Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 36.3s

Alternatives: 20

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -5.045750492562755e-8
  2. Ec = 4.7342196795636865e-298
  3. Vef = -1.540719854268969e-151
  4. EDonor = -5.317881575936641e+249
  5. mu = -5.645189716570899e-15
  6. KbT = 9.181998168615879e+182
  7. NaChar = 2.5046338328953265e-8
  8. Ev = -1.7979247345371327e-191
  9. EAccept = 9.104666484613699e-266

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.5× speedup

Math

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

FPCore

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

Java

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

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / math.exp(math.log1p(math.exp(((Vef + (Ev + (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(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / exp(log1p(exp(Float64(Float64(Vef + Float64(Ev + Float64(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[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[Exp[N[Log[1 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

   1. add-exp-log 100.0%

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

   2. log1p-udef 100.0%

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

   3. div-inv 100.0%

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

   4. associate-*r/ 100.0%

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

   5. *-commutative 100.0%

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

   6. *-un-lft-identity 100.0%

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

   7. +-commutative 100.0%

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

   8. associate-+l- 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{if}\;NdChar \leq -6.1 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -1.8 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 8 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.5 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (+ mu (+ EDonor Vef)) Ec) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))))
   (if (<= NdChar -6.1e+47)
     t_0
     (if (<= NdChar -1.8e-59)
       t_1
       (if (<= NdChar 8e-20)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ 1.0 (+ 1.0 (/ mu KbT)))))
         (if (<= NdChar 1.1e+14)
           (+
            (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
            (/
             NaChar
             (-
              (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
              (/ mu KbT))))
           (if (<= NdChar 1.5e+73) t_1 t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	double t_1 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	double tmp;
	if (NdChar <= -6.1e+47) {
		tmp = t_0;
	} else if (NdChar <= -1.8e-59) {
		tmp = t_1;
	} else if (NdChar <= 8e-20) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	} else if (NdChar <= 1.1e+14) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 1.5e+73) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((((mu + (edonor + vef)) - ec) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    if (ndchar <= (-6.1d+47)) then
        tmp = t_0
    else if (ndchar <= (-1.8d-59)) then
        tmp = t_1
    else if (ndchar <= 8d-20) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + (1.0d0 + (mu / kbt))))
    else if (ndchar <= 1.1d+14) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (ndchar <= 1.5d+73) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	double tmp;
	if (NdChar <= -6.1e+47) {
		tmp = t_0;
	} else if (NdChar <= -1.8e-59) {
		tmp = t_1;
	} else if (NdChar <= 8e-20) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	} else if (NdChar <= 1.1e+14) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 1.5e+73) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	tmp = 0
	if NdChar <= -6.1e+47:
		tmp = t_0
	elif NdChar <= -1.8e-59:
		tmp = t_1
	elif NdChar <= 8e-20:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))))
	elif NdChar <= 1.1e+14:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NdChar <= 1.5e+73:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Float64(EDonor + Vef)) - Ec) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))))
	tmp = 0.0
	if (NdChar <= -6.1e+47)
		tmp = t_0;
	elseif (NdChar <= -1.8e-59)
		tmp = t_1;
	elseif (NdChar <= 8e-20)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(mu / KbT)))));
	elseif (NdChar <= 1.1e+14)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NdChar <= 1.5e+73)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	t_1 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	tmp = 0.0;
	if (NdChar <= -6.1e+47)
		tmp = t_0;
	elseif (NdChar <= -1.8e-59)
		tmp = t_1;
	elseif (NdChar <= 8e-20)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	elseif (NdChar <= 1.1e+14)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NdChar <= 1.5e+73)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + N[(EDonor + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -6.1e+47], t$95$0, If[LessEqual[NdChar, -1.8e-59], t$95$1, If[LessEqual[NdChar, 8e-20], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.1e+14], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.5e+73], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -6.10000000000000019e47 or 1.50000000000000005e73 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.5%

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

   6. Taylor expanded in EAccept around inf 36.4%

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

      1. associate-/l* 34.3%

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

   8. Simplified 34.3%

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

   9. Taylor expanded in NdChar around inf 75.2%

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

   11. Simplified 75.2%

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

   if -6.10000000000000019e47 < NdChar < -1.8e-59 or 1.1e14 < NdChar < 1.50000000000000005e73

