Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 39.7s

Alternatives: 25

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -4.163758477254795e+225
  2. Ec = 6.962642601942249e+141
  3. Vef = -4.45824240969838e-38
  4. EDonor = 3.4406044329363864e-85
  5. mu = -4.4200399332879113e-293
  6. KbT = 6.859309508847048e-154
  7. NaChar = 2.52021280248779e+226
  8. Ev = -1.2639212899287026e+107
  9. EAccept = -7.402918772503285e-207

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{NdChar}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{\frac{EDonor - \left(\left(Ec - mu\right) - Vef\right)}{KbT}}\right)\right) + 1} + \frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ (expm1 (log1p (exp (/ (- EDonor (- (- Ec mu) Vef)) KbT)))) 1.0))
  (/ NaChar (+ (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (expm1(log1p(exp(((EDonor - ((Ec - mu) - Vef)) / KbT)))) + 1.0)) + (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0));
}

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (Math.expm1(Math.log1p(Math.exp(((EDonor - ((Ec - mu) - Vef)) / KbT)))) + 1.0)) + (NaChar / (Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0));
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (math.expm1(math.log1p(math.exp(((EDonor - ((Ec - mu) - Vef)) / KbT)))) + 1.0)) + (NaChar / (math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0))

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(expm1(log1p(exp(Float64(Float64(EDonor - Float64(Float64(Ec - mu) - Vef)) / KbT)))) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)) + 1.0)))
end

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Simplified 99.8%

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

   1. expm1-log1p-u 99.8%

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

   2. div-inv 99.8%

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

   3. associate-*r/ 99.8%

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

   4. *-commutative 99.8%

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

   5. *-un-lft-identity 99.8%

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

   6. +-commutative 99.8%

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

   7. associate-+l- 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

   \[\leadsto \frac{NdChar}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{\frac{EDonor - \left(\left(Ec - mu\right) - Vef\right)}{KbT}}\right)\right) + 1} + \frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} \]
8. Add Preprocessing

Alternative 2: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ t_1 := NaChar + t\_0\\ t_2 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ t_3 := \frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NdChar}{e^{\frac{\left(Vef + mu\right) - Ec}{KbT}} + 1}\\ \mathbf{if}\;Vef \leq -5 \cdot 10^{+29}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;Vef \leq -1.1 \cdot 10^{-138}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + 1\right) + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{elif}\;Vef \leq -4.9 \cdot 10^{-283}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{elif}\;Vef \leq 1.9 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq 1.85 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq 1.7 \cdot 10^{-46}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Ev}{KbT} + 1}\\ \mathbf{elif}\;Vef \leq 3.8 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq 8.2 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0)))
        (t_1 (+ NaChar t_0))
        (t_2
         (+
          (/ NdChar (+ (exp (/ mu KbT)) 1.0))
          (/ NaChar (+ (exp (/ mu (- KbT))) 1.0))))
        (t_3
         (+
          (/ NaChar (+ (exp (/ Vef KbT)) 1.0))
          (/ NdChar (+ (exp (/ (- (+ Vef mu) Ec) KbT)) 1.0)))))
   (if (<= Vef -5e+29)
     t_3
     (if (<= Vef -1.1e-138)
       (+
        t_0
        (/
         NaChar
         (+
          (- (+ (+ (/ EAccept KbT) 1.0) (+ (/ Ev KbT) (/ Vef KbT))) (/ mu KbT))
          1.0)))
       (if (<= Vef -4.9e-283)
         (+
          (/ NdChar (+ (exp (/ Ec (- KbT))) 1.0))
          (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)))
         (if (<= Vef 1.9e-216)
           t_1
           (if (<= Vef 1.85e-109)
             t_2
             (if (<= Vef 1.7e-46)
               (+ t_0 (/ NaChar (+ (/ Ev KbT) 1.0)))
               (if (<= Vef 3.8e+48) t_2 (if (<= Vef 8.2e+185) t_1 t_3))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double t_1 = NaChar + t_0;
	double t_2 = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / (exp((mu / -KbT)) + 1.0));
	double t_3 = (NaChar / (exp((Vef / KbT)) + 1.0)) + (NdChar / (exp((((Vef + mu) - Ec) / KbT)) + 1.0));
	double tmp;
	if (Vef <= -5e+29) {
		tmp = t_3;
	} else if (Vef <= -1.1e-138) {
		tmp = t_0 + (NaChar / (((((EAccept / KbT) + 1.0) + ((Ev / KbT) + (Vef / KbT))) - (mu / KbT)) + 1.0));
	} else if (Vef <= -4.9e-283) {
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) + (NaChar / (exp((EAccept / KbT)) + 1.0));
	} else if (Vef <= 1.9e-216) {
		tmp = t_1;
	} else if (Vef <= 1.85e-109) {
		tmp = t_2;
	} else if (Vef <= 1.7e-46) {
		tmp = t_0 + (NaChar / ((Ev / KbT) + 1.0));
	} else if (Vef <= 3.8e+48) {
		tmp = t_2;
	} else if (Vef <= 8.2e+185) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    t_1 = nachar + t_0
    t_2 = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (nachar / (exp((mu / -kbt)) + 1.0d0))
    t_3 = (nachar / (exp((vef / kbt)) + 1.0d0)) + (ndchar / (exp((((vef + mu) - ec) / kbt)) + 1.0d0))
    if (vef <= (-5d+29)) then
        tmp = t_3
    else if (vef <= (-1.1d-138)) then
        tmp = t_0 + (nachar / (((((eaccept / kbt) + 1.0d0) + ((ev / kbt) + (vef / kbt))) - (mu / kbt)) + 1.0d0))
    else if (vef <= (-4.9d-283)) then
        tmp = (ndchar / (exp((ec / -kbt)) + 1.0d0)) + (nachar / (exp((eaccept / kbt)) + 1.0d0))
    else if (vef <= 1.9d-216) then
        tmp = t_1
    else if (vef <= 1.85d-109) then
        tmp = t_2
    else if (vef <= 1.7d-46) then
        tmp = t_0 + (nachar / ((ev / kbt) + 1.0d0))
    else if (vef <= 3.8d+48) then
        tmp = t_2
    else if (vef <= 8.2d+185) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double t_1 = NaChar + t_0;
	double t_2 = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar / (Math.exp((mu / -KbT)) + 1.0));
	double t_3 = (NaChar / (Math.exp((Vef / KbT)) + 1.0)) + (NdChar / (Math.exp((((Vef + mu) - Ec) / KbT)) + 1.0));
	double tmp;
	if (Vef <= -5e+29) {
		tmp = t_3;
	} else if (Vef <= -1.1e-138) {
		tmp = t_0 + (NaChar / (((((EAccept / KbT) + 1.0) + ((Ev / KbT) + (Vef / KbT))) - (mu / KbT)) + 1.0));
	} else if (Vef <= -4.9e-283) {
		tmp = (NdChar / (Math.exp((Ec / -KbT)) + 1.0)) + (NaChar / (Math.exp((EAccept / KbT)) + 1.0));
	} else if (Vef <= 1.9e-216) {
		tmp = t_1;
	} else if (Vef <= 1.85e-109) {
		tmp = t_2;
	} else if (Vef <= 1.7e-46) {
		tmp = t_0 + (NaChar / ((Ev / KbT) + 1.0));
	} else if (Vef <= 3.8e+48) {
		tmp = t_2;
	} else if (Vef <= 8.2e+185) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	t_1 = NaChar + t_0
	t_2 = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar / (math.exp((mu / -KbT)) + 1.0))
	t_3 = (NaChar / (math.exp((Vef / KbT)) + 1.0)) + (NdChar / (math.exp((((Vef + mu) - Ec) / KbT)) + 1.0))
	tmp = 0
	if Vef <= -5e+29:
		tmp = t_3
	elif Vef <= -1.1e-138:
		tmp = t_0 + (NaChar / (((((EAccept / KbT) + 1.0) + ((Ev / KbT) + (Vef / KbT))) - (mu / KbT)) + 1.0))
	elif Vef <= -4.9e-283:
		tmp = (NdChar / (math.exp((Ec / -KbT)) + 1.0)) + (NaChar / (math.exp((EAccept / KbT)) + 1.0))
	elif Vef <= 1.9e-216:
		tmp = t_1
	elif Vef <= 1.85e-109:
		tmp = t_2
	elif Vef <= 1.7e-46:
		tmp = t_0 + (NaChar / ((Ev / KbT) + 1.0))
	elif Vef <= 3.8e+48:
		tmp = t_2
	elif Vef <= 8.2e+185:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	t_1 = Float64(NaChar + t_0)
	t_2 = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0)))
	t_3 = Float64(Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)) + 1.0)))
	tmp = 0.0
	if (Vef <= -5e+29)
		tmp = t_3;
	elseif (Vef <= -1.1e-138)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Float64(Float64(Float64(EAccept / KbT) + 1.0) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT))) - Float64(mu / KbT)) + 1.0)));
	elseif (Vef <= -4.9e-283)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Ec / Float64(-KbT))) + 1.0)) + Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)));
	elseif (Vef <= 1.9e-216)
		tmp = t_1;
	elseif (Vef <= 1.85e-109)
		tmp = t_2;
	elseif (Vef <= 1.7e-46)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Ev / KbT) + 1.0)));
	elseif (Vef <= 3.8e+48)
		tmp = t_2;
	elseif (Vef <= 8.2e+185)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	t_1 = NaChar + t_0;
	t_2 = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / (exp((mu / -KbT)) + 1.0));
	t_3 = (NaChar / (exp((Vef / KbT)) + 1.0)) + (NdChar / (exp((((Vef + mu) - Ec) / KbT)) + 1.0));
	tmp = 0.0;
	if (Vef <= -5e+29)
		tmp = t_3;
	elseif (Vef <= -1.1e-138)
		tmp = t_0 + (NaChar / (((((EAccept / KbT) + 1.0) + ((Ev / KbT) + (Vef / KbT))) - (mu / KbT)) + 1.0));
	elseif (Vef <= -4.9e-283)
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) + (NaChar / (exp((EAccept / KbT)) + 1.0));
	elseif (Vef <= 1.9e-216)
		tmp = t_1;
	elseif (Vef <= 1.85e-109)
		tmp = t_2;
	elseif (Vef <= 1.7e-46)
		tmp = t_0 + (NaChar / ((Ev / KbT) + 1.0));
	elseif (Vef <= 3.8e+48)
		tmp = t_2;
	elseif (Vef <= 8.2e+185)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -5e+29], t$95$3, If[LessEqual[Vef, -1.1e-138], N[(t$95$0 + N[(NaChar / N[(N[(N[(N[(N[(EAccept / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -4.9e-283], N[(N[(NdChar / N[(N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.9e-216], t$95$1, If[LessEqual[Vef, 1.85e-109], t$95$2, If[LessEqual[Vef, 1.7e-46], N[(t$95$0 + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 3.8e+48], t$95$2, If[LessEqual[Vef, 8.2e+185], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if Vef < -5.0000000000000001e29 or 8.2e185 < Vef

