1 = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double tmp;
	if (NaChar <= -4.2e+15) {
		tmp = t_1;
	} else if (NaChar <= 1.45e-226) {
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (NaChar <= 9.6e-44) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) - (NdChar / (-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(((EDonor + (mu + (Vef - Ec))) / KbT))
	t_1 = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	tmp = 0
	if NaChar <= -4.2e+15:
		tmp = t_1
	elif NaChar <= 1.45e-226:
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif NaChar <= 9.6e-44:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) - (NdChar / (-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(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	tmp = 0.0
	if (NaChar <= -4.2e+15)
		tmp = t_1;
	elseif (NaChar <= 1.45e-226)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (NaChar <= 9.6e-44)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) - Float64(NdChar / 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(((EDonor + (mu + (Vef - Ec))) / KbT));
	t_1 = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	tmp = 0.0;
	if (NaChar <= -4.2e+15)
		tmp = t_1;
	elseif (NaChar <= 1.45e-226)
		tmp = (NdChar / (1.0 + t_0)) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (NaChar <= 9.6e-44)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - (NdChar / (-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[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.2e+15], t$95$1, If[LessEqual[NaChar, 1.45e-226], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 9.6e-44], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -4.2e15 or 9.60000000000000035e-44 < 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 mu around inf 82.0%

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

   if -4.2e15 < NaChar < 1.45000000000000001e-226

   1. Initial program 100.0%

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

   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 77.0%

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

   if 1.45000000000000001e-226 < NaChar < 9.60000000000000035e-44

   1. Initial program 100.0%

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

   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 81.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-226}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 9.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -3.8 \cdot 10^{+138} \lor \neg \left(Vef \leq 8.2 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Vef -3.8e+138) (not (<= Vef 8.2e-109)))
   (+
    (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
    (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -3.8e+138) || !(Vef <= 8.2e-109)) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((vef <= (-3.8d+138)) .or. (.not. (vef <= 8.2d-109))) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -3.8e+138) || !(Vef <= 8.2e-109)) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Vef <= -3.8e+138) or not (Vef <= 8.2e-109):
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Vef <= -3.8e+138) || !(Vef <= 8.2e-109))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Vef <= -3.8e+138) || ~((Vef <= 8.2e-109)))
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Vef, -3.8e+138], N[Not[LessEqual[Vef, 8.2e-109]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -3.80000000000000012e138 or 8.2000000000000004e-109 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 81.7%

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

   6. Taylor expanded in EAccept around 0 77.4%

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

   if -3.80000000000000012e138 < Vef < 8.2000000000000004e-109

   1. Initial program 100.0%

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

   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 EDonor around inf 75.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.8 \cdot 10^{+138} \lor \neg \left(Vef \leq 8.2 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.05 \cdot 10^{-42} \lor \neg \left(NaChar \leq 4 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.05e-42) (not (<= NaChar 4e-44)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
   (-
    (/ NaChar (+ 1.0 (exp (/ EAccept 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 <= -2.05e-42) || !(NaChar <= 4e-44)) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / 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 <= (-2.05d-42)) .or. (.not. (nachar <= 4d-44))) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / 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 <= -2.05e-42) || !(NaChar <= 4e-44)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / 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 <= -2.05e-42) or not (NaChar <= 4e-44):
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / 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 <= -2.05e-42) || !(NaChar <= 4e-44))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / 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 <= -2.05e-42) || ~((NaChar <= 4e-44)))
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / 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, -2.05e-42], N[Not[LessEqual[NaChar, 4e-44]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / 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 < -2.0500000000000001e-42 or 3.99999999999999981e-44 < 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 mu around inf 80.7%

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

   if -2.0500000000000001e-42 < NaChar < 3.99999999999999981e-44

   1. Initial program 100.0%

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

   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 82.1%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.05 \cdot 10^{-42} \lor \neg \left(NaChar \leq 4 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -1 \cdot 10^{+141}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ Vef KbT))))))
   (if (<= Vef -1e+141)
     (+ t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
     (if (<= Vef 1.9e-125)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
       (+ 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 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = NdChar / (1.0 + exp((Vef / KbT)));
	double tmp;
	if (Vef <= -1e+141) {
		tmp = t_1 + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	} else if (Vef <= 1.9e-125) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_0 + 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 - ((mu - eaccept) - ev)) / kbt)))
    t_1 = ndchar / (1.0d0 + exp((vef / kbt)))
    if (vef <= (-1d+141)) then
        tmp = t_1 + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    else if (vef <= 1.9d-125) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_0 + 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 - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp((Vef / KbT)));
	double tmp;
	if (Vef <= -1e+141) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	} else if (Vef <= 1.9e-125) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_0 + t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = NdChar / (1.0 + math.exp((Vef / KbT)))
	tmp = 0
	if Vef <= -1e+141:
		tmp = t_1 + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	elif Vef <= 1.9e-125:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_0 + 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(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	tmp = 0.0
	if (Vef <= -1e+141)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	elseif (Vef <= 1.9e-125)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = Float64(t_0 + 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 - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = NdChar / (1.0 + exp((Vef / KbT)));
	tmp = 0.0;
	if (Vef <= -1e+141)
		tmp = t_1 + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	elseif (Vef <= 1.9e-125)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_0 + 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[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -1e+141], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.9e-125], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -1.00000000000000002e141