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 89.2%

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

   6. Taylor expanded in mu around inf 74.7%

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

      1. associate-*r/ 74.7%

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

      2. mul-1-neg 74.7%

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

   8. Simplified 74.7%

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

   if -1.8e-59 < NdChar < 7.99999999999999956e-20

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 78.5%

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

   6. Taylor expanded in mu around 0 71.2%

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

   if 7.99999999999999956e-20 < NdChar < 1.1e14

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 78.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6.1 \cdot 10^{+47}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -1.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 8 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -2.3 \cdot 10^{+159}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -5 \cdot 10^{-43}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.8 \cdot 10^{+63}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ Vef KbT))))))
   (if (<= Vef -2.3e+159)
     (+ t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
     (if (<= Vef -5e-43)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
       (if (<= Vef 4.5e-53)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         (if (<= Vef 4.8e+63)
           (+
            (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
            (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
           (+ t_0 t_1)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + exp((Vef / KbT)));
	double tmp;
	if (Vef <= -2.3e+159) {
		tmp = t_1 + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	} else if (Vef <= -5e-43) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (Vef <= 4.5e-53) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= 4.8e+63) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = t_0 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = ndchar / (1.0d0 + exp((vef / kbt)))
    if (vef <= (-2.3d+159)) then
        tmp = t_1 + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    else if (vef <= (-5d-43)) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (vef <= 4.5d-53) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= 4.8d+63) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = t_0 + t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp((Vef / KbT)));
	double tmp;
	if (Vef <= -2.3e+159) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	} else if (Vef <= -5e-43) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (Vef <= 4.5e-53) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= 4.8e+63) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = t_0 + t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = NdChar / (1.0 + math.exp((Vef / KbT)))
	tmp = 0
	if Vef <= -2.3e+159:
		tmp = t_1 + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	elif Vef <= -5e-43:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif Vef <= 4.5e-53:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= 4.8e+63:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = t_0 + t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	tmp = 0.0
	if (Vef <= -2.3e+159)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	elseif (Vef <= -5e-43)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (Vef <= 4.5e-53)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= 4.8e+63)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(t_0 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = NdChar / (1.0 + exp((Vef / KbT)));
	tmp = 0.0;
	if (Vef <= -2.3e+159)
		tmp = t_1 + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	elseif (Vef <= -5e-43)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (Vef <= 4.5e-53)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= 4.8e+63)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = t_0 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -2.3e+159], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -5e-43], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 4.5e-53], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 4.8e+63], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if Vef < -2.29999999999999995e159

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 96.4%

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

   6. Taylor expanded in EAccept around 0 96.4%

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

      1. +-commutative 51.9%

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

   8. Simplified 96.4%

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

   if -2.29999999999999995e159 < Vef < -5.00000000000000019e-43

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 82.6%

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

   if -5.00000000000000019e-43 < Vef < 4.49999999999999985e-53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 83.3%

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

   if 4.49999999999999985e-53 < Vef < 4.8e63

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 76.3%

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

   if 4.8e63 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 88.2%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.3 \cdot 10^{+159}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -5 \cdot 10^{-43}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.8 \cdot 10^{+63}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;EDonor \leq -1.4 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;EDonor \leq 4.8 \cdot 10^{-126}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 1.2 \cdot 10^{+162}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= EDonor -1.4e+72)
     t_1
     (if (<= EDonor 4.8e-126)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
       (if (<= EDonor 1.2e+162)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -1.4e+72) {
		tmp = t_1;
	} else if (EDonor <= 4.8e-126) {
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	} else if (EDonor <= 1.2e+162) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (edonor <= (-1.4d+72)) then
        tmp = t_1
    else if (edonor <= 4.8d-126) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    else if (edonor <= 1.2d+162) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -1.4e+72) {
		tmp = t_1;
	} else if (EDonor <= 4.8e-126) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	} else if (EDonor <= 1.2e+162) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if EDonor <= -1.4e+72:
		tmp = t_1
	elif EDonor <= 4.8e-126:
		tmp = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	elif EDonor <= 1.2e+162:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (EDonor <= -1.4e+72)
		tmp = t_1;
	elseif (EDonor <= 4.8e-126)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	elseif (EDonor <= 1.2e+162)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (EDonor <= -1.4e+72)
		tmp = t_1;
	elseif (EDonor <= 4.8e-126)
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	elseif (EDonor <= 1.2e+162)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -1.4e+72], t$95$1, If[LessEqual[EDonor, 4.8e-126], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 1.2e+162], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if EDonor < -1.4e72 or 1.20000000000000005e162 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 93.4%

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

   if -1.4e72 < EDonor < 4.80000000000000014e-126

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.0%

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

   if 4.80000000000000014e-126 < EDonor < 1.20000000000000005e162

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 86.4%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -1.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 4.8 \cdot 10^{-126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 1.2 \cdot 10^{+162}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;EDonor \leq -4.1 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;EDonor \leq 1.65 \cdot 10^{-104}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + t\_0\\ \mathbf{elif}\;EDonor \leq 8.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= EDonor -4.1e+79)
     t_1
     (if (<= EDonor 1.65e-104)
       (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) t_0)
       (if (<= EDonor 8.2e+55)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
         t_1)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -4.1e+79) {
		tmp = t_1;
	} else if (EDonor <= 1.65e-104) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + t_0;
	} else if (EDonor <= 8.2e+55) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (edonor <= (-4.1d+79)) then
        tmp = t_1
    else if (edonor <= 1.65d-104) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + t_0
    else if (edonor <= 8.2d+55) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -4.1e+79) {
		tmp = t_1;
	} else if (EDonor <= 1.65e-104) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + t_0;
	} else if (EDonor <= 8.2e+55) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if EDonor <= -4.1e+79:
		tmp = t_1
	elif EDonor <= 1.65e-104:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + t_0
	elif EDonor <= 8.2e+55:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (EDonor <= -4.1e+79)
		tmp = t_1;
	elseif (EDonor <= 1.65e-104)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + t_0);
	elseif (EDonor <= 8.2e+55)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (EDonor <= -4.1e+79)
		tmp = t_1;
	elseif (EDonor <= 1.65e-104)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + t_0;
	elseif (EDonor <= 8.2e+55)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -4.1e+79], t$95$1, If[LessEqual[EDonor, 1.65e-104], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[EDonor, 8.2e+55], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if EDonor < -4.1e79 or 8.19999999999999962e55 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 87.7%