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 86.8%

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

   6. Taylor expanded in EDonor around 0 84.3%

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

   if -5.0000000000000001e29 < Vef < -1.0999999999999999e-138

   1. Initial program 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in KbT around inf 75.0%

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

      1. associate-+r+ 75.0%

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

      2. +-commutative 75.0%

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

   7. Simplified 75.0%

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

   if -1.0999999999999999e-138 < Vef < -4.9e-283

   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 78.8%

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

   6. Taylor expanded in Ec around inf 69.8%

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

      1. associate-*r/ 69.8%

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

      2. mul-1-neg 69.8%

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

   8. Simplified 69.8%

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

   if -4.9e-283 < Vef < 1.9e-216 or 3.8e48 < Vef < 8.2e185

   1. Initial program 100.0%

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

   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 42.1%

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

      1. associate-+r+ 42.1%

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

      2. +-commutative 42.1%

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

   7. Simplified 42.1%

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

   8. Taylor expanded in mu around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. distribute-frac-neg 50.5%

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

   10. Simplified 50.5%

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

   11. Taylor expanded in mu around 0 78.1%

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

   if 1.9e-216 < Vef < 1.8499999999999999e-109 or 1.69999999999999998e-46 < Vef < 3.8e48

   1. Initial program 100.0%

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

   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 77.8%

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

   6. Taylor expanded in mu around inf 71.4%

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

      1. mul-1-neg 36.5%

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

   8. Simplified 71.4%

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

   if 1.8499999999999999e-109 < Vef < 1.69999999999999998e-46

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 37.3%

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

      1. associate-+r+ 37.3%

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

      2. +-commutative 37.3%

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

   7. Simplified 37.3%

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

   8. Taylor expanded in Ev around inf 62.5%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NdChar}{e^{\frac{\left(Vef + mu\right) - Ec}{KbT}} + 1}\\ \mathbf{elif}\;Vef \leq -1.1 \cdot 10^{-138}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + 1\right) + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{elif}\;Vef \leq -4.9 \cdot 10^{-283}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{elif}\;Vef \leq 1.9 \cdot 10^{-216}:\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{elif}\;Vef \leq 1.85 \cdot 10^{-109}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{elif}\;Vef \leq 1.7 \cdot 10^{-46}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 1}\\ \mathbf{elif}\;Vef \leq 3.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{elif}\;Vef \leq 8.2 \cdot 10^{+185}:\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NdChar}{e^{\frac{\left(Vef + mu\right) - Ec}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ t_1 := t\_0 + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ t_2 := \frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{if}\;mu \leq -4.5 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -5.5 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq 2.6 \cdot 10^{-119}:\\ \;\;\;\;t\_0 + \frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;mu \leq 0.16:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0)))
        (t_1 (+ t_0 (/ NaChar (+ (exp (/ Ev KbT)) 1.0))))
        (t_2
         (+
          (/ NaChar (+ (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)) 1.0))
          (/ NdChar (+ (exp (/ mu KbT)) 1.0)))))
   (if (<= mu -4.5e-24)
     t_2
     (if (<= mu -5.5e-256)
       t_1
       (if (<= mu 2.6e-119)
         (+ t_0 (/ NaChar (+ (exp (/ Vef KbT)) 1.0)))
         (if (<= mu 0.16) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double t_1 = t_0 + (NaChar / (exp((Ev / KbT)) + 1.0));
	double t_2 = (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	double tmp;
	if (mu <= -4.5e-24) {
		tmp = t_2;
	} else if (mu <= -5.5e-256) {
		tmp = t_1;
	} else if (mu <= 2.6e-119) {
		tmp = t_0 + (NaChar / (exp((Vef / KbT)) + 1.0));
	} else if (mu <= 0.16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    t_1 = t_0 + (nachar / (exp((ev / kbt)) + 1.0d0))
    t_2 = (nachar / (exp(((vef + (ev - (mu - eaccept))) / kbt)) + 1.0d0)) + (ndchar / (exp((mu / kbt)) + 1.0d0))
    if (mu <= (-4.5d-24)) then
        tmp = t_2
    else if (mu <= (-5.5d-256)) then
        tmp = t_1
    else if (mu <= 2.6d-119) then
        tmp = t_0 + (nachar / (exp((vef / kbt)) + 1.0d0))
    else if (mu <= 0.16d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double t_1 = t_0 + (NaChar / (Math.exp((Ev / KbT)) + 1.0));
	double t_2 = (NaChar / (Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / (Math.exp((mu / KbT)) + 1.0));
	double tmp;
	if (mu <= -4.5e-24) {
		tmp = t_2;
	} else if (mu <= -5.5e-256) {
		tmp = t_1;
	} else if (mu <= 2.6e-119) {
		tmp = t_0 + (NaChar / (Math.exp((Vef / KbT)) + 1.0));
	} else if (mu <= 0.16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	t_1 = t_0 + (NaChar / (math.exp((Ev / KbT)) + 1.0))
	t_2 = (NaChar / (math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / (math.exp((mu / KbT)) + 1.0))
	tmp = 0
	if mu <= -4.5e-24:
		tmp = t_2
	elif mu <= -5.5e-256:
		tmp = t_1
	elif mu <= 2.6e-119:
		tmp = t_0 + (NaChar / (math.exp((Vef / KbT)) + 1.0))
	elif mu <= 0.16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)))
	t_2 = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)))
	tmp = 0.0
	if (mu <= -4.5e-24)
		tmp = t_2;
	elseif (mu <= -5.5e-256)
		tmp = t_1;
	elseif (mu <= 2.6e-119)
		tmp = Float64(t_0 + Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0)));
	elseif (mu <= 0.16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	t_1 = t_0 + (NaChar / (exp((Ev / KbT)) + 1.0));
	t_2 = (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	tmp = 0.0;
	if (mu <= -4.5e-24)
		tmp = t_2;
	elseif (mu <= -5.5e-256)
		tmp = t_1;
	elseif (mu <= 2.6e-119)
		tmp = t_0 + (NaChar / (exp((Vef / KbT)) + 1.0));
	elseif (mu <= 0.16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -4.5e-24], t$95$2, If[LessEqual[mu, -5.5e-256], t$95$1, If[LessEqual[mu, 2.6e-119], N[(t$95$0 + N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 0.16], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -4.4999999999999997e-24 or 0.160000000000000003 < mu