   1. Initial program 100.0%

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

   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 88.0%

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

   6. Taylor expanded in EAccept around 0 88.0%

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

   if -1.00000000000000002e141 < Vef < 1.9000000000000001e-125

   1. Initial program 100.0%

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

   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 EDonor around inf 74.6%

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

   if 1.9000000000000001e-125 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.25 \cdot 10^{-42}:\\ \;\;\;\;t\_0 - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 3.2 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{+44}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + Vef \cdot \left(\frac{1}{KbT} + EDonor \cdot \frac{\frac{1}{KbT} + \left(\frac{1}{EDonor} + \left(\frac{mu}{EDonor \cdot KbT} - \frac{\frac{Ec}{KbT}}{EDonor}\right)\right)}{Vef}\right)}\\ \mathbf{elif}\;NaChar \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))
   (if (<= NaChar -1.25e-42)
     (-
      t_0
      (/
       NdChar
       (+
        -1.0
        (*
         EDonor
         (+
          (/ (+ (/ Ec KbT) (- -1.0 (+ (/ Vef KbT) (/ mu KbT)))) EDonor)
          (/ -1.0 KbT))))))
     (if (<= NaChar 3.2e-157)
       t_1
       (if (<= NaChar 8e+44)
         (+
          t_0
          (/
           NdChar
           (+
            1.0
            (*
             Vef
             (+
              (/ 1.0 KbT)
              (*
               EDonor
               (/
                (+
                 (/ 1.0 KbT)
                 (+
                  (/ 1.0 EDonor)
                  (- (/ mu (* EDonor KbT)) (/ (/ Ec KbT) EDonor))))
                Vef)))))))
         (if (<= NaChar 8.8e+58)
           t_1
           (+ t_0 (/ NdChar (+ 1.0 (/ Vef KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NaChar <= -1.25e-42) {
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (NaChar <= 3.2e-157) {
		tmp = t_1;
	} else if (NaChar <= 8e+44) {
		tmp = t_0 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + ((mu / (EDonor * KbT)) - ((Ec / KbT) / EDonor)))) / Vef))))));
	} else if (NaChar <= 8.8e+58) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    if (nachar <= (-1.25d-42)) then
        tmp = t_0 - (ndchar / ((-1.0d0) + (edonor * ((((ec / kbt) + ((-1.0d0) - ((vef / kbt) + (mu / kbt)))) / edonor) + ((-1.0d0) / kbt)))))
    else if (nachar <= 3.2d-157) then
        tmp = t_1
    else if (nachar <= 8d+44) then
        tmp = t_0 + (ndchar / (1.0d0 + (vef * ((1.0d0 / kbt) + (edonor * (((1.0d0 / kbt) + ((1.0d0 / edonor) + ((mu / (edonor * kbt)) - ((ec / kbt) / edonor)))) / vef))))))
    else if (nachar <= 8.8d+58) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NaChar <= -1.25e-42) {
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (NaChar <= 3.2e-157) {
		tmp = t_1;
	} else if (NaChar <= 8e+44) {
		tmp = t_0 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + ((mu / (EDonor * KbT)) - ((Ec / KbT) / EDonor)))) / Vef))))));
	} else if (NaChar <= 8.8e+58) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	tmp = 0
	if NaChar <= -1.25e-42:
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))))
	elif NaChar <= 3.2e-157:
		tmp = t_1
	elif NaChar <= 8e+44:
		tmp = t_0 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + ((mu / (EDonor * KbT)) - ((Ec / KbT) / EDonor)))) / Vef))))))
	elif NaChar <= 8.8e+58:
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	tmp = 0.0
	if (NaChar <= -1.25e-42)
		tmp = Float64(t_0 - Float64(NdChar / Float64(-1.0 + Float64(EDonor * Float64(Float64(Float64(Float64(Ec / KbT) + Float64(-1.0 - Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / EDonor) + Float64(-1.0 / KbT))))));
	elseif (NaChar <= 3.2e-157)
		tmp = t_1;
	elseif (NaChar <= 8e+44)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(EDonor * Float64(Float64(Float64(1.0 / KbT) + Float64(Float64(1.0 / EDonor) + Float64(Float64(mu / Float64(EDonor * KbT)) - Float64(Float64(Ec / KbT) / EDonor)))) / Vef)))))));
	elseif (NaChar <= 8.8e+58)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	tmp = 0.0;
	if (NaChar <= -1.25e-42)
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	elseif (NaChar <= 3.2e-157)
		tmp = t_1;
	elseif (NaChar <= 8e+44)
		tmp = t_0 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + (EDonor * (((1.0 / KbT) + ((1.0 / EDonor) + ((mu / (EDonor * KbT)) - ((Ec / KbT) / EDonor)))) / Vef))))));
	elseif (NaChar <= 8.8e+58)
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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[NaChar, -1.25e-42], N[(t$95$0 - N[(NdChar / N[(-1.0 + N[(EDonor * N[(N[(N[(N[(Ec / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.2e-157], t$95$1, If[LessEqual[NaChar, 8e+44], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(EDonor * N[(N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(1.0 / EDonor), $MachinePrecision] + N[(N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision] - N[(N[(Ec / KbT), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8.8e+58], t$95$1, N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.25000000000000001e-42

   1. Initial program 100.0%

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

   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 67.3%

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

   6. Taylor expanded in EDonor around -inf 75.4%

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

   if -1.25000000000000001e-42 < NaChar < 3.20000000000000021e-157 or 8.0000000000000007e44 < NaChar < 8.8000000000000003e58

   1. Initial program 100.0%

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

   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 79.7%

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

   6. Taylor expanded in EAccept around 0 68.1%

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

   if 3.20000000000000021e-157 < NaChar < 8.0000000000000007e44

   1. Initial program 100.0%

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

   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 62.2%

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

   6. Taylor expanded in EDonor around -inf 67.7%

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

   7. Taylor expanded in Vef around inf 67.7%

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

      1. associate-/l* 67.7%

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

      2. mul-1-neg 67.7%

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

      3. associate--l+ 67.7%

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

      4. *-commutative 67.7%

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

      5. associate-/l/ 70.5%

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

   9. Simplified 70.5%

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

   if 8.8000000000000003e58 < 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 62.7%

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

   6. Taylor expanded in Vef around inf 75.0%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.25 \cdot 10^{-42}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 3.2 \cdot 10^{-157}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + Vef \cdot \left(\frac{1}{KbT} + EDonor \cdot \frac{\frac{1}{KbT} + \left(\frac{1}{EDonor} + \left(\frac{mu}{EDonor \cdot KbT} - \frac{\frac{Ec}{KbT}}{EDonor}\right)\right)}{Vef}\right)}\\ \mathbf{elif}\;NaChar \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{-41}:\\ \;\;\;\;t\_1 - \frac{NdChar}{-1 - \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 6.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 - \left(\frac{Ec}{KbT} + \left(-1 + EDonor \cdot \left(\frac{-1}{KbT} - \left(\frac{mu}{EDonor \cdot KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -2.7e-41)
     (-
      t_1
      (/
       NdChar
       (- -1.0 (/ (* EDonor (+ 1.0 (/ (- (+ mu Vef) Ec) EDonor))) KbT))))
     (if (<= NaChar 3.5e-38)
       t_0
       (if (<= NaChar 6.6e+44)
         (+
          t_1
          (/
           NdChar
           (-
            1.0
            (+
             (/ Ec KbT)
             (+
              -1.0
              (*
               EDonor
               (-
                (/ -1.0 KbT)
                (+ (/ mu (* EDonor KbT)) (/ Vef (* EDonor KbT))))))))))
         (if (<= NaChar 8e+54) t_0 (+ t_1 (/ NdChar (+ 1.0 (/ Vef KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.7e-41) {
		tmp = t_1 - (NdChar / (-1.0 - ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	} else if (NaChar <= 3.5e-38) {
		tmp = t_0;
	} else if (NaChar <= 6.6e+44) {
		tmp = t_1 + (NdChar / (1.0 - ((Ec / KbT) + (-1.0 + (EDonor * ((-1.0 / KbT) - ((mu / (EDonor * KbT)) + (Vef / (EDonor * KbT)))))))));
	} else if (NaChar <= 8e+54) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-2.7d-41)) then
        tmp = t_1 - (ndchar / ((-1.0d0) - ((edonor * (1.0d0 + (((mu + vef) - ec) / edonor))) / kbt)))
    else if (nachar <= 3.5d-38) then
        tmp = t_0
    else if (nachar <= 6.6d+44) then
        tmp = t_1 + (ndchar / (1.0d0 - ((ec / kbt) + ((-1.0d0) + (edonor * (((-1.0d0) / kbt) - ((mu / (edonor * kbt)) + (vef / (edonor * kbt)))))))))
    else if (nachar <= 8d+54) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.7e-41) {
		tmp = t_1 - (NdChar / (-1.0 - ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	} else if (NaChar <= 3.5e-38) {
		tmp = t_0;
	} else if (NaChar <= 6.6e+44) {
		tmp = t_1 + (NdChar / (1.0 - ((Ec / KbT) + (-1.0 + (EDonor * ((-1.0 / KbT) - ((mu / (EDonor * KbT)) + (Vef / (EDonor * KbT)))))))));
	} else if (NaChar <= 8e+54) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -2.7e-41:
		tmp = t_1 - (NdChar / (-1.0 - ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)))
	elif NaChar <= 3.5e-38:
		tmp = t_0
	elif NaChar <= 6.6e+44:
		tmp = t_1 + (NdChar / (1.0 - ((Ec / KbT) + (-1.0 + (EDonor * ((-1.0 / KbT) - ((mu / (EDonor * KbT)) + (Vef / (EDonor * KbT)))))))))
	elif NaChar <= 8e+54:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - 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(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.7e-41)
		tmp = Float64(t_1 - Float64(NdChar / Float64(-1.0 - Float64(Float64(EDonor * Float64(1.0 + Float64(Float64(Float64(mu + Vef) - Ec) / EDonor))) / KbT))));
	elseif (NaChar <= 3.5e-38)
		tmp = t_0;
	elseif (NaChar <= 6.6e+44)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 - Float64(Float64(Ec / KbT) + Float64(-1.0 + Float64(EDonor * Float64(Float64(-1.0 / KbT) - Float64(Float64(mu / Float64(EDonor * KbT)) + Float64(Vef / Float64(EDonor * KbT))))))))));
	elseif (NaChar <= 8e+54)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.7e-41)
		tmp = t_1 - (NdChar / (-1.0 - ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	elseif (NaChar <= 3.5e-38)
		tmp = t_0;
	elseif (NaChar <= 6.6e+44)
		tmp = t_1 + (NdChar / (1.0 - ((Ec / KbT) + (-1.0 + (EDonor * ((-1.0 / KbT) - ((mu / (EDonor * KbT)) + (Vef / (EDonor * KbT)))))))));
	elseif (NaChar <= 8e+54)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.7e-41], N[(t$95$1 - N[(NdChar / N[(-1.0 - N[(N[(EDonor * N[(1.0 + N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.5e-38], t$95$0, If[LessEqual[NaChar, 6.6e+44], N[(t$95$1 + N[(NdChar / N[(1.0 - N[(N[(Ec / KbT), $MachinePrecision] + N[(-1.0 + N[(EDonor * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision] + N[(Vef / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8e+54], t$95$0, N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.7e-41