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

   6. Taylor expanded in EAccept around 0 78.5%

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

      1. +-commutative 78.5%

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

   8. Simplified 78.5%

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

   if -4.1e79 < EDonor < 1.65000000000000001e-104

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 79.9%

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

   6. Taylor expanded in EAccept around 0 71.8%

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

      1. +-commutative 55.0%

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

   8. Simplified 71.8%

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

   if 1.65000000000000001e-104 < EDonor < 8.19999999999999962e55

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 92.6%

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

   6. Taylor expanded in mu around inf 79.1%

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

      1. associate-*r/ 53.1%

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

      2. mul-1-neg 53.1%

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

   8. Simplified 79.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -4.1 \cdot 10^{+79}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 1.65 \cdot 10^{-104}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 8.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -4.1 \cdot 10^{+161} \lor \neg \left(Vef \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Vef -4.1e+161) (not (<= Vef 5e+61)))
   (+
    (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
    (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -4.1e+161) || !(Vef <= 5e+61)) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((vef <= (-4.1d+161)) .or. (.not. (vef <= 5d+61))) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -4.1e+161) || !(Vef <= 5e+61)) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Vef <= -4.1e+161) or not (Vef <= 5e+61):
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Vef <= -4.1e+161) || !(Vef <= 5e+61))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Vef <= -4.1e+161) || ~((Vef <= 5e+61)))
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Vef, -4.1e+161], N[Not[LessEqual[Vef, 5e+61]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -4.1000000000000001e161 or 5.00000000000000018e61 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 90.0%

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

   6. Taylor expanded in EAccept around 0 84.9%

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

      1. +-commutative 56.8%

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

   8. Simplified 84.9%

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

   if -4.1000000000000001e161 < Vef < 5.00000000000000018e61

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 76.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4.1 \cdot 10^{+161} \lor \neg \left(Vef \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;EDonor \leq -2.3 \cdot 10^{+75} \lor \neg \left(EDonor \leq 9.5 \cdot 10^{+72}\right):\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (or (<= EDonor -2.3e+75) (not (<= EDonor 9.5e+72)))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if ((EDonor <= -2.3e+75) || !(EDonor <= 9.5e+72)) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    if ((edonor <= (-2.3d+75)) .or. (.not. (edonor <= 9.5d+72))) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if ((EDonor <= -2.3e+75) || !(EDonor <= 9.5e+72)) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	tmp = 0
	if (EDonor <= -2.3e+75) or not (EDonor <= 9.5e+72):
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	tmp = 0.0
	if ((EDonor <= -2.3e+75) || !(EDonor <= 9.5e+72))
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if ((EDonor <= -2.3e+75) || ~((EDonor <= 9.5e+72)))
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[EDonor, -2.3e+75], N[Not[LessEqual[EDonor, 9.5e+72]], $MachinePrecision]], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -2.2999999999999999e75 or 9.50000000000000054e72 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 88.3%

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

   if -2.2999999999999999e75 < EDonor < 9.50000000000000054e72

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 78.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -2.3 \cdot 10^{+75} \lor \neg \left(EDonor \leq 9.5 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.2 \cdot 10^{+100} \lor \neg \left(KbT \leq -1.5 \cdot 10^{-215}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -2.2e+100) (not (<= KbT -1.5e-215)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
   (/ NdChar (+ 1.0 (exp (/ (- (+ mu (+ EDonor Vef)) Ec) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -2.2e+100) || !(KbT <= -1.5e-215)) {
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((kbt <= (-2.2d+100)) .or. (.not. (kbt <= (-1.5d-215)))) then
        tmp = (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = ndchar / (1.0d0 + exp((((mu + (edonor + vef)) - ec) / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -2.2e+100) || !(KbT <= -1.5e-215)) {
		tmp = (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = NdChar / (1.0 + Math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -2.2e+100) or not (KbT <= -1.5e-215):
		tmp = (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = NdChar / (1.0 + math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -2.2e+100) || !(KbT <= -1.5e-215))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Float64(EDonor + Vef)) - Ec) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -2.2e+100) || ~((KbT <= -1.5e-215)))
		tmp = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -2.2e+100], N[Not[LessEqual[KbT, -1.5e-215]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + N[(EDonor + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -2.2000000000000001e100 or -1.50000000000000013e-215 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 77.5%