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in mu around inf 87.5%

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

   if -4.4999999999999997e-24 < mu < -5.4999999999999998e-256 or 2.60000000000000012e-119 < mu < 0.160000000000000003

   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 Ev around inf 73.5%

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

   if -5.4999999999999998e-256 < mu < 2.60000000000000012e-119

   1. Initial program 100.0%

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

   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 84.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -4.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;mu \leq -5.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;mu \leq 2.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;mu \leq 0.16:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq -5.5 \cdot 10^{-27} \lor \neg \left(EDonor \leq 3.3 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NdChar}{e^{\frac{\left(Vef + mu\right) - Ec}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= EDonor -5.5e-27) (not (<= EDonor 3.3e-15)))
   (-
    (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))
    (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
   (+
    (/ NaChar (+ (exp (/ Vef KbT)) 1.0))
    (/ NdChar (+ (exp (/ (- (+ Vef mu) Ec) KbT)) 1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((EDonor <= -5.5e-27) || !(EDonor <= 3.3e-15)) {
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = (NaChar / (exp((Vef / KbT)) + 1.0)) + (NdChar / (exp((((Vef + mu) - Ec) / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((edonor <= (-5.5d-27)) .or. (.not. (edonor <= 3.3d-15))) then
        tmp = (ndchar / (exp((edonor / kbt)) + 1.0d0)) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else
        tmp = (nachar / (exp((vef / kbt)) + 1.0d0)) + (ndchar / (exp((((vef + mu) - ec) / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((EDonor <= -5.5e-27) || !(EDonor <= 3.3e-15)) {
		tmp = (NdChar / (Math.exp((EDonor / KbT)) + 1.0)) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = (NaChar / (Math.exp((Vef / KbT)) + 1.0)) + (NdChar / (Math.exp((((Vef + mu) - Ec) / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (EDonor <= -5.5e-27) or not (EDonor <= 3.3e-15):
		tmp = (NdChar / (math.exp((EDonor / KbT)) + 1.0)) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	else:
		tmp = (NaChar / (math.exp((Vef / KbT)) + 1.0)) + (NdChar / (math.exp((((Vef + mu) - Ec) / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((EDonor <= -5.5e-27) || !(EDonor <= 3.3e-15))
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((EDonor <= -5.5e-27) || ~((EDonor <= 3.3e-15)))
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	else
		tmp = (NaChar / (exp((Vef / KbT)) + 1.0)) + (NdChar / (exp((((Vef + mu) - Ec) / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[EDonor, -5.5e-27], N[Not[LessEqual[EDonor, 3.3e-15]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -5.5000000000000002e-27 or 3.3e-15 < EDonor

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in EDonor around inf 83.0%

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

   if -5.5000000000000002e-27 < EDonor < 3.3e-15

   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 Vef around inf 66.1%

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

   6. Taylor expanded in EDonor around 0 66.1%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -5.5 \cdot 10^{-27} \lor \neg \left(EDonor \leq 3.3 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NdChar}{e^{\frac{\left(Vef + mu\right) - Ec}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}\\ \mathbf{if}\;mu \leq -1.4 \cdot 10^{-71} \lor \neg \left(mu \leq 0.09\right):\\ \;\;\;\;\frac{NaChar}{t\_0 + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} - \frac{NaChar}{-1 - t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))
   (if (or (<= mu -1.4e-71) (not (<= mu 0.09)))
     (+ (/ NaChar (+ t_0 1.0)) (/ NdChar (+ (exp (/ mu KbT)) 1.0)))
     (- (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)) (/ NaChar (- -1.0 t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double tmp;
	if ((mu <= -1.4e-71) || !(mu <= 0.09)) {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(((vef + (ev - (mu - eaccept))) / kbt))
    if ((mu <= (-1.4d-71)) .or. (.not. (mu <= 0.09d0))) then
        tmp = (nachar / (t_0 + 1.0d0)) + (ndchar / (exp((mu / kbt)) + 1.0d0))
    else
        tmp = (ndchar / (exp((edonor / kbt)) + 1.0d0)) - (nachar / ((-1.0d0) - t_0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	double tmp;
	if ((mu <= -1.4e-71) || !(mu <= 0.09)) {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (Math.exp((mu / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp((EDonor / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))
	tmp = 0
	if (mu <= -1.4e-71) or not (mu <= 0.09):
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (math.exp((mu / KbT)) + 1.0))
	else:
		tmp = (NdChar / (math.exp((EDonor / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT))
	tmp = 0.0
	if ((mu <= -1.4e-71) || !(mu <= 0.09))
		tmp = Float64(Float64(NaChar / Float64(t_0 + 1.0)) + Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)) - Float64(NaChar / Float64(-1.0 - t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((Vef + (Ev - (mu - EAccept))) / KbT));
	tmp = 0.0;
	if ((mu <= -1.4e-71) || ~((mu <= 0.09)))
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	else
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[mu, -1.4e-71], N[Not[LessEqual[mu, 0.09]], $MachinePrecision]], N[(N[(NaChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if mu < -1.4e-71 or 0.089999999999999997 < mu

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in mu around inf 87.6%

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

   if -1.4e-71 < mu < 0.089999999999999997

   1. Initial program 100.0%

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

   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 76.9%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -1.4 \cdot 10^{-71} \lor \neg \left(mu \leq 0.09\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -9.5 \cdot 10^{-27} \lor \neg \left(mu \leq 0.034\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= mu -9.5e-27) (not (<= mu 0.034)))
   (+
    (/ NaChar (+ (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)) 1.0))
    (/ NdChar (+ (exp (/ mu KbT)) 1.0)))
   (+
    (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))
    (/ NaChar (+ (exp (/ Ev KbT)) 1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -9.5e-27) || !(mu <= 0.034)) {
		tmp = (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp((Ev / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((mu <= (-9.5d-27)) .or. (.not. (mu <= 0.034d0))) then
        tmp = (nachar / (exp(((vef + (ev - (mu - eaccept))) / kbt)) + 1.0d0)) + (ndchar / (exp((mu / kbt)) + 1.0d0))
    else
        tmp = (ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (exp((ev / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -9.5e-27) || !(mu <= 0.034)) {
		tmp = (NaChar / (Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / (Math.exp((mu / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (Math.exp((Ev / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (mu <= -9.5e-27) or not (mu <= 0.034):
		tmp = (NaChar / (math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / (math.exp((mu / KbT)) + 1.0))
	else:
		tmp = (NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (math.exp((Ev / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((mu <= -9.5e-27) || !(mu <= 0.034))
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((mu <= -9.5e-27) || ~((mu <= 0.034)))
		tmp = (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	else
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp((Ev / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[mu, -9.5e-27], N[Not[LessEqual[mu, 0.034]], $MachinePrecision]], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if mu < -9.50000000000000037e-27 or 0.034000000000000002 < mu