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.3%

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

   6. Taylor expanded in EDonor around -inf 75.4%

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

   7. Taylor expanded in KbT around 0 73.6%

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

   if -2.7e-41 < NaChar < 3.5000000000000001e-38 or 6.60000000000000027e44 < NaChar < 8.0000000000000006e54

   1. Initial program 100.0%

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

   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 81.9%

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

   6. Taylor expanded in EAccept around 0 66.6%

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

   if 3.5000000000000001e-38 < NaChar < 6.60000000000000027e44

   1. Initial program 100.0%

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

   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 65.8%

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

   6. Taylor expanded in EDonor around inf 80.0%

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

   if 8.0000000000000006e54 < 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 62.7%

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

   6. Taylor expanded in Vef around inf 75.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{-41}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{-1 - \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 6.6 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 - \left(\frac{Ec}{KbT} + \left(-1 + EDonor \cdot \left(\frac{-1}{KbT} - \left(\frac{mu}{EDonor \cdot KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{+54}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.6 \cdot 10^{-43}:\\ \;\;\;\;t\_0 - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 - \left(\frac{Ec}{KbT} + \left(-1 + EDonor \cdot \left(\frac{-1}{KbT} - \left(\frac{mu}{EDonor \cdot KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 4.4 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))
   (if (<= NaChar -1.6e-43)
     (-
      t_0
      (/
       NdChar
       (+
        -1.0
        (*
         EDonor
         (+
          (/ (+ (/ Ec KbT) (- -1.0 (+ (/ Vef KbT) (/ mu KbT)))) EDonor)
          (/ -1.0 KbT))))))
     (if (<= NaChar 1.85e-40)
       t_1
       (if (<= NaChar 5.4e+44)
         (+
          t_0
          (/
           NdChar
           (-
            1.0
            (+
             (/ Ec KbT)
             (+
              -1.0
              (*
               EDonor
               (-
                (/ -1.0 KbT)
                (+ (/ mu (* EDonor KbT)) (/ Vef (* EDonor KbT))))))))))
         (if (<= NaChar 4.4e+61)
           t_1
           (+ t_0 (/ NdChar (+ 1.0 (/ Vef KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NaChar <= -1.6e-43) {
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (NaChar <= 1.85e-40) {
		tmp = t_1;
	} else if (NaChar <= 5.4e+44) {
		tmp = t_0 + (NdChar / (1.0 - ((Ec / KbT) + (-1.0 + (EDonor * ((-1.0 / KbT) - ((mu / (EDonor * KbT)) + (Vef / (EDonor * KbT)))))))));
	} else if (NaChar <= 4.4e+61) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    if (nachar <= (-1.6d-43)) then
        tmp = t_0 - (ndchar / ((-1.0d0) + (edonor * ((((ec / kbt) + ((-1.0d0) - ((vef / kbt) + (mu / kbt)))) / edonor) + ((-1.0d0) / kbt)))))
    else if (nachar <= 1.85d-40) then
        tmp = t_1
    else if (nachar <= 5.4d+44) then
        tmp = t_0 + (ndchar / (1.0d0 - ((ec / kbt) + ((-1.0d0) + (edonor * (((-1.0d0) / kbt) - ((mu / (edonor * kbt)) + (vef / (edonor * kbt)))))))))
    else if (nachar <= 4.4d+61) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NaChar <= -1.6e-43) {
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	} else if (NaChar <= 1.85e-40) {
		tmp = t_1;
	} else if (NaChar <= 5.4e+44) {
		tmp = t_0 + (NdChar / (1.0 - ((Ec / KbT) + (-1.0 + (EDonor * ((-1.0 / KbT) - ((mu / (EDonor * KbT)) + (Vef / (EDonor * KbT)))))))));
	} else if (NaChar <= 4.4e+61) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	tmp = 0
	if NaChar <= -1.6e-43:
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))))
	elif NaChar <= 1.85e-40:
		tmp = t_1
	elif NaChar <= 5.4e+44:
		tmp = t_0 + (NdChar / (1.0 - ((Ec / KbT) + (-1.0 + (EDonor * ((-1.0 / KbT) - ((mu / (EDonor * KbT)) + (Vef / (EDonor * KbT)))))))))
	elif NaChar <= 4.4e+61:
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	tmp = 0.0
	if (NaChar <= -1.6e-43)
		tmp = Float64(t_0 - Float64(NdChar / Float64(-1.0 + Float64(EDonor * Float64(Float64(Float64(Float64(Ec / KbT) + Float64(-1.0 - Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / EDonor) + Float64(-1.0 / KbT))))));
	elseif (NaChar <= 1.85e-40)
		tmp = t_1;
	elseif (NaChar <= 5.4e+44)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 - Float64(Float64(Ec / KbT) + Float64(-1.0 + Float64(EDonor * Float64(Float64(-1.0 / KbT) - Float64(Float64(mu / Float64(EDonor * KbT)) + Float64(Vef / Float64(EDonor * KbT))))))))));
	elseif (NaChar <= 4.4e+61)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	tmp = 0.0;
	if (NaChar <= -1.6e-43)
		tmp = t_0 - (NdChar / (-1.0 + (EDonor * ((((Ec / KbT) + (-1.0 - ((Vef / KbT) + (mu / KbT)))) / EDonor) + (-1.0 / KbT)))));
	elseif (NaChar <= 1.85e-40)
		tmp = t_1;
	elseif (NaChar <= 5.4e+44)
		tmp = t_0 + (NdChar / (1.0 - ((Ec / KbT) + (-1.0 + (EDonor * ((-1.0 / KbT) - ((mu / (EDonor * KbT)) + (Vef / (EDonor * KbT)))))))));
	elseif (NaChar <= 4.4e+61)
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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[NaChar, -1.6e-43], N[(t$95$0 - N[(NdChar / N[(-1.0 + N[(EDonor * N[(N[(N[(N[(Ec / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.85e-40], t$95$1, If[LessEqual[NaChar, 5.4e+44], N[(t$95$0 + N[(NdChar / N[(1.0 - N[(N[(Ec / KbT), $MachinePrecision] + N[(-1.0 + N[(EDonor * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision] + N[(Vef / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.4e+61], t$95$1, N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.59999999999999992e-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 67.3%