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

   6. Taylor expanded in EAccept around 0 72.0%

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

      1. +-commutative 72.0%

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

   8. Simplified 72.0%

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

   if -2.2000000000000001e100 < KbT < -1.50000000000000013e-215

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 43.9%

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

   6. Taylor expanded in EAccept around inf 27.7%

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

      1. associate-/l* 26.2%

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

   8. Simplified 26.2%

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

   9. Taylor expanded in NdChar around inf 62.3%

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

   11. Simplified 62.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.2 \cdot 10^{+100} \lor \neg \left(KbT \leq -1.5 \cdot 10^{-215}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 10: 62.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -6.5 \cdot 10^{+33} \lor \neg \left(NdChar \leq -2.3 \cdot 10^{-250} \lor \neg \left(NdChar \leq -1.2 \cdot 10^{-261}\right) \land \left(NdChar \leq 4.7 \cdot 10^{-132} \lor \neg \left(NdChar \leq 1.32 \cdot 10^{-64}\right) \land \left(NdChar \leq 9.2 \cdot 10^{-27} \lor \neg \left(NdChar \leq 105000000000\right) \land NdChar \leq 1.2 \cdot 10^{+73}\right)\right)\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -6.5e+33)
         (not
          (or (<= NdChar -2.3e-250)
              (and (not (<= NdChar -1.2e-261))
                   (or (<= NdChar 4.7e-132)
                       (and (not (<= NdChar 1.32e-64))
                            (or (<= NdChar 9.2e-27)
                                (and (not (<= NdChar 105000000000.0))
                                     (<= NdChar 1.2e+73)))))))))
   (/ NdChar (+ 1.0 (exp (/ (- (+ mu (+ EDonor Vef)) Ec) KbT))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -6.5e+33) || !((NdChar <= -2.3e-250) || (!(NdChar <= -1.2e-261) && ((NdChar <= 4.7e-132) || (!(NdChar <= 1.32e-64) && ((NdChar <= 9.2e-27) || (!(NdChar <= 105000000000.0) && (NdChar <= 1.2e+73)))))))) {
		tmp = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-6.5d+33)) .or. (.not. (ndchar <= (-2.3d-250)) .or. (.not. (ndchar <= (-1.2d-261))) .and. (ndchar <= 4.7d-132) .or. (.not. (ndchar <= 1.32d-64)) .and. (ndchar <= 9.2d-27) .or. (.not. (ndchar <= 105000000000.0d0)) .and. (ndchar <= 1.2d+73))) then
        tmp = ndchar / (1.0d0 + exp((((mu + (edonor + vef)) - ec) / kbt)))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -6.5e+33) || !((NdChar <= -2.3e-250) || (!(NdChar <= -1.2e-261) && ((NdChar <= 4.7e-132) || (!(NdChar <= 1.32e-64) && ((NdChar <= 9.2e-27) || (!(NdChar <= 105000000000.0) && (NdChar <= 1.2e+73)))))))) {
		tmp = NdChar / (1.0 + Math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -6.5e+33) or not ((NdChar <= -2.3e-250) or (not (NdChar <= -1.2e-261) and ((NdChar <= 4.7e-132) or (not (NdChar <= 1.32e-64) and ((NdChar <= 9.2e-27) or (not (NdChar <= 105000000000.0) and (NdChar <= 1.2e+73))))))):
		tmp = NdChar / (1.0 + math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -6.5e+33) || !((NdChar <= -2.3e-250) || (!(NdChar <= -1.2e-261) && ((NdChar <= 4.7e-132) || (!(NdChar <= 1.32e-64) && ((NdChar <= 9.2e-27) || (!(NdChar <= 105000000000.0) && (NdChar <= 1.2e+73))))))))
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Float64(EDonor + Vef)) - Ec) / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -6.5e+33) || ~(((NdChar <= -2.3e-250) || (~((NdChar <= -1.2e-261)) && ((NdChar <= 4.7e-132) || (~((NdChar <= 1.32e-64)) && ((NdChar <= 9.2e-27) || (~((NdChar <= 105000000000.0)) && (NdChar <= 1.2e+73)))))))))
		tmp = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -6.5e+33], N[Not[Or[LessEqual[NdChar, -2.3e-250], And[N[Not[LessEqual[NdChar, -1.2e-261]], $MachinePrecision], Or[LessEqual[NdChar, 4.7e-132], And[N[Not[LessEqual[NdChar, 1.32e-64]], $MachinePrecision], Or[LessEqual[NdChar, 9.2e-27], And[N[Not[LessEqual[NdChar, 105000000000.0]], $MachinePrecision], LessEqual[NdChar, 1.2e+73]]]]]]]], $MachinePrecision]], N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + N[(EDonor + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -6.49999999999999993e33 or -2.2999999999999999e-250 < NdChar < -1.20000000000000007e-261 or 4.7000000000000002e-132 < NdChar < 1.32e-64 or 9.1999999999999998e-27 < NdChar < 1.05e11 or 1.20000000000000001e73 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 58.6%

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

   6. Taylor expanded in EAccept around inf 34.0%

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

      1. associate-/l* 32.5%

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

   8. Simplified 32.5%

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

   9. Taylor expanded in NdChar around inf 74.1%

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

   11. Simplified 74.1%

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

   if -6.49999999999999993e33 < NdChar < -2.2999999999999999e-250 or -1.20000000000000007e-261 < NdChar < 4.7000000000000002e-132 or 1.32e-64 < NdChar < 9.1999999999999998e-27 or 1.05e11 < NdChar < 1.20000000000000001e73