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in mu around inf 87.5%

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

   if -9.50000000000000037e-27 < mu < 0.034000000000000002

   1. Initial program 100.0%

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

   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 69.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -9.5 \cdot 10^{-27} \lor \neg \left(mu \leq 0.034\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 8: 64.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{\frac{mu}{KbT} + 2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NdChar \leq -3.3 \cdot 10^{+47}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-143}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 85000000000:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;NaChar + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NdChar (+ (/ mu KbT) 2.0))
          (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT))))))
        (t_1 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))))
   (if (<= NdChar -3.3e+47)
     (+ t_1 (/ NaChar (+ (/ Vef KbT) 1.0)))
     (if (<= NdChar 3.3e-143)
       t_0
       (if (<= NdChar 85000000000.0)
         (+ t_1 (/ NaChar (- 1.0 (/ mu KbT))))
         (if (<= NdChar 1.9e+43) t_0 (+ NaChar t_1)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	double t_1 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -3.3e+47) {
		tmp = t_1 + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= 3.3e-143) {
		tmp = t_0;
	} else if (NdChar <= 85000000000.0) {
		tmp = t_1 + (NaChar / (1.0 - (mu / KbT)));
	} else if (NdChar <= 1.9e+43) {
		tmp = t_0;
	} else {
		tmp = NaChar + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / ((mu / kbt) + 2.0d0)) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    t_1 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    if (ndchar <= (-3.3d+47)) then
        tmp = t_1 + (nachar / ((vef / kbt) + 1.0d0))
    else if (ndchar <= 3.3d-143) then
        tmp = t_0
    else if (ndchar <= 85000000000.0d0) then
        tmp = t_1 + (nachar / (1.0d0 - (mu / kbt)))
    else if (ndchar <= 1.9d+43) then
        tmp = t_0
    else
        tmp = nachar + t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	double t_1 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -3.3e+47) {
		tmp = t_1 + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= 3.3e-143) {
		tmp = t_0;
	} else if (NdChar <= 85000000000.0) {
		tmp = t_1 + (NaChar / (1.0 - (mu / KbT)));
	} else if (NdChar <= 1.9e+43) {
		tmp = t_0;
	} else {
		tmp = NaChar + t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	t_1 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	tmp = 0
	if NdChar <= -3.3e+47:
		tmp = t_1 + (NaChar / ((Vef / KbT) + 1.0))
	elif NdChar <= 3.3e-143:
		tmp = t_0
	elif NdChar <= 85000000000.0:
		tmp = t_1 + (NaChar / (1.0 - (mu / KbT)))
	elif NdChar <= 1.9e+43:
		tmp = t_0
	else:
		tmp = NaChar + t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))))
	t_1 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	tmp = 0.0
	if (NdChar <= -3.3e+47)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(Vef / KbT) + 1.0)));
	elseif (NdChar <= 3.3e-143)
		tmp = t_0;
	elseif (NdChar <= 85000000000.0)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 - Float64(mu / KbT))));
	elseif (NdChar <= 1.9e+43)
		tmp = t_0;
	else
		tmp = Float64(NaChar + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	t_1 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NdChar <= -3.3e+47)
		tmp = t_1 + (NaChar / ((Vef / KbT) + 1.0));
	elseif (NdChar <= 3.3e-143)
		tmp = t_0;
	elseif (NdChar <= 85000000000.0)
		tmp = t_1 + (NaChar / (1.0 - (mu / KbT)));
	elseif (NdChar <= 1.9e+43)
		tmp = t_0;
	else
		tmp = NaChar + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.3e+47], N[(t$95$1 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.3e-143], t$95$0, If[LessEqual[NdChar, 85000000000.0], N[(t$95$1 + N[(NaChar / N[(1.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.9e+43], t$95$0, N[(NaChar + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -3.2999999999999999e47

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 56.6%

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

      1. associate-+r+ 56.6%

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

      2. +-commutative 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in Vef around inf 71.6%

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

   if -3.2999999999999999e47 < NdChar < 3.3000000000000001e-143 or 8.5e10 < NdChar < 1.90000000000000004e43

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in mu around inf 81.2%

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

   6. Taylor expanded in mu around 0 66.0%

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

   if 3.3000000000000001e-143 < NdChar < 8.5e10

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 47.2%

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

      1. associate-+r+ 47.2%

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

      2. +-commutative 47.2%

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

   7. Simplified 47.2%

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

   8. Taylor expanded in mu around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. distribute-frac-neg 65.4%

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

   10. Simplified 65.4%

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

   if 1.90000000000000004e43 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 55.4%

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

      1. associate-+r+ 55.4%

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

      2. +-commutative 55.4%

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

   7. Simplified 55.4%

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

   8. Taylor expanded in mu around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. distribute-frac-neg 64.9%

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

   10. Simplified 64.9%

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

   11. Taylor expanded in mu around 0 68.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.3 \cdot 10^{+47}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-143}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT} + 2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 85000000000:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{1 - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT} + 2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NdChar \leq -2 \cdot 10^{+47}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq 2.65 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{EDonor - \left(\left(Ec - mu\right) - Vef\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;NaChar + t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))))
   (if (<= NdChar -2e+47)
     (+ t_0 (/ NaChar (+ (/ Vef KbT) 1.0)))
     (if (<= NdChar 2.65e-101)
       (+
        (/ NaChar (+ (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)) 1.0))
        (/ NdChar (+ (+ (/ (- EDonor (- (- Ec mu) Vef)) KbT) 1.0) 1.0)))
       (+ NaChar t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -2e+47) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= 2.65e-101) {
		tmp = (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / ((((EDonor - ((Ec - mu) - Vef)) / KbT) + 1.0) + 1.0));
	} else {
		tmp = NaChar + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    if (ndchar <= (-2d+47)) then
        tmp = t_0 + (nachar / ((vef / kbt) + 1.0d0))
    else if (ndchar <= 2.65d-101) then
        tmp = (nachar / (exp(((vef + (ev - (mu - eaccept))) / kbt)) + 1.0d0)) + (ndchar / ((((edonor - ((ec - mu) - vef)) / kbt) + 1.0d0) + 1.0d0))
    else
        tmp = nachar + t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -2e+47) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= 2.65e-101) {
		tmp = (NaChar / (Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / ((((EDonor - ((Ec - mu) - Vef)) / KbT) + 1.0) + 1.0));
	} else {
		tmp = NaChar + t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	tmp = 0
	if NdChar <= -2e+47:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0))
	elif NdChar <= 2.65e-101:
		tmp = (NaChar / (math.exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / ((((EDonor - ((Ec - mu) - Vef)) / KbT) + 1.0) + 1.0))
	else:
		tmp = NaChar + t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	tmp = 0.0
	if (NdChar <= -2e+47)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 1.0)));
	elseif (NdChar <= 2.65e-101)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Float64(Float64(EDonor - Float64(Float64(Ec - mu) - Vef)) / KbT) + 1.0) + 1.0)));
	else
		tmp = Float64(NaChar + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NdChar <= -2e+47)
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0));
	elseif (NdChar <= 2.65e-101)
		tmp = (NaChar / (exp(((Vef + (Ev - (mu - EAccept))) / KbT)) + 1.0)) + (NdChar / ((((EDonor - ((Ec - mu) - Vef)) / KbT) + 1.0) + 1.0));
	else
		tmp = NaChar + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -2e+47], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.65e-101], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(EDonor - N[(N[(Ec - mu), $MachinePrecision] - Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -2.0000000000000001e47

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 56.6%

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

      1. associate-+r+ 56.6%

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

      2. +-commutative 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in Vef around inf 71.6%

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

   if -2.0000000000000001e47 < NdChar < 2.6500000000000001e-101

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

      3. div-inv 99.8%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in KbT around inf 68.6%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(1 + \left(0.3333333333333333 \cdot \frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT} + 0.6666666666666666 \cdot \frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}\right)\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   8. Step-by-step derivation

      1. distribute-rgt-out 68.6%

         \[\leadsto \frac{NdChar}{1 + \left(1 + \color{blue}{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT} \cdot \left(0.3333333333333333 + 0.6666666666666666\right)}\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      2. metadata-eval 68.6%

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

      3. *-rgt-identity 68.6%

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

      4. associate--l+ 68.6%

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

      5. sub-neg 68.6%

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

      6. associate-+r+ 68.6%

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

      7. mul-1-neg 68.6%

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

      8. +-commutative 68.6%

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

      9. mul-1-neg 68.6%

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

      10. sub-neg 68.6%

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

   9. Simplified 68.6%

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

   if 2.6500000000000001e-101 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 54.2%

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

      1. associate-+r+ 54.2%

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

      2. +-commutative 54.2%

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

   7. Simplified 54.2%

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

   8. Taylor expanded in mu around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. distribute-frac-neg 60.3%

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

   10. Simplified 60.3%

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

   11. Taylor expanded in mu around 0 66.3%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2 \cdot 10^{+47}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq 2.65 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{EDonor - \left(\left(Ec - mu\right) - Vef\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -7.5 \cdot 10^{-308} \lor \neg \left(NaChar \leq 2.65 \cdot 10^{-61}\right):\\ \;\;\;\;NaChar + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))))
   (if (<= NaChar -1.9e+17)
     (-
      (/ NdChar 2.0)
      (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
     (if (or (<= NaChar -7.5e-308) (not (<= NaChar 2.65e-61)))
       (+ NaChar t_0)
       (+ t_0 (/ NaChar (+ (/ Vef KbT) 1.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -1.9e+17) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else if ((NaChar <= -7.5e-308) || !(NaChar <= 2.65e-61)) {
		tmp = NaChar + t_0;
	} else {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    if (nachar <= (-1.9d+17)) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else if ((nachar <= (-7.5d-308)) .or. (.not. (nachar <= 2.65d-61))) then
        tmp = nachar + t_0
    else
        tmp = t_0 + (nachar / ((vef / kbt) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -1.9e+17) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else if ((NaChar <= -7.5e-308) || !(NaChar <= 2.65e-61)) {
		tmp = NaChar + t_0;
	} else {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	tmp = 0
	if NaChar <= -1.9e+17:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	elif (NaChar <= -7.5e-308) or not (NaChar <= 2.65e-61):
		tmp = NaChar + t_0
	else:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	tmp = 0.0
	if (NaChar <= -1.9e+17)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	elseif ((NaChar <= -7.5e-308) || !(NaChar <= 2.65e-61))
		tmp = Float64(NaChar + t_0);
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NaChar <= -1.9e+17)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	elseif ((NaChar <= -7.5e-308) || ~((NaChar <= 2.65e-61)))
		tmp = NaChar + t_0;
	else
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.9e+17], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, -7.5e-308], N[Not[LessEqual[NaChar, 2.65e-61]], $MachinePrecision]], N[(NaChar + t$95$0), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.9e17