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

   6. Taylor expanded in EDonor around -inf 75.4%

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

   if -1.59999999999999992e-43 < NaChar < 1.84999999999999999e-40 or 5.4e44 < NaChar < 4.4000000000000001e61

   1. Initial program 100.0%

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

   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 81.9%

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

   6. Taylor expanded in EAccept around 0 66.6%

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

   if 1.84999999999999999e-40 < NaChar < 5.4e44

   1. Initial program 100.0%

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

   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 65.8%

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

   6. Taylor expanded in EDonor around inf 80.0%

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

   if 4.4000000000000001e61 < 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 62.7%

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

   6. Taylor expanded in Vef around inf 75.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{-1 + EDonor \cdot \left(\frac{\frac{Ec}{KbT} + \left(-1 - \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{EDonor} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-40}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 - \left(\frac{Ec}{KbT} + \left(-1 + EDonor \cdot \left(\frac{-1}{KbT} - \left(\frac{mu}{EDonor \cdot KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 4.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{if}\;NaChar \leq -3.75 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 200:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 7 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 2.2 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.12 \cdot 10^{+208}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_2 (+ t_1 (/ NdChar (+ 1.0 (/ EDonor KbT))))))
   (if (<= NaChar -3.75e-34)
     t_2
     (if (<= NaChar 200.0)
       t_0
       (if (<= NaChar 7e+44)
         t_2
         (if (<= NaChar 2.2e+58)
           t_0
           (if (<= NaChar 1.12e+208) (+ t_1 (/ NdChar 2.0)) t_2)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + (EDonor / KbT)));
	double tmp;
	if (NaChar <= -3.75e-34) {
		tmp = t_2;
	} else if (NaChar <= 200.0) {
		tmp = t_0;
	} else if (NaChar <= 7e+44) {
		tmp = t_2;
	} else if (NaChar <= 2.2e+58) {
		tmp = t_0;
	} else if (NaChar <= 1.12e+208) {
		tmp = t_1 + (NdChar / 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_2 = t_1 + (ndchar / (1.0d0 + (edonor / kbt)))
    if (nachar <= (-3.75d-34)) then
        tmp = t_2
    else if (nachar <= 200.0d0) then
        tmp = t_0
    else if (nachar <= 7d+44) then
        tmp = t_2
    else if (nachar <= 2.2d+58) then
        tmp = t_0
    else if (nachar <= 1.12d+208) then
        tmp = t_1 + (ndchar / 2.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + (EDonor / KbT)));
	double tmp;
	if (NaChar <= -3.75e-34) {
		tmp = t_2;
	} else if (NaChar <= 200.0) {
		tmp = t_0;
	} else if (NaChar <= 7e+44) {
		tmp = t_2;
	} else if (NaChar <= 2.2e+58) {
		tmp = t_0;
	} else if (NaChar <= 1.12e+208) {
		tmp = t_1 + (NdChar / 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_2 = t_1 + (NdChar / (1.0 + (EDonor / KbT)))
	tmp = 0
	if NaChar <= -3.75e-34:
		tmp = t_2
	elif NaChar <= 200.0:
		tmp = t_0
	elif NaChar <= 7e+44:
		tmp = t_2
	elif NaChar <= 2.2e+58:
		tmp = t_0
	elif NaChar <= 1.12e+208:
		tmp = t_1 + (NdChar / 2.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - 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(Float64(mu - EAccept) - Ev)) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))))
	tmp = 0.0
	if (NaChar <= -3.75e-34)
		tmp = t_2;
	elseif (NaChar <= 200.0)
		tmp = t_0;
	elseif (NaChar <= 7e+44)
		tmp = t_2;
	elseif (NaChar <= 2.2e+58)
		tmp = t_0;
	elseif (NaChar <= 1.12e+208)
		tmp = Float64(t_1 + Float64(NdChar / 2.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_2 = t_1 + (NdChar / (1.0 + (EDonor / KbT)));
	tmp = 0.0;
	if (NaChar <= -3.75e-34)
		tmp = t_2;
	elseif (NaChar <= 200.0)
		tmp = t_0;
	elseif (NaChar <= 7e+44)
		tmp = t_2;
	elseif (NaChar <= 2.2e+58)
		tmp = t_0;
	elseif (NaChar <= 1.12e+208)
		tmp = t_1 + (NdChar / 2.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -3.75e-34], t$95$2, If[LessEqual[NaChar, 200.0], t$95$0, If[LessEqual[NaChar, 7e+44], t$95$2, If[LessEqual[NaChar, 2.2e+58], t$95$0, If[LessEqual[NaChar, 1.12e+208], N[(t$95$1 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -3.7500000000000002e-34 or 200 < NaChar < 6.9999999999999998e44 or 1.12000000000000004e208 < 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 64.1%

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

   6. Taylor expanded in EDonor around inf 67.0%

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

   if -3.7500000000000002e-34 < NaChar < 200 or 6.9999999999999998e44 < NaChar < 2.2000000000000001e58