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 82.0%

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

   6. Taylor expanded in mu around 0 67.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6.5 \cdot 10^{+33} \lor \neg \left(NdChar \leq -2.3 \cdot 10^{-250} \lor \neg \left(NdChar \leq -1.2 \cdot 10^{-261}\right) \land \left(NdChar \leq 4.7 \cdot 10^{-132} \lor \neg \left(NdChar \leq 1.32 \cdot 10^{-64}\right) \land \left(NdChar \leq 9.2 \cdot 10^{-27} \lor \neg \left(NdChar \leq 105000000000\right) \land NdChar \leq 1.2 \cdot 10^{+73}\right)\right)\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NdChar \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -4.5 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -1.22 \cdot 10^{-261}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 1.5 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 5.6 \cdot 10^{-65} \lor \neg \left(NdChar \leq 1.18 \cdot 10^{-26}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (+ mu (+ EDonor Vef)) Ec) KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))
          (/ NdChar 2.0))))
   (if (<= NdChar -1.3e+33)
     t_0
     (if (<= NdChar -4.5e-105)
       t_1
       (if (<= NdChar -1.22e-261)
         t_0
         (if (<= NdChar 1.5e-131)
           t_1
           (if (or (<= NdChar 5.6e-65) (not (<= NdChar 1.18e-26)))
             t_0
             (+
              (/ NdChar (+ 1.0 (+ 1.0 (/ mu KbT))))
              (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	double t_1 = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= -1.3e+33) {
		tmp = t_0;
	} else if (NdChar <= -4.5e-105) {
		tmp = t_1;
	} else if (NdChar <= -1.22e-261) {
		tmp = t_0;
	} else if (NdChar <= 1.5e-131) {
		tmp = t_1;
	} else if ((NdChar <= 5.6e-65) || !(NdChar <= 1.18e-26)) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (1.0 + (1.0 + (mu / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((((mu + (edonor + vef)) - ec) / kbt)))
    t_1 = (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))) + (ndchar / 2.0d0)
    if (ndchar <= (-1.3d+33)) then
        tmp = t_0
    else if (ndchar <= (-4.5d-105)) then
        tmp = t_1
    else if (ndchar <= (-1.22d-261)) then
        tmp = t_0
    else if (ndchar <= 1.5d-131) then
        tmp = t_1
    else if ((ndchar <= 5.6d-65) .or. (.not. (ndchar <= 1.18d-26))) then
        tmp = t_0
    else
        tmp = (ndchar / (1.0d0 + (1.0d0 + (mu / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= -1.3e+33) {
		tmp = t_0;
	} else if (NdChar <= -4.5e-105) {
		tmp = t_1;
	} else if (NdChar <= -1.22e-261) {
		tmp = t_0;
	} else if (NdChar <= 1.5e-131) {
		tmp = t_1;
	} else if ((NdChar <= 5.6e-65) || !(NdChar <= 1.18e-26)) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (1.0 + (1.0 + (mu / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NdChar <= -1.3e+33:
		tmp = t_0
	elif NdChar <= -4.5e-105:
		tmp = t_1
	elif NdChar <= -1.22e-261:
		tmp = t_0
	elif NdChar <= 1.5e-131:
		tmp = t_1
	elif (NdChar <= 5.6e-65) or not (NdChar <= 1.18e-26):
		tmp = t_0
	else:
		tmp = (NdChar / (1.0 + (1.0 + (mu / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Float64(EDonor + Vef)) - Ec) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NdChar <= -1.3e+33)
		tmp = t_0;
	elseif (NdChar <= -4.5e-105)
		tmp = t_1;
	elseif (NdChar <= -1.22e-261)
		tmp = t_0;
	elseif (NdChar <= 1.5e-131)
		tmp = t_1;
	elseif ((NdChar <= 5.6e-65) || !(NdChar <= 1.18e-26))
		tmp = t_0;
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	t_1 = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -1.3e+33)
		tmp = t_0;
	elseif (NdChar <= -4.5e-105)
		tmp = t_1;
	elseif (NdChar <= -1.22e-261)
		tmp = t_0;
	elseif (NdChar <= 1.5e-131)
		tmp = t_1;
	elseif ((NdChar <= 5.6e-65) || ~((NdChar <= 1.18e-26)))
		tmp = t_0;
	else
		tmp = (NdChar / (1.0 + (1.0 + (mu / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + N[(EDonor + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.3e+33], t$95$0, If[LessEqual[NdChar, -4.5e-105], t$95$1, If[LessEqual[NdChar, -1.22e-261], t$95$0, If[LessEqual[NdChar, 1.5e-131], t$95$1, If[Or[LessEqual[NdChar, 5.6e-65], N[Not[LessEqual[NdChar, 1.18e-26]], $MachinePrecision]], t$95$0, N[(N[(NdChar / N[(1.0 + N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -1.2999999999999999e33 or -4.4999999999999997e-105 < NdChar < -1.2199999999999999e-261 or 1.49999999999999998e-131 < NdChar < 5.6000000000000001e-65 or 1.17999999999999996e-26 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.1%

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

   6. Taylor expanded in EAccept around inf 30.3%

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

      1. associate-/l* 29.6%

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

   8. Simplified 29.6%

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

   9. Taylor expanded in NdChar around inf 66.9%

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

   11. Simplified 66.9%

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

   if -1.2999999999999999e33 < NdChar < -4.4999999999999997e-105 or -1.2199999999999999e-261 < NdChar < 1.49999999999999998e-131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 85.4%