   1. Initial program 100.0%

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

   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 61.0%

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

   if -1.9e17 < NaChar < -7.4999999999999998e-308 or 2.65e-61 < NaChar

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in KbT around inf 44.3%

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

      1. associate-+r+ 44.3%

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

      2. +-commutative 44.3%

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

   7. Simplified 44.3%

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

   8. Taylor expanded in mu around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. distribute-frac-neg 49.3%

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

   10. Simplified 49.3%

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

   11. Taylor expanded in mu around 0 64.8%

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

   if -7.4999999999999998e-308 < NaChar < 2.65e-61

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.2%

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

      1. associate-+r+ 73.2%

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

      2. +-commutative 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in Vef around inf 74.7%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -7.5 \cdot 10^{-308} \lor \neg \left(NaChar \leq 2.65 \cdot 10^{-61}\right):\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.8 \cdot 10^{-271} \lor \neg \left(NaChar \leq 7.5 \cdot 10^{-233}\right):\\ \;\;\;\;NaChar + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{KbT \cdot NaChar}{EAccept}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))))
   (if (<= NaChar -1.9e+16)
     (-
      (/ NdChar 2.0)
      (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
     (if (or (<= NaChar -1.8e-271) (not (<= NaChar 7.5e-233)))
       (+ NaChar t_0)
       (+ t_0 (/ (* KbT NaChar) EAccept))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -1.9e+16) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else if ((NaChar <= -1.8e-271) || !(NaChar <= 7.5e-233)) {
		tmp = NaChar + t_0;
	} else {
		tmp = t_0 + ((KbT * NaChar) / EAccept);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    if (nachar <= (-1.9d+16)) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else if ((nachar <= (-1.8d-271)) .or. (.not. (nachar <= 7.5d-233))) then
        tmp = nachar + t_0
    else
        tmp = t_0 + ((kbt * nachar) / eaccept)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -1.9e+16) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else if ((NaChar <= -1.8e-271) || !(NaChar <= 7.5e-233)) {
		tmp = NaChar + t_0;
	} else {
		tmp = t_0 + ((KbT * NaChar) / EAccept);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	tmp = 0
	if NaChar <= -1.9e+16:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	elif (NaChar <= -1.8e-271) or not (NaChar <= 7.5e-233):
		tmp = NaChar + t_0
	else:
		tmp = t_0 + ((KbT * NaChar) / EAccept)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	tmp = 0.0
	if (NaChar <= -1.9e+16)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	elseif ((NaChar <= -1.8e-271) || !(NaChar <= 7.5e-233))
		tmp = Float64(NaChar + t_0);
	else
		tmp = Float64(t_0 + Float64(Float64(KbT * NaChar) / EAccept));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NaChar <= -1.9e+16)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	elseif ((NaChar <= -1.8e-271) || ~((NaChar <= 7.5e-233)))
		tmp = NaChar + t_0;
	else
		tmp = t_0 + ((KbT * NaChar) / EAccept);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.9e+16], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, -1.8e-271], N[Not[LessEqual[NaChar, 7.5e-233]], $MachinePrecision]], N[(NaChar + t$95$0), $MachinePrecision], N[(t$95$0 + N[(N[(KbT * NaChar), $MachinePrecision] / EAccept), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.9e16

   1. Initial program 100.0%

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

   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 61.0%

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

   if -1.9e16 < NaChar < -1.7999999999999999e-271 or 7.49999999999999974e-233 < NaChar

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 48.3%

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

      1. associate-+r+ 48.3%

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

      2. +-commutative 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in mu around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. distribute-frac-neg 50.9%

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

   10. Simplified 50.9%

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

   11. Taylor expanded in mu around 0 63.3%

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

   if -1.7999999999999999e-271 < NaChar < 7.49999999999999974e-233

   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 KbT around inf 76.9%

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

      1. associate-+r+ 76.9%

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

      2. +-commutative 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in EAccept around inf 77.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.8 \cdot 10^{-271} \lor \neg \left(NaChar \leq 7.5 \cdot 10^{-233}\right):\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{KbT \cdot NaChar}{EAccept}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -8.5 \cdot 10^{-308} \lor \neg \left(NaChar \leq 3.35 \cdot 10^{-251}\right):\\ \;\;\;\;NaChar + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{KbT \cdot NaChar}{Vef}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))))
   (if (<= NaChar -1.9e+17)
     (-
      (/ NdChar 2.0)
      (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
     (if (or (<= NaChar -8.5e-308) (not (<= NaChar 3.35e-251)))
       (+ NaChar t_0)
       (+ t_0 (/ (* KbT NaChar) Vef))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -1.9e+17) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else if ((NaChar <= -8.5e-308) || !(NaChar <= 3.35e-251)) {
		tmp = NaChar + t_0;
	} else {
		tmp = t_0 + ((KbT * NaChar) / Vef);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    if (nachar <= (-1.9d+17)) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else if ((nachar <= (-8.5d-308)) .or. (.not. (nachar <= 3.35d-251))) then
        tmp = nachar + t_0
    else
        tmp = t_0 + ((kbt * nachar) / vef)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -1.9e+17) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else if ((NaChar <= -8.5e-308) || !(NaChar <= 3.35e-251)) {
		tmp = NaChar + t_0;
	} else {
		tmp = t_0 + ((KbT * NaChar) / Vef);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	tmp = 0
	if NaChar <= -1.9e+17:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	elif (NaChar <= -8.5e-308) or not (NaChar <= 3.35e-251):
		tmp = NaChar + t_0
	else:
		tmp = t_0 + ((KbT * NaChar) / Vef)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	tmp = 0.0
	if (NaChar <= -1.9e+17)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	elseif ((NaChar <= -8.5e-308) || !(NaChar <= 3.35e-251))
		tmp = Float64(NaChar + t_0);
	else
		tmp = Float64(t_0 + Float64(Float64(KbT * NaChar) / Vef));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NaChar <= -1.9e+17)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	elseif ((NaChar <= -8.5e-308) || ~((NaChar <= 3.35e-251)))
		tmp = NaChar + t_0;
	else
		tmp = t_0 + ((KbT * NaChar) / Vef);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.9e+17], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, -8.5e-308], N[Not[LessEqual[NaChar, 3.35e-251]], $MachinePrecision]], N[(NaChar + t$95$0), $MachinePrecision], N[(t$95$0 + N[(N[(KbT * NaChar), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.9e17

   1. Initial program 100.0%

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

   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 61.0%

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

   if -1.9e17 < NaChar < -8.49999999999999972e-308 or 3.34999999999999989e-251 < NaChar

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 49.3%

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

      1. associate-+r+ 49.3%

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

      2. +-commutative 49.3%

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

   7. Simplified 49.3%

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

   8. Taylor expanded in mu around inf 52.1%

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

      1. mul-1-neg 52.1%

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

      2. distribute-frac-neg 52.1%

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

   10. Simplified 52.1%

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

   11. Taylor expanded in mu around 0 64.0%

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

   if -8.49999999999999972e-308 < NaChar < 3.34999999999999989e-251

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 89.8%

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

      1. associate-+r+ 89.8%

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

      2. +-commutative 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in Vef around inf 99.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -8.5 \cdot 10^{-308} \lor \neg \left(NaChar \leq 3.35 \cdot 10^{-251}\right):\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{KbT \cdot NaChar}{Vef}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NdChar \leq -9.5 \cdot 10^{+47}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq 2.8 \cdot 10^{-100}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT} + 2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NaChar + t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))))
   (if (<= NdChar -9.5e+47)
     (+ t_0 (/ NaChar (+ (/ Vef KbT) 1.0)))
     (if (<= NdChar 2.8e-100)
       (-
        (/ NdChar (+ (/ mu KbT) 2.0))
        (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
       (+ NaChar t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -9.5e+47) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= 2.8e-100) {
		tmp = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = NaChar + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    if (ndchar <= (-9.5d+47)) then
        tmp = t_0 + (nachar / ((vef / kbt) + 1.0d0))
    else if (ndchar <= 2.8d-100) then
        tmp = (ndchar / ((mu / kbt) + 2.0d0)) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else
        tmp = nachar + t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -9.5e+47) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0));
	} else if (NdChar <= 2.8e-100) {
		tmp = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = NaChar + t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	tmp = 0
	if NdChar <= -9.5e+47:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0))
	elif NdChar <= 2.8e-100:
		tmp = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	else:
		tmp = NaChar + t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	tmp = 0.0
	if (NdChar <= -9.5e+47)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 1.0)));
	elseif (NdChar <= 2.8e-100)
		tmp = Float64(Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	else
		tmp = Float64(NaChar + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NdChar <= -9.5e+47)
		tmp = t_0 + (NaChar / ((Vef / KbT) + 1.0));
	elseif (NdChar <= 2.8e-100)
		tmp = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	else
		tmp = NaChar + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -9.5e+47], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.8e-100], N[(N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -9.50000000000000001e47