   1. Initial program 100.0%

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

   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 80.8%

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

   6. Taylor expanded in EAccept around 0 66.5%

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

   if 2.2000000000000001e58 < NaChar < 1.12000000000000004e208

   1. Initial program 100.0%

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

   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 Ec around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. mul-1-neg 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in Ec around 0 74.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.75 \cdot 10^{-34}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 200:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 7 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.12 \cdot 10^{+208}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{if}\;NaChar \leq -2.8 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 3.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 6.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_2 (+ t_1 (/ NdChar (+ 1.0 (/ Vef KbT))))))
   (if (<= NaChar -2.8e-20)
     t_2
     (if (<= NaChar 3.4)
       t_0
       (if (<= NaChar 6.6e+44)
         (+ t_1 (/ NdChar (+ 1.0 (/ EDonor KbT))))
         (if (<= NaChar 1.65e+58) t_0 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -2.8e-20) {
		tmp = t_2;
	} else if (NaChar <= 3.4) {
		tmp = t_0;
	} else if (NaChar <= 6.6e+44) {
		tmp = t_1 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NaChar <= 1.65e+58) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_2 = t_1 + (ndchar / (1.0d0 + (vef / kbt)))
    if (nachar <= (-2.8d-20)) then
        tmp = t_2
    else if (nachar <= 3.4d0) then
        tmp = t_0
    else if (nachar <= 6.6d+44) then
        tmp = t_1 + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (nachar <= 1.65d+58) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -2.8e-20) {
		tmp = t_2;
	} else if (NaChar <= 3.4) {
		tmp = t_0;
	} else if (NaChar <= 6.6e+44) {
		tmp = t_1 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NaChar <= 1.65e+58) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_2 = t_1 + (NdChar / (1.0 + (Vef / KbT)))
	tmp = 0
	if NaChar <= -2.8e-20:
		tmp = t_2
	elif NaChar <= 3.4:
		tmp = t_0
	elif NaChar <= 6.6e+44:
		tmp = t_1 + (NdChar / (1.0 + (EDonor / KbT)))
	elif NaChar <= 1.65e+58:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - 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(Float64(mu - EAccept) - Ev)) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))))
	tmp = 0.0
	if (NaChar <= -2.8e-20)
		tmp = t_2;
	elseif (NaChar <= 3.4)
		tmp = t_0;
	elseif (NaChar <= 6.6e+44)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (NaChar <= 1.65e+58)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_2 = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.8e-20)
		tmp = t_2;
	elseif (NaChar <= 3.4)
		tmp = t_0;
	elseif (NaChar <= 6.6e+44)
		tmp = t_1 + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (NaChar <= 1.65e+58)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.8e-20], t$95$2, If[LessEqual[NaChar, 3.4], t$95$0, If[LessEqual[NaChar, 6.6e+44], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.65e+58], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2.8000000000000003e-20 or 1.64999999999999991e58 < 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 66.6%

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

   6. Taylor expanded in Vef around inf 73.0%

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

   if -2.8000000000000003e-20 < NaChar < 3.39999999999999991 or 6.60000000000000027e44 < NaChar < 1.64999999999999991e58

   1. Initial program 100.0%

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

   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 78.9%

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

   6. Taylor expanded in EAccept around 0 64.6%

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

   if 3.39999999999999991 < NaChar < 6.60000000000000027e44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.2%

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

   6. Taylor expanded in EDonor around inf 87.8%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.4:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 6.6 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.2 \cdot 10^{-42}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.2 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -2.2e-42)
     (+ t_1 (/ NdChar (+ 1.0 (/ mu KbT))))
     (if (<= NaChar 2.4)
       t_0
       (if (<= NaChar 1.5e+45)
         (+ t_1 (/ NdChar (+ 1.0 (/ EDonor KbT))))
         (if (<= NaChar 3.2e+54)
           t_0
           (+ t_1 (/ NdChar (+ 1.0 (/ Vef KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.2e-42) {
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	} else if (NaChar <= 2.4) {
		tmp = t_0;
	} else if (NaChar <= 1.5e+45) {
		tmp = t_1 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NaChar <= 3.2e+54) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-2.2d-42)) then
        tmp = t_1 + (ndchar / (1.0d0 + (mu / kbt)))
    else if (nachar <= 2.4d0) then
        tmp = t_0
    else if (nachar <= 1.5d+45) then
        tmp = t_1 + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (nachar <= 3.2d+54) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.2e-42) {
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	} else if (NaChar <= 2.4) {
		tmp = t_0;
	} else if (NaChar <= 1.5e+45) {
		tmp = t_1 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NaChar <= 3.2e+54) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -2.2e-42:
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)))
	elif NaChar <= 2.4:
		tmp = t_0
	elif NaChar <= 1.5e+45:
		tmp = t_1 + (NdChar / (1.0 + (EDonor / KbT)))
	elif NaChar <= 3.2e+54:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - 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(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.2e-42)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(mu / KbT))));
	elseif (NaChar <= 2.4)
		tmp = t_0;
	elseif (NaChar <= 1.5e+45)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (NaChar <= 3.2e+54)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.2e-42)
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	elseif (NaChar <= 2.4)
		tmp = t_0;
	elseif (NaChar <= 1.5e+45)
		tmp = t_1 + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (NaChar <= 3.2e+54)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.2e-42], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.4], t$95$0, If[LessEqual[NaChar, 1.5e+45], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.2e+54], t$95$0, N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.20000000000000005e-42

   1. Initial program 100.0%

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

   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 67.3%

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

   6. Taylor expanded in mu around inf 71.4%

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

   if -2.20000000000000005e-42 < NaChar < 2.39999999999999991 or 1.50000000000000005e45 < NaChar < 3.2e54

   1. Initial program 100.0%

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

   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 81.3%

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

   6. Taylor expanded in EAccept around 0 66.7%

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

   if 2.39999999999999991 < NaChar < 1.50000000000000005e45

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.2%

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

   6. Taylor expanded in EDonor around inf 87.8%

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

   if 3.2e54 < 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 62.7%

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

   6. Taylor expanded in Vef around inf 75.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.4:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.45 \cdot 10^{-42}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 110:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;t\_1 + \frac{NdChar \cdot KbT}{EDonor \cdot \left(1 + \frac{Vef}{EDonor}\right)}\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -1.45e-42)
     (+ t_1 (/ NdChar (+ 1.0 (/ mu KbT))))
     (if (<= NaChar 110.0)
       t_0
       (if (<= NaChar 1.65e+44)
         (+ t_1 (/ (* NdChar KbT) (* EDonor (+ 1.0 (/ Vef EDonor)))))
         (if (<= NaChar 1.9e+58)
           t_0
           (+ t_1 (/ NdChar (+ 1.0 (/ Vef KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -1.45e-42) {
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	} else if (NaChar <= 110.0) {
		tmp = t_0;
	} else if (NaChar <= 1.65e+44) {
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))));
	} else if (NaChar <= 1.9e+58) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-1.45d-42)) then
        tmp = t_1 + (ndchar / (1.0d0 + (mu / kbt)))
    else if (nachar <= 110.0d0) then
        tmp = t_0
    else if (nachar <= 1.65d+44) then
        tmp = t_1 + ((ndchar * kbt) / (edonor * (1.0d0 + (vef / edonor))))
    else if (nachar <= 1.9d+58) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -1.45e-42) {
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	} else if (NaChar <= 110.0) {
		tmp = t_0;
	} else if (NaChar <= 1.65e+44) {
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))));
	} else if (NaChar <= 1.9e+58) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -1.45e-42:
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)))
	elif NaChar <= 110.0:
		tmp = t_0
	elif NaChar <= 1.65e+44:
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))))
	elif NaChar <= 1.9e+58:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - 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(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.45e-42)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(mu / KbT))));
	elseif (NaChar <= 110.0)
		tmp = t_0;
	elseif (NaChar <= 1.65e+44)
		tmp = Float64(t_1 + Float64(Float64(NdChar * KbT) / Float64(EDonor * Float64(1.0 + Float64(Vef / EDonor)))));
	elseif (NaChar <= 1.9e+58)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.45e-42)
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	elseif (NaChar <= 110.0)
		tmp = t_0;
	elseif (NaChar <= 1.65e+44)
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))));
	elseif (NaChar <= 1.9e+58)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.45e-42], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 110.0], t$95$0, If[LessEqual[NaChar, 1.65e+44], N[(t$95$1 + N[(N[(NdChar * KbT), $MachinePrecision] / N[(EDonor * N[(1.0 + N[(Vef / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.9e+58], t$95$0, N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.4500000000000001e-42