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

   6. Taylor expanded in EAccept around 0 77.8%

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

      1. +-commutative 77.8%

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

   8. Simplified 77.8%

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

   9. Taylor expanded in EDonor around 0 63.8%

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

   if 5.6000000000000001e-65 < NdChar < 1.17999999999999996e-26

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 91.2%

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

   6. Taylor expanded in mu around 0 82.5%

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

   7. Taylor expanded in EAccept around inf 67.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -4.5 \cdot 10^{-105}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq -1.22 \cdot 10^{-261}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.5 \cdot 10^{-131}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 5.6 \cdot 10^{-65} \lor \neg \left(NdChar \leq 1.18 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -7.8 \cdot 10^{+130}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 3 \cdot 10^{-282} \lor \neg \left(KbT \leq 3.75 \cdot 10^{-149}\right) \land \left(KbT \leq 1.15 \cdot 10^{+55} \lor \neg \left(KbT \leq 1.65 \cdot 10^{+83}\right) \land KbT \leq 5.6 \cdot 10^{+209}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -7.8e+130)
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
   (if (or (<= KbT 3e-282)
           (and (not (<= KbT 3.75e-149))
                (or (<= KbT 1.15e+55)
                    (and (not (<= KbT 1.65e+83)) (<= KbT 5.6e+209)))))
     (/ NdChar (+ 1.0 (exp (/ (- (+ mu (+ EDonor Vef)) Ec) KbT))))
     (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -7.8e+130) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if ((KbT <= 3e-282) || (!(KbT <= 3.75e-149) && ((KbT <= 1.15e+55) || (!(KbT <= 1.65e+83) && (KbT <= 5.6e+209))))) {
		tmp = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-7.8d+130)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else if ((kbt <= 3d-282) .or. (.not. (kbt <= 3.75d-149)) .and. (kbt <= 1.15d+55) .or. (.not. (kbt <= 1.65d+83)) .and. (kbt <= 5.6d+209)) then
        tmp = ndchar / (1.0d0 + exp((((mu + (edonor + vef)) - ec) / kbt)))
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -7.8e+130) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if ((KbT <= 3e-282) || (!(KbT <= 3.75e-149) && ((KbT <= 1.15e+55) || (!(KbT <= 1.65e+83) && (KbT <= 5.6e+209))))) {
		tmp = NdChar / (1.0 + Math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -7.8e+130:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	elif (KbT <= 3e-282) or (not (KbT <= 3.75e-149) and ((KbT <= 1.15e+55) or (not (KbT <= 1.65e+83) and (KbT <= 5.6e+209)))):
		tmp = NdChar / (1.0 + math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)))
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -7.8e+130)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	elseif ((KbT <= 3e-282) || (!(KbT <= 3.75e-149) && ((KbT <= 1.15e+55) || (!(KbT <= 1.65e+83) && (KbT <= 5.6e+209)))))
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Float64(EDonor + Vef)) - Ec) / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -7.8e+130)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	elseif ((KbT <= 3e-282) || (~((KbT <= 3.75e-149)) && ((KbT <= 1.15e+55) || (~((KbT <= 1.65e+83)) && (KbT <= 5.6e+209)))))
		tmp = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -7.8e+130], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[KbT, 3e-282], And[N[Not[LessEqual[KbT, 3.75e-149]], $MachinePrecision], Or[LessEqual[KbT, 1.15e+55], And[N[Not[LessEqual[KbT, 1.65e+83]], $MachinePrecision], LessEqual[KbT, 5.6e+209]]]]], N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + N[(EDonor + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -7.8000000000000004e130

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 74.9%

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

   6. Taylor expanded in EDonor around inf 74.5%

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

   if -7.8000000000000004e130 < KbT < 3.0000000000000001e-282 or 3.74999999999999998e-149 < KbT < 1.14999999999999994e55 or 1.64999999999999992e83 < KbT < 5.60000000000000026e209

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 46.0%

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

   6. Taylor expanded in EAccept around inf 28.4%

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

      1. associate-/l* 27.1%

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

   8. Simplified 27.1%

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

   9. Taylor expanded in NdChar around inf 62.2%

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

   11. Simplified 62.2%

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

   if 3.0000000000000001e-282 < KbT < 3.74999999999999998e-149 or 1.14999999999999994e55 < KbT < 1.64999999999999992e83 or 5.60000000000000026e209 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 85.8%

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

   6. Taylor expanded in Ev around inf 63.5%

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

   7. Taylor expanded in EDonor around 0 57.3%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -7.8 \cdot 10^{+130}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 3 \cdot 10^{-282} \lor \neg \left(KbT \leq 3.75 \cdot 10^{-149}\right) \land \left(KbT \leq 1.15 \cdot 10^{+55} \lor \neg \left(KbT \leq 1.65 \cdot 10^{+83}\right) \land KbT \leq 5.6 \cdot 10^{+209}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NdChar \leq -6.2 \cdot 10^{+34}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -2.5 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -4.7 \cdot 10^{-262}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 9.5 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 3.1 \cdot 10^{-65} \lor \neg \left(NdChar \leq 8 \cdot 10^{-21}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (+ mu (+ EDonor Vef)) Ec) KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))
          (/ NdChar 2.0))))
   (if (<= NdChar -6.2e+34)
     t_0
     (if (<= NdChar -2.5e-100)
       t_1
       (if (<= NdChar -4.7e-262)
         t_0
         (if (<= NdChar 9.5e-131)
           t_1
           (if (or (<= NdChar 3.1e-65) (not (<= NdChar 8e-21)))
             t_0
             (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	double t_1 = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= -6.2e+34) {
		tmp = t_0;
	} else if (NdChar <= -2.5e-100) {
		tmp = t_1;
	} else if (NdChar <= -4.7e-262) {
		tmp = t_0;
	} else if (NdChar <= 9.5e-131) {
		tmp = t_1;
	} else if ((NdChar <= 3.1e-65) || !(NdChar <= 8e-21)) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((((mu + (edonor + vef)) - ec) / kbt)))
    t_1 = (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt)))) + (ndchar / 2.0d0)
    if (ndchar <= (-6.2d+34)) then
        tmp = t_0
    else if (ndchar <= (-2.5d-100)) then
        tmp = t_1
    else if (ndchar <= (-4.7d-262)) then
        tmp = t_0
    else if (ndchar <= 9.5d-131) then
        tmp = t_1
    else if ((ndchar <= 3.1d-65) .or. (.not. (ndchar <= 8d-21))) then
        tmp = t_0
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= -6.2e+34) {
		tmp = t_0;
	} else if (NdChar <= -2.5e-100) {
		tmp = t_1;
	} else if (NdChar <= -4.7e-262) {
		tmp = t_0;
	} else if (NdChar <= 9.5e-131) {
		tmp = t_1;
	} else if ((NdChar <= 3.1e-65) || !(NdChar <= 8e-21)) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NdChar <= -6.2e+34:
		tmp = t_0
	elif NdChar <= -2.5e-100:
		tmp = t_1
	elif NdChar <= -4.7e-262:
		tmp = t_0
	elif NdChar <= 9.5e-131:
		tmp = t_1
	elif (NdChar <= 3.1e-65) or not (NdChar <= 8e-21):
		tmp = t_0
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Float64(EDonor + Vef)) - Ec) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NdChar <= -6.2e+34)
		tmp = t_0;
	elseif (NdChar <= -2.5e-100)
		tmp = t_1;
	elseif (NdChar <= -4.7e-262)
		tmp = t_0;
	elseif (NdChar <= 9.5e-131)
		tmp = t_1;
	elseif ((NdChar <= 3.1e-65) || !(NdChar <= 8e-21))
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	t_1 = (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -6.2e+34)
		tmp = t_0;
	elseif (NdChar <= -2.5e-100)
		tmp = t_1;
	elseif (NdChar <= -4.7e-262)
		tmp = t_0;
	elseif (NdChar <= 9.5e-131)
		tmp = t_1;
	elseif ((NdChar <= 3.1e-65) || ~((NdChar <= 8e-21)))
		tmp = t_0;
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + N[(EDonor + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -6.2e+34], t$95$0, If[LessEqual[NdChar, -2.5e-100], t$95$1, If[LessEqual[NdChar, -4.7e-262], t$95$0, If[LessEqual[NdChar, 9.5e-131], t$95$1, If[Or[LessEqual[NdChar, 3.1e-65], N[Not[LessEqual[NdChar, 8e-21]], $MachinePrecision]], t$95$0, N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -6.19999999999999955e34 or -2.5e-100 < NdChar < -4.6999999999999998e-262 or 9.4999999999999996e-131 < NdChar < 3.10000000000000016e-65 or 7.99999999999999926e-21 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.1%