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 56.6%

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

      1. associate-+r+ 56.6%

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

      2. +-commutative 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in Vef around inf 71.6%

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

   if -9.50000000000000001e47 < NdChar < 2.79999999999999995e-100

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in mu around inf 80.0%

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

   6. Taylor expanded in mu around 0 62.7%

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

   if 2.79999999999999995e-100 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 54.2%

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

      1. associate-+r+ 54.2%

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

      2. +-commutative 54.2%

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

   7. Simplified 54.2%

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

   8. Taylor expanded in mu around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. distribute-frac-neg 60.3%

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

   10. Simplified 60.3%

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

   11. Taylor expanded in mu around 0 66.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -9.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\frac{Vef}{KbT} + 1}\\ \mathbf{elif}\;NdChar \leq 2.8 \cdot 10^{-100}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT} + 2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -5.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.95 \cdot 10^{-261}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + KbT \cdot \frac{NaChar}{Ev}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -5.1e-92)
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (* NdChar 0.5))
   (if (<= KbT 1.95e-261)
     (+ (/ NdChar (+ (exp (/ mu KbT)) 1.0)) (* KbT (/ NaChar Ev)))
     (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ Ev KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -5.1e-92) {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5);
	} else if (KbT <= 1.95e-261) {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (KbT * (NaChar / Ev));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-5.1d-92)) then
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar * 0.5d0)
    else if (kbt <= 1.95d-261) then
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (kbt * (nachar / ev))
    else
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -5.1e-92) {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5);
	} else if (KbT <= 1.95e-261) {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (KbT * (NaChar / Ev));
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -5.1e-92:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5)
	elif KbT <= 1.95e-261:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (KbT * (NaChar / Ev))
	else:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -5.1e-92)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar * 0.5));
	elseif (KbT <= 1.95e-261)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(KbT * Float64(NaChar / Ev)));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -5.1e-92)
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5);
	elseif (KbT <= 1.95e-261)
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (KbT * (NaChar / Ev));
	else
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -5.1e-92], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.95e-261], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NaChar / Ev), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -5.09999999999999972e-92

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in EAccept around inf 69.0%

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

   6. Taylor expanded in KbT around inf 42.8%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   7. Step-by-step derivation

      1. *-commutative 28.9%

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

   8. Simplified 42.8%

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

   if -5.09999999999999972e-92 < KbT < 1.95000000000000009e-261

   1. Initial program 100.0%

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

   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 42.0%

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

      1. associate-+r+ 42.0%

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

      2. +-commutative 42.0%

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

   7. Simplified 42.0%

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

   8. Taylor expanded in Ev around inf 49.4%

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

      1. associate-/l* 44.3%

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

   10. Simplified 44.3%

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

   11. Taylor expanded in mu around inf 30.7%

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

   if 1.95000000000000009e-261 < KbT

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in Ev around inf 65.1%

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

   6. Taylor expanded in KbT around inf 35.0%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -5.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.95 \cdot 10^{-261}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + KbT \cdot \frac{NaChar}{Ev}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -1.9e+17)
   (-
    (/ NdChar 2.0)
    (/ NaChar (- -1.0 (exp (/ (+ Vef (- Ev (- mu EAccept))) KbT)))))
   (+ NaChar (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.9e+17) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = NaChar + (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-1.9d+17)) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef + (ev - (mu - eaccept))) / kbt))))
    else
        tmp = nachar + (ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.9e+17) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	} else {
		tmp = NaChar + (NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -1.9e+17:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef + (Ev - (mu - EAccept))) / KbT))))
	else:
		tmp = NaChar + (NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -1.9e+17)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev - Float64(mu - EAccept))) / KbT)))));
	else
		tmp = Float64(NaChar + Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -1.9e+17)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef + (Ev - (mu - EAccept))) / KbT))));
	else
		tmp = NaChar + (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -1.9e+17], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev - N[(mu - EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar + N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.9e17

   1. Initial program 100.0%

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

   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 61.0%

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

   if -1.9e17 < NaChar

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 51.4%

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

      1. associate-+r+ 51.4%

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

      2. +-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in mu around inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. distribute-frac-neg 53.7%

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

   10. Simplified 53.7%

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

   11. Taylor expanded in mu around 0 63.5%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev - \left(mu - EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 1.55 \cdot 10^{-202}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 4.1 \cdot 10^{+121}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 1.55e-202)
   (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ Ev KbT)))))
   (if (<= EAccept 4.1e+121)
     (+ (/ NdChar (+ (exp (/ mu KbT)) 1.0)) (* NaChar 0.5))
     (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (* 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 (EAccept <= 1.55e-202) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	} else if (EAccept <= 4.1e+121) {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (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 (eaccept <= 1.55d-202) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    else if (eaccept <= 4.1d+121) then
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (nachar * 0.5d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (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 (EAccept <= 1.55e-202) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	} else if (EAccept <= 4.1e+121) {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 1.55e-202:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	elif EAccept <= 4.1e+121:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar * 0.5)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 1.55e-202)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	elseif (EAccept <= 4.1e+121)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + 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 (EAccept <= 1.55e-202)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	elseif (EAccept <= 4.1e+121)
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar * 0.5);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 1.55e-202], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 4.1e+121], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 1.55e-202

   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 Ev around inf 65.8%

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

   6. Taylor expanded in KbT around inf 31.7%

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

   if 1.55e-202 < EAccept < 4.1e121

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in mu around inf 73.0%

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

   6. Taylor expanded in KbT around inf 39.7%

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

   if 4.1e121 < EAccept

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in EAccept around inf 85.6%

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

   6. Taylor expanded in KbT around inf 41.2%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   7. Step-by-step derivation

      1. *-commutative 22.4%

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

   8. Simplified 41.2%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 1.55 \cdot 10^{-202}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 4.1 \cdot 10^{+121}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+192}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -6.8e+192)
   (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ mu (- KbT))))))
   (+ NaChar (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -6.8e+192) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((mu / -KbT))));
	} else {
		tmp = NaChar + (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-6.8d+192)) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((mu / -kbt))))
    else
        tmp = nachar + (ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -6.8e+192) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((mu / -KbT))));
	} else {
		tmp = NaChar + (NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -6.8e+192:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((mu / -KbT))))
	else:
		tmp = NaChar + (NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -6.8e+192)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(mu / Float64(-KbT))))));
	else
		tmp = Float64(NaChar + Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -6.8e+192)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((mu / -KbT))));
	else
		tmp = NaChar + (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -6.8e+192], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar + N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -6.79999999999999992e192

   1. Initial program 100.0%

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

   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 79.3%

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

   6. Taylor expanded in mu around inf 63.6%

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

      1. mul-1-neg 63.6%

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

   8. Simplified 63.6%

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

   if -6.79999999999999992e192 < NaChar

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 49.7%

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

      1. associate-+r+ 49.7%

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

      2. +-commutative 49.7%

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

   7. Simplified 49.7%

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

   8. Taylor expanded in mu around inf 52.7%

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

      1. mul-1-neg 52.7%

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

      2. distribute-frac-neg 52.7%

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

   10. Simplified 52.7%

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

   11. Taylor expanded in mu around 0 61.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+192}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NaChar + \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 8 \cdot 10^{+106}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 8e+106)
   (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ Ev KbT)))))
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (* 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 (EAccept <= 8e+106) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (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 (eaccept <= 8d+106) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (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 (EAccept <= 8e+106) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 8e+106:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 8e+106)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + 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 (EAccept <= 8e+106)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 8e+106], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 8.00000000000000073e106