   1. Initial program 100.0%

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

   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 67.3%

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

   6. Taylor expanded in mu around inf 71.4%

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

   if -1.4500000000000001e-42 < NaChar < 110 or 1.65000000000000007e44 < NaChar < 1.8999999999999999e58

   1. Initial program 100.0%

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

   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 81.3%

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

   6. Taylor expanded in EAccept around 0 66.7%

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

   if 110 < NaChar < 1.65000000000000007e44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.2%

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

   6. Taylor expanded in EDonor around -inf 76.1%

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

   7. Taylor expanded in KbT around 0 88.6%

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

   8. Taylor expanded in Vef around inf 88.6%

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

   if 1.8999999999999999e58 < 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 62.7%

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

   6. Taylor expanded in Vef around inf 75.0%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.45 \cdot 10^{-42}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 110:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar \cdot KbT}{EDonor \cdot \left(1 + \frac{Vef}{EDonor}\right)}\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{+58}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.6 \cdot 10^{-41}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + Vef \cdot \left(\frac{1}{KbT} + \frac{\frac{mu}{KbT}}{Vef}\right)}\\ \mathbf{elif}\;NaChar \leq 1.7:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;t\_1 + \frac{NdChar \cdot KbT}{EDonor \cdot \left(1 + \frac{Vef}{EDonor}\right)}\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{+57}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -2.6e-41)
     (+ t_1 (/ NdChar (+ 1.0 (* Vef (+ (/ 1.0 KbT) (/ (/ mu KbT) Vef))))))
     (if (<= NaChar 1.7)
       t_0
       (if (<= NaChar 1.55e+44)
         (+ t_1 (/ (* NdChar KbT) (* EDonor (+ 1.0 (/ Vef EDonor)))))
         (if (<= NaChar 1.8e+57)
           t_0
           (+ t_1 (/ NdChar (+ 1.0 (/ Vef KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.6e-41) {
		tmp = t_1 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + ((mu / KbT) / Vef)))));
	} else if (NaChar <= 1.7) {
		tmp = t_0;
	} else if (NaChar <= 1.55e+44) {
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))));
	} else if (NaChar <= 1.8e+57) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-2.6d-41)) then
        tmp = t_1 + (ndchar / (1.0d0 + (vef * ((1.0d0 / kbt) + ((mu / kbt) / vef)))))
    else if (nachar <= 1.7d0) then
        tmp = t_0
    else if (nachar <= 1.55d+44) then
        tmp = t_1 + ((ndchar * kbt) / (edonor * (1.0d0 + (vef / edonor))))
    else if (nachar <= 1.8d+57) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.6e-41) {
		tmp = t_1 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + ((mu / KbT) / Vef)))));
	} else if (NaChar <= 1.7) {
		tmp = t_0;
	} else if (NaChar <= 1.55e+44) {
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))));
	} else if (NaChar <= 1.8e+57) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -2.6e-41:
		tmp = t_1 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + ((mu / KbT) / Vef)))))
	elif NaChar <= 1.7:
		tmp = t_0
	elif NaChar <= 1.55e+44:
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))))
	elif NaChar <= 1.8e+57:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - 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(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.6e-41)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef * Float64(Float64(1.0 / KbT) + Float64(Float64(mu / KbT) / Vef))))));
	elseif (NaChar <= 1.7)
		tmp = t_0;
	elseif (NaChar <= 1.55e+44)
		tmp = Float64(t_1 + Float64(Float64(NdChar * KbT) / Float64(EDonor * Float64(1.0 + Float64(Vef / EDonor)))));
	elseif (NaChar <= 1.8e+57)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.6e-41)
		tmp = t_1 + (NdChar / (1.0 + (Vef * ((1.0 / KbT) + ((mu / KbT) / Vef)))));
	elseif (NaChar <= 1.7)
		tmp = t_0;
	elseif (NaChar <= 1.55e+44)
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))));
	elseif (NaChar <= 1.8e+57)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.6e-41], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(mu / KbT), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.7], t$95$0, If[LessEqual[NaChar, 1.55e+44], N[(t$95$1 + N[(N[(NdChar * KbT), $MachinePrecision] / N[(EDonor * N[(1.0 + N[(Vef / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.8e+57], t$95$0, N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.5999999999999999e-41

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.3%

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

   6. Taylor expanded in EDonor around -inf 75.4%

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

   7. Taylor expanded in Vef around inf 74.2%

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

      1. associate-/l* 71.6%

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

      2. mul-1-neg 71.6%

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

      3. associate--l+ 71.6%

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

      4. *-commutative 71.6%

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

      5. associate-/l/ 70.3%

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

   9. Simplified 70.3%

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

   10. Taylor expanded in mu around inf 71.1%

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

       1. mul-1-neg 71.1%

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

       2. associate-/r* 72.6%

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

       3. distribute-neg-frac 72.6%

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

       4. distribute-neg-frac2 72.6%

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

   12. Simplified 72.6%

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

   if -2.5999999999999999e-41 < NaChar < 1.69999999999999996 or 1.54999999999999998e44 < NaChar < 1.8000000000000001e57

   1. Initial program 100.0%

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

   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 81.3%

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

   6. Taylor expanded in EAccept around 0 66.7%

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

   if 1.69999999999999996 < NaChar < 1.54999999999999998e44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.2%

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

   6. Taylor expanded in EDonor around -inf 76.1%

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

   7. Taylor expanded in KbT around 0 88.6%

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

   8. Taylor expanded in Vef around inf 88.6%

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

   if 1.8000000000000001e57 < 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 62.7%