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

   6. Taylor expanded in EAccept around inf 30.3%

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

      1. associate-/l* 29.6%

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

   8. Simplified 29.6%

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

   9. Taylor expanded in NdChar around inf 66.9%

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

   11. Simplified 66.9%

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

   if -6.19999999999999955e34 < NdChar < -2.5e-100 or -4.6999999999999998e-262 < NdChar < 9.4999999999999996e-131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 85.4%

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

   6. Taylor expanded in EAccept around 0 77.8%

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

      1. +-commutative 77.8%

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

   8. Simplified 77.8%

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

   9. Taylor expanded in EDonor around 0 63.8%

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

   if 3.10000000000000016e-65 < NdChar < 7.99999999999999926e-21

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 82.5%

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

   6. Taylor expanded in Ev around inf 75.1%

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

   7. Taylor expanded in EDonor around 0 76.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -2.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq -4.7 \cdot 10^{-262}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 9.5 \cdot 10^{-131}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 3.1 \cdot 10^{-65} \lor \neg \left(NdChar \leq 8 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{if}\;NdChar \leq -8.5 \cdot 10^{+42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 9 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 9500000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (+ mu (+ EDonor Vef)) Ec) KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ 1.0 (+ 1.0 (/ mu KbT)))))))
   (if (<= NdChar -8.5e+42)
     t_0
     (if (<= NdChar 9e-19)
       t_1
       (if (<= NdChar 9500000000.0)
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar 2.0))
         (if (<= NdChar 1e+73) t_1 t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	double t_1 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	double tmp;
	if (NdChar <= -8.5e+42) {
		tmp = t_0;
	} else if (NdChar <= 9e-19) {
		tmp = t_1;
	} else if (NdChar <= 9500000000.0) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else if (NdChar <= 1e+73) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((((mu + (edonor + vef)) - ec) / kbt)))
    t_1 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + (1.0d0 + (mu / kbt))))
    if (ndchar <= (-8.5d+42)) then
        tmp = t_0
    else if (ndchar <= 9d-19) then
        tmp = t_1
    else if (ndchar <= 9500000000.0d0) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    else if (ndchar <= 1d+73) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	double tmp;
	if (NdChar <= -8.5e+42) {
		tmp = t_0;
	} else if (NdChar <= 9e-19) {
		tmp = t_1;
	} else if (NdChar <= 9500000000.0) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else if (NdChar <= 1e+73) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((mu + (EDonor + Vef)) - Ec) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))))
	tmp = 0
	if NdChar <= -8.5e+42:
		tmp = t_0
	elif NdChar <= 9e-19:
		tmp = t_1
	elif NdChar <= 9500000000.0:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	elif NdChar <= 1e+73:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Float64(EDonor + Vef)) - Ec) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(mu / KbT)))))
	tmp = 0.0
	if (NdChar <= -8.5e+42)
		tmp = t_0;
	elseif (NdChar <= 9e-19)
		tmp = t_1;
	elseif (NdChar <= 9500000000.0)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0));
	elseif (NdChar <= 1e+73)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((((mu + (EDonor + Vef)) - Ec) / KbT)));
	t_1 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	tmp = 0.0;
	if (NdChar <= -8.5e+42)
		tmp = t_0;
	elseif (NdChar <= 9e-19)
		tmp = t_1;
	elseif (NdChar <= 9500000000.0)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	elseif (NdChar <= 1e+73)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + N[(EDonor + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -8.5e+42], t$95$0, If[LessEqual[NdChar, 9e-19], t$95$1, If[LessEqual[NdChar, 9500000000.0], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1e+73], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -8.5000000000000003e42 or 9.99999999999999983e72 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.1%

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

   6. Taylor expanded in EAccept around inf 36.1%

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

      1. associate-/l* 34.0%

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

   8. Simplified 34.0%

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

   9. Taylor expanded in NdChar around inf 74.6%

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

   11. Simplified 74.6%

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

   if -8.5000000000000003e42 < NdChar < 9.00000000000000026e-19 or 9.5e9 < NdChar < 9.99999999999999983e72