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in Ev around inf 68.8%

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

   6. Taylor expanded in KbT around inf 33.3%

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

   if 8.00000000000000073e106 < EAccept

   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 87.2%

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

   6. Taylor expanded in KbT around inf 44.1%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   7. Step-by-step derivation

      1. *-commutative 25.2%

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

   8. Simplified 44.1%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 8 \cdot 10^{+106}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.6% accurate, 2.1× speedup

Math

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (* 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 / (exp((EAccept / KbT)) + 1.0)) + (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 / (exp((eaccept / kbt)) + 1.0d0)) + (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 / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar * 0.5);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in EAccept around inf 68.7%

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

6. Taylor expanded in KbT around inf 35.1%

   \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
7. Step-by-step derivation

   1. *-commutative 24.7%

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

8. Simplified 35.1%

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

9. Final simplification 35.1%

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

Alternative 20: 25.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{mu}{KbT} + \frac{Vef}{KbT}\\ \mathbf{if}\;EAccept \leq -1.5 \cdot 10^{-306} \lor \neg \left(EAccept \leq 4.4 \cdot 10^{+164}\right):\\ \;\;\;\;\frac{NaChar}{1 - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\left(\frac{EDonor}{KbT} + t\_0\right) + 1\right) - \frac{Ec}{KbT}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\left(t\_0 + \left(\frac{EDonor}{KbT} + 2\right)\right) - \frac{Ec}{KbT}} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(\left(-1 - \frac{EAccept}{KbT}\right) - \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ mu KbT) (/ Vef KbT))))
   (if (or (<= EAccept -1.5e-306) (not (<= EAccept 4.4e+164)))
     (+
      (/ NaChar (- 1.0 (/ mu KbT)))
      (/ NdChar (+ (- (+ (+ (/ EDonor KbT) t_0) 1.0) (/ Ec KbT)) 1.0)))
     (-
      (/ NdChar (- (+ t_0 (+ (/ EDonor KbT) 2.0)) (/ Ec KbT)))
      (/
       NaChar
       (+
        -1.0
        (+
         (/ mu KbT)
         (- (- -1.0 (/ EAccept KbT)) (+ (/ Ev KbT) (/ 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 / KbT) + (Vef / KbT);
	double tmp;
	if ((EAccept <= -1.5e-306) || !(EAccept <= 4.4e+164)) {
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar / (((((EDonor / KbT) + t_0) + 1.0) - (Ec / KbT)) + 1.0));
	} else {
		tmp = (NdChar / ((t_0 + ((EDonor / KbT) + 2.0)) - (Ec / KbT))) - (NaChar / (-1.0 + ((mu / KbT) + ((-1.0 - (EAccept / KbT)) - ((Ev / KbT) + (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) :: tmp
    t_0 = (mu / kbt) + (vef / kbt)
    if ((eaccept <= (-1.5d-306)) .or. (.not. (eaccept <= 4.4d+164))) then
        tmp = (nachar / (1.0d0 - (mu / kbt))) + (ndchar / (((((edonor / kbt) + t_0) + 1.0d0) - (ec / kbt)) + 1.0d0))
    else
        tmp = (ndchar / ((t_0 + ((edonor / kbt) + 2.0d0)) - (ec / kbt))) - (nachar / ((-1.0d0) + ((mu / kbt) + (((-1.0d0) - (eaccept / kbt)) - ((ev / kbt) + (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 / KbT) + (Vef / KbT);
	double tmp;
	if ((EAccept <= -1.5e-306) || !(EAccept <= 4.4e+164)) {
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar / (((((EDonor / KbT) + t_0) + 1.0) - (Ec / KbT)) + 1.0));
	} else {
		tmp = (NdChar / ((t_0 + ((EDonor / KbT) + 2.0)) - (Ec / KbT))) - (NaChar / (-1.0 + ((mu / KbT) + ((-1.0 - (EAccept / KbT)) - ((Ev / KbT) + (Vef / KbT))))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (mu / KbT) + (Vef / KbT)
	tmp = 0
	if (EAccept <= -1.5e-306) or not (EAccept <= 4.4e+164):
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar / (((((EDonor / KbT) + t_0) + 1.0) - (Ec / KbT)) + 1.0))
	else:
		tmp = (NdChar / ((t_0 + ((EDonor / KbT) + 2.0)) - (Ec / KbT))) - (NaChar / (-1.0 + ((mu / KbT) + ((-1.0 - (EAccept / KbT)) - ((Ev / KbT) + (Vef / KbT))))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(mu / KbT) + Float64(Vef / KbT))
	tmp = 0.0
	if ((EAccept <= -1.5e-306) || !(EAccept <= 4.4e+164))
		tmp = Float64(Float64(NaChar / Float64(1.0 - Float64(mu / KbT))) + Float64(NdChar / Float64(Float64(Float64(Float64(Float64(EDonor / KbT) + t_0) + 1.0) - Float64(Ec / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(Float64(t_0 + Float64(Float64(EDonor / KbT) + 2.0)) - Float64(Ec / KbT))) - Float64(NaChar / Float64(-1.0 + Float64(Float64(mu / KbT) + Float64(Float64(-1.0 - Float64(EAccept / KbT)) - Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (mu / KbT) + (Vef / KbT);
	tmp = 0.0;
	if ((EAccept <= -1.5e-306) || ~((EAccept <= 4.4e+164)))
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar / (((((EDonor / KbT) + t_0) + 1.0) - (Ec / KbT)) + 1.0));
	else
		tmp = (NdChar / ((t_0 + ((EDonor / KbT) + 2.0)) - (Ec / KbT))) - (NaChar / (-1.0 + ((mu / KbT) + ((-1.0 - (EAccept / KbT)) - ((Ev / KbT) + (Vef / KbT))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[EAccept, -1.5e-306], N[Not[LessEqual[EAccept, 4.4e+164]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + t$95$0), $MachinePrecision] + 1.0), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[(t$95$0 + N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(N[(-1.0 - N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision] - N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if EAccept < -1.50000000000000012e-306 or 4.40000000000000011e164 < EAccept

   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 KbT around inf 47.0%

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

      1. associate-+r+ 47.0%

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

      2. +-commutative 47.0%

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

   7. Simplified 47.0%

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

   8. Taylor expanded in mu around inf 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-frac-neg 49.6%

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

   10. Simplified 49.6%

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

   11. Taylor expanded in KbT around inf 24.5%

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

   if -1.50000000000000012e-306 < EAccept < 4.40000000000000011e164

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 56.3%

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

      1. associate-+r+ 56.3%

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

      2. +-commutative 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in KbT around inf 28.4%

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

      1. associate-+r+ 28.4%

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

   10. Simplified 28.4%

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

4. Final simplification 25.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -1.5 \cdot 10^{-306} \lor \neg \left(EAccept \leq 4.4 \cdot 10^{+164}\right):\\ \;\;\;\;\frac{NaChar}{1 - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\left(\frac{EDonor}{KbT} + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{Ec}{KbT}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\left(\left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right) + \left(\frac{EDonor}{KbT} + 2\right)\right) - \frac{Ec}{KbT}} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(\left(-1 - \frac{EAccept}{KbT}\right) - \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 25.9% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq -2.3 \cdot 10^{-229} \lor \neg \left(EAccept \leq 4 \cdot 10^{+228}\right):\\ \;\;\;\;\frac{NaChar}{1 - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\left(\frac{EDonor}{KbT} + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{Ec}{KbT}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= EAccept -2.3e-229) (not (<= EAccept 4e+228)))
   (+
    (/ NaChar (- 1.0 (/ mu KbT)))
    (/
     NdChar
     (+
      (- (+ (+ (/ EDonor KbT) (+ (/ mu KbT) (/ Vef KbT))) 1.0) (/ Ec KbT))
      1.0)))
   (* 0.5 (+ NdChar NaChar))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((EAccept <= -2.3e-229) || !(EAccept <= 4e+228)) {
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar / (((((EDonor / KbT) + ((mu / KbT) + (Vef / KbT))) + 1.0) - (Ec / KbT)) + 1.0));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((eaccept <= (-2.3d-229)) .or. (.not. (eaccept <= 4d+228))) then
        tmp = (nachar / (1.0d0 - (mu / kbt))) + (ndchar / (((((edonor / kbt) + ((mu / kbt) + (vef / kbt))) + 1.0d0) - (ec / kbt)) + 1.0d0))
    else
        tmp = 0.5d0 * (ndchar + nachar)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((EAccept <= -2.3e-229) || !(EAccept <= 4e+228)) {
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar / (((((EDonor / KbT) + ((mu / KbT) + (Vef / KbT))) + 1.0) - (Ec / KbT)) + 1.0));
	} else {
		tmp = 0.5 * (NdChar + NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (EAccept <= -2.3e-229) or not (EAccept <= 4e+228):
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar / (((((EDonor / KbT) + ((mu / KbT) + (Vef / KbT))) + 1.0) - (Ec / KbT)) + 1.0))
	else:
		tmp = 0.5 * (NdChar + NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((EAccept <= -2.3e-229) || !(EAccept <= 4e+228))
		tmp = Float64(Float64(NaChar / Float64(1.0 - Float64(mu / KbT))) + Float64(NdChar / Float64(Float64(Float64(Float64(Float64(EDonor / KbT) + Float64(Float64(mu / KbT) + Float64(Vef / KbT))) + 1.0) - Float64(Ec / KbT)) + 1.0)));
	else
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((EAccept <= -2.3e-229) || ~((EAccept <= 4e+228)))
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar / (((((EDonor / KbT) + ((mu / KbT) + (Vef / KbT))) + 1.0) - (Ec / KbT)) + 1.0));
	else
		tmp = 0.5 * (NdChar + NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[EAccept, -2.3e-229], N[Not[LessEqual[EAccept, 4e+228]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < -2.29999999999999996e-229 or 3.9999999999999997e228 < EAccept