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

   6. Taylor expanded in Vef around inf 75.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.6 \cdot 10^{-41}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + Vef \cdot \left(\frac{1}{KbT} + \frac{\frac{mu}{KbT}}{Vef}\right)}\\ \mathbf{elif}\;NaChar \leq 1.7:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar \cdot KbT}{EDonor \cdot \left(1 + \frac{Vef}{EDonor}\right)}\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -6.3 \cdot 10^{-43}:\\ \;\;\;\;t\_1 - \frac{NdChar}{-1 - \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 440:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;t\_1 + \frac{NdChar \cdot KbT}{EDonor \cdot \left(1 + \frac{Vef}{EDonor}\right)}\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{+57}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -6.3e-43)
     (-
      t_1
      (/
       NdChar
       (- -1.0 (/ (* EDonor (+ 1.0 (/ (- (+ mu Vef) Ec) EDonor))) KbT))))
     (if (<= NaChar 440.0)
       t_0
       (if (<= NaChar 1.55e+44)
         (+ t_1 (/ (* NdChar KbT) (* EDonor (+ 1.0 (/ Vef EDonor)))))
         (if (<= NaChar 1.3e+57)
           t_0
           (+ t_1 (/ NdChar (+ 1.0 (/ Vef KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -6.3e-43) {
		tmp = t_1 - (NdChar / (-1.0 - ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	} else if (NaChar <= 440.0) {
		tmp = t_0;
	} else if (NaChar <= 1.55e+44) {
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))));
	} else if (NaChar <= 1.3e+57) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-6.3d-43)) then
        tmp = t_1 - (ndchar / ((-1.0d0) - ((edonor * (1.0d0 + (((mu + vef) - ec) / edonor))) / kbt)))
    else if (nachar <= 440.0d0) then
        tmp = t_0
    else if (nachar <= 1.55d+44) then
        tmp = t_1 + ((ndchar * kbt) / (edonor * (1.0d0 + (vef / edonor))))
    else if (nachar <= 1.3d+57) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / (1.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -6.3e-43) {
		tmp = t_1 - (NdChar / (-1.0 - ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	} else if (NaChar <= 440.0) {
		tmp = t_0;
	} else if (NaChar <= 1.55e+44) {
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))));
	} else if (NaChar <= 1.3e+57) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -6.3e-43:
		tmp = t_1 - (NdChar / (-1.0 - ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)))
	elif NaChar <= 440.0:
		tmp = t_0
	elif NaChar <= 1.55e+44:
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))))
	elif NaChar <= 1.3e+57:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - 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(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -6.3e-43)
		tmp = Float64(t_1 - Float64(NdChar / Float64(-1.0 - Float64(Float64(EDonor * Float64(1.0 + Float64(Float64(Float64(mu + Vef) - Ec) / EDonor))) / KbT))));
	elseif (NaChar <= 440.0)
		tmp = t_0;
	elseif (NaChar <= 1.55e+44)
		tmp = Float64(t_1 + Float64(Float64(NdChar * KbT) / Float64(EDonor * Float64(1.0 + Float64(Vef / EDonor)))));
	elseif (NaChar <= 1.3e+57)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -6.3e-43)
		tmp = t_1 - (NdChar / (-1.0 - ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT)));
	elseif (NaChar <= 440.0)
		tmp = t_0;
	elseif (NaChar <= 1.55e+44)
		tmp = t_1 + ((NdChar * KbT) / (EDonor * (1.0 + (Vef / EDonor))));
	elseif (NaChar <= 1.3e+57)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.3e-43], N[(t$95$1 - N[(NdChar / N[(-1.0 - N[(N[(EDonor * N[(1.0 + N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 440.0], t$95$0, If[LessEqual[NaChar, 1.55e+44], N[(t$95$1 + N[(N[(NdChar * KbT), $MachinePrecision] / N[(EDonor * N[(1.0 + N[(Vef / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.3e+57], t$95$0, N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -6.3000000000000002e-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 67.3%

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

   6. Taylor expanded in EDonor around -inf 75.4%

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

   7. Taylor expanded in KbT around 0 73.6%

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

   if -6.3000000000000002e-43 < NaChar < 440 or 1.54999999999999998e44 < NaChar < 1.3e57

   1. Initial program 100.0%

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

   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 81.3%

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

   6. Taylor expanded in EAccept around 0 66.7%

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

   if 440 < NaChar < 1.54999999999999998e44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.2%

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

   6. Taylor expanded in EDonor around -inf 76.1%

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

   7. Taylor expanded in KbT around 0 88.6%

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

   8. Taylor expanded in Vef around inf 88.6%

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

   if 1.3e57 < 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 62.7%

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

   6. Taylor expanded in Vef around inf 75.0%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.3 \cdot 10^{-43}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{-1 - \frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 440:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar \cdot KbT}{EDonor \cdot \left(1 + \frac{Vef}{EDonor}\right)}\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{+57}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 60.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{-12} \lor \neg \left(NaChar \leq 3.1 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.7e-12) (not (<= NaChar 3.1e-39)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar 2.0))
   (-
    (/ NaChar (+ (/ EAccept KbT) 2.0))
    (/ 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 <= -2.7e-12) || !(NaChar <= 3.1e-39)) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (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 <= (-2.7d-12)) .or. (.not. (nachar <= 3.1d-39))) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (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 <= -2.7e-12) || !(NaChar <= 3.1e-39)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (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 <= -2.7e-12) or not (NaChar <= 3.1e-39):
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (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 <= -2.7e-12) || !(NaChar <= 3.1e-39))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - 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 <= -2.7e-12) || ~((NaChar <= 3.1e-39)))
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (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, -2.7e-12], N[Not[LessEqual[NaChar, 3.1e-39]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $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]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.6999999999999998e-12 or 3.0999999999999997e-39 < 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 Ec around inf 75.9%

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

      1. associate-*r/ 75.9%

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

      2. mul-1-neg 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in Ec around 0 63.5%

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

   if -2.6999999999999998e-12 < NaChar < 3.0999999999999997e-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 79.5%

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

   6. Taylor expanded in EAccept around 0 64.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{-12} \lor \neg \left(NaChar \leq 3.1 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 49.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.15 \cdot 10^{-36} \lor \neg \left(NaChar \leq 9 \cdot 10^{-217}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.15e-36) (not (<= NaChar 9e-217)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar 2.0))
   (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (* NaChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.15e-36) || !(NaChar <= 9e-217)) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-2.15d-36)) .or. (.not. (nachar <= 9d-217))) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.15e-36) || !(NaChar <= 9e-217)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2.15e-36) or not (NaChar <= 9e-217):
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -2.15e-36) || !(NaChar <= 9e-217))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -2.15e-36) || ~((NaChar <= 9e-217)))
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -2.15e-36], N[Not[LessEqual[NaChar, 9e-217]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.1500000000000001e-36 or 8.9999999999999997e-217 < 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 Ec around inf 73.5%

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

      1. associate-*r/ 73.5%

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

      2. mul-1-neg 73.5%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in Ec around 0 58.9%

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

   if -2.1500000000000001e-36 < NaChar < 8.9999999999999997e-217

   1. Initial program 100.0%

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

   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 Ec around inf 74.1%

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

      1. associate-*r/ 74.1%

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

      2. mul-1-neg 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in KbT around inf 51.1%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.15 \cdot 10^{-36} \lor \neg \left(NaChar \leq 9 \cdot 10^{-217}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 57.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.95 \cdot 10^{-23} \lor \neg \left(NaChar \leq 5.4 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.95e-23) (not (<= NaChar 5.4e-38)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar 2.0))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))
    (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.95e-23) || !(NaChar <= 5.4e-38)) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-1.95d-23)) .or. (.not. (nachar <= 5.4d-38))) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.95e-23) || !(NaChar <= 5.4e-38)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.95e-23) or not (NaChar <= 5.4e-38):
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.95e-23) || !(NaChar <= 5.4e-38))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1.95e-23) || ~((NaChar <= 5.4e-38)))
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.95e-23], N[Not[LessEqual[NaChar, 5.4e-38]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.95e-23 or 5.40000000000000011e-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 Ec around inf 75.9%

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

      1. associate-*r/ 75.9%

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

      2. mul-1-neg 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in Ec around 0 63.5%

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

   if -1.95e-23 < NaChar < 5.40000000000000011e-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 61.1%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.95 \cdot 10^{-23} \lor \neg \left(NaChar \leq 5.4 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 46.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.35 \cdot 10^{-35} \lor \neg \left(NaChar \leq 7.2 \cdot 10^{-170}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.35e-35) (not (<= NaChar 7.2e-170)))
   (+ (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))) (/ NdChar 2.0))
   (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (* NaChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.35e-35) || !(NaChar <= 7.2e-170)) {
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-2.35d-35)) .or. (.not. (nachar <= 7.2d-170))) then
        tmp = (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.35e-35) || !(NaChar <= 7.2e-170)) {
		tmp = (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2.35e-35) or not (NaChar <= 7.2e-170):
		tmp = (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -2.35e-35) || !(NaChar <= 7.2e-170))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -2.35e-35) || ~((NaChar <= 7.2e-170)))
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -2.35e-35], N[Not[LessEqual[NaChar, 7.2e-170]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.35e-35 or 7.2000000000000006e-170 < 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 Ec around inf 74.8%