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 78.3%

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

   6. Taylor expanded in mu around 0 69.5%

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

   if 9.00000000000000026e-19 < NdChar < 9.5e9

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 77.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -8.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 9 \cdot 10^{-19}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 9500000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 10^{+73}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + \left(EDonor + Vef\right)\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -6.2e+106)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ NaChar 2.0) (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -6.2e+106) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-6.2d+106)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / 2.0d0) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -6.2e+106) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -6.2e+106:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -6.2e+106)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -6.2e+106)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -6.2e+106], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -6.1999999999999999e106

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 70.5%

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

   6. Taylor expanded in Ev around inf 61.8%

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

   7. Taylor expanded in EDonor around 0 46.1%

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

   if -6.1999999999999999e106 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 46.8%

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

   6. Taylor expanded in Ec around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. distribute-neg-frac 40.3%

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

   8. Simplified 40.3%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -1.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -1.6e+86)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -1.6e+86) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-1.6d+86)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -1.6e+86) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -1.6e+86:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -1.6e+86)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -1.6e+86)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -1.6e+86], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -1.6e86

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 72.2%

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

   6. Taylor expanded in Ev around inf 62.5%

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

   7. Taylor expanded in EDonor around 0 47.0%

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

   if -1.6e86 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 46.9%

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

   6. Taylor expanded in EDonor around inf 40.0%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.7% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in EDonor around inf 72.0%

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

6. Taylor expanded in Ev around inf 52.3%

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

7. Taylor expanded in EDonor around 0 40.5%

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

8. Final simplification 40.5%

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

Alternative 18: 28.7% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq 1.1 \cdot 10^{+171}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{KbT}{\frac{Vef}{NaChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Vef 1.1e+171)
   (+ (/ NaChar 2.0) (* NdChar 0.5))
   (/ KbT (/ Vef 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 (Vef <= 1.1e+171) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else {
		tmp = KbT / (Vef / 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 (vef <= 1.1d+171) then
        tmp = (nachar / 2.0d0) + (ndchar * 0.5d0)
    else
        tmp = kbt / (vef / 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 (Vef <= 1.1e+171) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else {
		tmp = KbT / (Vef / NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Vef <= 1.1e+171:
		tmp = (NaChar / 2.0) + (NdChar * 0.5)
	else:
		tmp = KbT / (Vef / NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Vef <= 1.1e+171)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar * 0.5));
	else
		tmp = Float64(KbT / Float64(Vef / NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Vef <= 1.1e+171)
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	else
		tmp = KbT / (Vef / NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Vef, 1.1e+171], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(KbT / N[(Vef / NaChar), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < 1.1e171

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 48.5%

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

   6. Taylor expanded in KbT around inf 34.4%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{2} \]

   if 1.1e171 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 46.2%

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

   6. Taylor expanded in Vef around inf 39.9%

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

   7. Taylor expanded in NdChar around 0 23.3%

      \[\leadsto \color{blue}{\frac{KbT \cdot NaChar}{Vef}} \]
   8. Step-by-step derivation

      1. associate-*l/ 26.8%

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

   9. Simplified 26.8%

      \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NaChar} \]
   10. Step-by-step derivation

       1. associate-*l/ 23.3%

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

       2. associate-/l* 26.8%

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

   11. Applied egg-rr 26.8%

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

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq 1.1 \cdot 10^{+171}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{KbT}{\frac{Vef}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 9.2% accurate, 45.8× speedup

Math

\[\begin{array}{l} \\ KbT \cdot \frac{NaChar}{Vef} \end{array} \]

FPCore

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

C

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

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 = kbt * (nachar / vef)
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 KbT * (NaChar / Vef);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(KbT * N[(NaChar / Vef), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 51.6%

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

6. Taylor expanded in Vef around inf 25.9%

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

7. Taylor expanded in NdChar around 0 7.4%

   \[\leadsto \color{blue}{\frac{KbT \cdot NaChar}{Vef}} \]
8. Step-by-step derivation

   1. associate-*l/ 7.5%

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

9. Simplified 7.5%

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

10. Taylor expanded in KbT around 0 7.4%

    \[\leadsto \color{blue}{\frac{KbT \cdot NaChar}{Vef}} \]
11. Step-by-step derivation

    1. *-commutative 7.4%

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

    2. associate-*l/ 7.9%

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

    3. *-commutative 7.9%

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

12. Simplified 7.9%

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

13. Final simplification 7.9%

    \[\leadsto KbT \cdot \frac{NaChar}{Vef} \]
14. Add Preprocessing

Alternative 20: 9.3% accurate, 45.8× speedup

Math

\[\begin{array}{l} \\ \frac{KbT}{\frac{Vef}{NaChar}} \end{array} \]

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return KbT / (Vef / 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 = kbt / (vef / 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 KbT / (Vef / NaChar);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(KbT / N[(Vef / NaChar), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 51.6%

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

6. Taylor expanded in Vef around inf 25.9%

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

7. Taylor expanded in NdChar around 0 7.4%

   \[\leadsto \color{blue}{\frac{KbT \cdot NaChar}{Vef}} \]
8. Step-by-step derivation

   1. associate-*l/ 7.5%

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

9. Simplified 7.5%

   \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NaChar} \]
10. Step-by-step derivation

    1. associate-*l/ 7.4%

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

    2. associate-/l* 8.2%

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

11. Applied egg-rr 8.2%

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

12. Final simplification 8.2%

    \[\leadsto \frac{KbT}{\frac{Vef}{NaChar}} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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))))))