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 48.1%

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

      1. associate-+r+ 48.1%

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

      2. +-commutative 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in mu around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. distribute-frac-neg 51.9%

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

   10. Simplified 51.9%

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

   11. Taylor expanded in KbT around inf 25.4%

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

   if -2.29999999999999996e-229 < EAccept < 3.9999999999999997e228

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 45.1%

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

   6. Taylor expanded in mu around inf 36.4%

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

      1. mul-1-neg 36.4%

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

   8. Simplified 36.4%

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

   9. Taylor expanded in mu around 0 25.1%

      \[\leadsto \frac{NdChar}{1 + 1} + \color{blue}{\left(0.25 \cdot \frac{NaChar \cdot mu}{KbT} + 0.5 \cdot NaChar\right)} \]

   10. Taylor expanded in mu around 0 29.6%

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

       1. distribute-lft-out 29.6%

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

   12. Simplified 29.6%

       \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -2.3 \cdot 10^{-229} \lor \neg \left(EAccept \leq 4 \cdot 10^{+228}\right):\\ \;\;\;\;\frac{NaChar}{1 - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\left(\frac{EDonor}{KbT} + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{Ec}{KbT}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 26.8% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -3.5 \cdot 10^{+51}:\\ \;\;\;\;NdChar \cdot 0.5 + NaChar \cdot \left(0.5 + \frac{mu}{KbT} \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -3.5e+51)
   (+ (* NdChar 0.5) (* NaChar (+ 0.5 (* (/ mu KbT) 0.25))))
   (+ (/ NaChar (- 1.0 (/ mu 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 (KbT <= -3.5e+51) {
		tmp = (NdChar * 0.5) + (NaChar * (0.5 + ((mu / KbT) * 0.25)));
	} else {
		tmp = (NaChar / (1.0 - (mu / 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 (kbt <= (-3.5d+51)) then
        tmp = (ndchar * 0.5d0) + (nachar * (0.5d0 + ((mu / kbt) * 0.25d0)))
    else
        tmp = (nachar / (1.0d0 - (mu / 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 (KbT <= -3.5e+51) {
		tmp = (NdChar * 0.5) + (NaChar * (0.5 + ((mu / KbT) * 0.25)));
	} else {
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -3.5e+51:
		tmp = (NdChar * 0.5) + (NaChar * (0.5 + ((mu / KbT) * 0.25)))
	else:
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -3.5e+51)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar * Float64(0.5 + Float64(Float64(mu / KbT) * 0.25))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 - Float64(mu / 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 (KbT <= -3.5e+51)
		tmp = (NdChar * 0.5) + (NaChar * (0.5 + ((mu / KbT) * 0.25)));
	else
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -3.5e+51], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar * N[(0.5 + N[(N[(mu / KbT), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -3.5e51

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in KbT around inf 69.8%

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

   6. Taylor expanded in mu around inf 58.1%

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

      1. mul-1-neg 58.1%

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

   8. Simplified 58.1%

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

   9. Taylor expanded in mu around 0 48.7%

      \[\leadsto \frac{NdChar}{1 + 1} + \color{blue}{\left(0.25 \cdot \frac{NaChar \cdot mu}{KbT} + 0.5 \cdot NaChar\right)} \]

   10. Taylor expanded in NaChar around 0 52.7%

       \[\leadsto \color{blue}{0.5 \cdot NdChar + NaChar \cdot \left(0.5 + 0.25 \cdot \frac{mu}{KbT}\right)} \]

   if -3.5e51 < KbT

   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 KbT around inf 46.6%

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

      1. associate-+r+ 46.6%

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

      2. +-commutative 46.6%

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

   7. Simplified 46.6%

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

   8. Taylor expanded in mu around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. distribute-frac-neg 53.2%

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

   10. Simplified 53.2%

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

   11. Taylor expanded in KbT around inf 22.5%

       \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + \frac{-mu}{KbT}} \]
   12. Step-by-step derivation

       1. *-commutative 22.5%

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

   13. Simplified 22.5%

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

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.5 \cdot 10^{+51}:\\ \;\;\;\;NdChar \cdot 0.5 + NaChar \cdot \left(0.5 + \frac{mu}{KbT} \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 27.0% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -7 \cdot 10^{+56}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -7e+56)
   (* 0.5 (+ NdChar NaChar))
   (+ (/ NaChar (- 1.0 (/ mu 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 (KbT <= -7e+56) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = (NaChar / (1.0 - (mu / 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 (kbt <= (-7d+56)) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = (nachar / (1.0d0 - (mu / 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 (KbT <= -7e+56) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -7e+56:
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -7e+56)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 - Float64(mu / 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 (KbT <= -7e+56)
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = (NaChar / (1.0 - (mu / KbT))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -7e+56], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -6.99999999999999999e56

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in KbT around inf 69.8%

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

   6. Taylor expanded in mu around inf 58.1%

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

      1. mul-1-neg 58.1%

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

   8. Simplified 58.1%

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

   9. Taylor expanded in mu around 0 48.7%

      \[\leadsto \frac{NdChar}{1 + 1} + \color{blue}{\left(0.25 \cdot \frac{NaChar \cdot mu}{KbT} + 0.5 \cdot NaChar\right)} \]

   10. Taylor expanded in mu around 0 51.4%

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

       1. distribute-lft-out 51.4%

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

   12. Simplified 51.4%

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

   if -6.99999999999999999e56 < KbT

   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 KbT around inf 46.6%

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

      1. associate-+r+ 46.6%

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

      2. +-commutative 46.6%

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

   7. Simplified 46.6%

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

   8. Taylor expanded in mu around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. distribute-frac-neg 53.2%

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

   10. Simplified 53.2%

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

   11. Taylor expanded in KbT around inf 22.5%

       \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + \frac{-mu}{KbT}} \]
   12. Step-by-step derivation

       1. *-commutative 22.5%

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

   13. Simplified 22.5%

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

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -7 \cdot 10^{+56}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 - \frac{mu}{KbT}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 27.5% accurate, 45.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in KbT around inf 45.4%

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

6. Taylor expanded in mu around inf 32.3%

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

   1. mul-1-neg 32.3%

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

8. Simplified 32.3%

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

9. Taylor expanded in mu around 0 20.9%

   \[\leadsto \frac{NdChar}{1 + 1} + \color{blue}{\left(0.25 \cdot \frac{NaChar \cdot mu}{KbT} + 0.5 \cdot NaChar\right)} \]

10. Taylor expanded in mu around 0 25.3%

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

    1. distribute-lft-out 25.3%

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

12. Simplified 25.3%

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

13. Final simplification 25.3%

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

Alternative 25: 18.2% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in KbT around inf 45.4%

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

6. Taylor expanded in mu around inf 32.3%

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

   1. mul-1-neg 32.3%

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

8. Simplified 32.3%

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

9. Taylor expanded in mu around 0 20.9%

   \[\leadsto \frac{NdChar}{1 + 1} + \color{blue}{\left(0.25 \cdot \frac{NaChar \cdot mu}{KbT} + 0.5 \cdot NaChar\right)} \]

10. Taylor expanded in NdChar around inf 16.6%

    \[\leadsto \color{blue}{0.5 \cdot NdChar} \]

11. Final simplification 16.6%

    \[\leadsto NdChar \cdot 0.5 \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(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))))))