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

      1. associate-*r/ 74.8%

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

      2. mul-1-neg 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in Ec around 0 60.3%

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

   9. Taylor expanded in EAccept around 0 54.4%

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

   if -2.35e-35 < NaChar < 7.2000000000000006e-170

   1. Initial program 100.0%

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

   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 Ec around inf 71.4%

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

      1. associate-*r/ 71.4%

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

      2. mul-1-neg 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in KbT around inf 49.1%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.35 \cdot 10^{-35} \lor \neg \left(NaChar \leq 7.2 \cdot 10^{-170}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 39.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -2.2 \cdot 10^{+83} \lor \neg \left(NdChar \leq 3.5 \cdot 10^{-183}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -2.2e+83) (not (<= NdChar 3.5e-183)))
   (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (* NaChar 0.5))
   (+ (/ NaChar (+ 1.0 (exp (/ Ev 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 ((NdChar <= -2.2e+83) || !(NdChar <= 3.5e-183)) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / 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 ((ndchar <= (-2.2d+83)) .or. (.not. (ndchar <= 3.5d-183))) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar * 0.5d0)
    else
        tmp = (nachar / (1.0d0 + exp((ev / 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 ((NdChar <= -2.2e+83) || !(NdChar <= 3.5e-183)) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -2.2e+83) or not (NdChar <= 3.5e-183):
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -2.2e+83) || !(NdChar <= 3.5e-183))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / 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 ((NdChar <= -2.2e+83) || ~((NdChar <= 3.5e-183)))
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -2.2e+83], N[Not[LessEqual[NdChar, 3.5e-183]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -2.19999999999999999e83 or 3.49999999999999991e-183 < 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 Ec around inf 64.2%

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

      1. associate-*r/ 64.2%

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

      2. mul-1-neg 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in KbT around inf 39.3%

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

   if -2.19999999999999999e83 < NdChar < 3.49999999999999991e-183

   1. Initial program 100.0%

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

   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 Ec around inf 86.3%

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

      1. associate-*r/ 86.3%

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

      2. mul-1-neg 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in Ec around 0 71.8%

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

   9. Taylor expanded in Ev around inf 51.0%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.2 \cdot 10^{+83} \lor \neg \left(NdChar \leq 3.5 \cdot 10^{-183}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 38.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -2.4 \cdot 10^{+83} \lor \neg \left(NdChar \leq 1.45 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -2.4e+83) (not (<= NdChar 1.45e-133)))
   (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (* NaChar 0.5))
   (+ (/ NaChar (+ 1.0 (exp (/ Ev 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 ((NdChar <= -2.4e+83) || !(NdChar <= 1.45e-133)) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / 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 ((ndchar <= (-2.4d+83)) .or. (.not. (ndchar <= 1.45d-133))) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar * 0.5d0)
    else
        tmp = (nachar / (1.0d0 + exp((ev / 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 ((NdChar <= -2.4e+83) || !(NdChar <= 1.45e-133)) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -2.4e+83) or not (NdChar <= 1.45e-133):
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -2.4e+83) || !(NdChar <= 1.45e-133))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / 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 ((NdChar <= -2.4e+83) || ~((NdChar <= 1.45e-133)))
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar * 0.5);
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -2.4e+83], N[Not[LessEqual[NdChar, 1.45e-133]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -2.39999999999999991e83 or 1.4499999999999999e-133 < 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 Vef around inf 58.3%

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

   6. Taylor expanded in KbT around inf 33.8%

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

   if -2.39999999999999991e83 < NdChar < 1.4499999999999999e-133

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 85.0%

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

      1. associate-*r/ 85.0%

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

      2. mul-1-neg 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in Ec around 0 69.0%

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

   9. Taylor expanded in Ev around inf 48.5%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.4 \cdot 10^{+83} \lor \neg \left(NdChar \leq 1.45 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -9 \cdot 10^{+125} \lor \neg \left(NdChar \leq 4.6 \cdot 10^{-129}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -9e+125) (not (<= NdChar 4.6e-129)))
   (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (/ NaChar 2.0))
   (+ (/ NaChar (+ 1.0 (exp (/ Ev 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 ((NdChar <= -9e+125) || !(NdChar <= 4.6e-129)) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / 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 ((ndchar <= (-9d+125)) .or. (.not. (ndchar <= 4.6d-129))) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((ev / 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 ((NdChar <= -9e+125) || !(NdChar <= 4.6e-129)) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -9e+125) or not (NdChar <= 4.6e-129):
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -9e+125) || !(NdChar <= 4.6e-129))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / 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 ((NdChar <= -9e+125) || ~((NdChar <= 4.6e-129)))
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -9e+125], N[Not[LessEqual[NdChar, 4.6e-129]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -9.0000000000000001e125 or 4.5999999999999999e-129 < 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 mu around inf 65.4%

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

   6. Taylor expanded in KbT around inf 37.3%

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

   if -9.0000000000000001e125 < NdChar < 4.5999999999999999e-129

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 82.9%

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

      1. associate-*r/ 82.9%

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

      2. mul-1-neg 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in Ec around 0 65.7%

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

   9. Taylor expanded in Ev around inf 46.9%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -9 \cdot 10^{+125} \lor \neg \left(NdChar \leq 4.6 \cdot 10^{-129}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 37.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -3.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -3.8e-19)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* NdChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -3.8e-19) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-3.8d-19)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -3.8e-19) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -3.8e-19:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -3.8e-19)
		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 * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -3.8e-19)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -3.8e-19], 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 * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -3.8e-19

   1. Initial program 100.0%

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

   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 Ec around inf 70.4%

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

      1. associate-*r/ 70.4%

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

      2. mul-1-neg 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in Ec around 0 47.8%

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

   9. Taylor expanded in Ev around inf 43.4%

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

   if -3.8e-19 < 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 EAccept around inf 70.4%

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

   6. Taylor expanded in KbT around inf 38.0%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -3.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 35.5% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Python

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

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 * 0.5))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
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 * 0.5), $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 EAccept around inf 68.6%

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

6. Taylor expanded in KbT around inf 36.5%

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

7. Final simplification 36.5%

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

Alternative 29: 27.9% accurate, 32.7× speedup

Math

\[\begin{array}{l} \\ \frac{NdChar}{2} + \frac{NaChar}{2} \end{array} \]

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / 2.0) + (NaChar / 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 = (ndchar / 2.0d0) + (nachar / 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 (NdChar / 2.0) + (NaChar / 2.0);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / 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 Ec around inf 73.7%

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

   1. associate-*r/ 73.7%

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

   2. mul-1-neg 73.7%

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

7. Simplified 73.7%

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

8. Taylor expanded in Ec around 0 50.2%

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

9. Taylor expanded in KbT around inf 28.1%

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

10. Final simplification 28.1%

    \[\leadsto \frac{NdChar}{2} + \frac{NaChar}{2} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(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))))))