Bulmash initializePoisson

Percentage Accurate: 100.0% → 99.9%

Time: 28.2s

Alternatives: 22

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = 58027453.17640856
  2. Ec = -4.5977882048976184e-111
  3. Vef = 4.376652436232065e-294
  4. EDonor = 3.586727042098232e-18
  5. mu = 2.0148481597970808e+45
  6. KbT = 1.0885856639948748e+160
  7. NaChar = 14491190.458481085
  8. Ev = 2.978127045728389e-262
  9. EAccept = -3.7684113962479563e+225

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: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{NdChar}{\sqrt[3]{{\left(e^{\frac{EDonor + \left(Vef + \left(mu - Ec\right)\right)}{KbT}}\right)}^{3}} + 1} + \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/
   NdChar
   (+ (cbrt (pow (exp (/ (+ EDonor (+ Vef (- mu Ec))) KbT)) 3.0)) 1.0))
  (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (cbrt(pow(exp(((EDonor + (Vef + (mu - Ec))) / KbT)), 3.0)) + 1.0)) + (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0));
}

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (Math.cbrt(Math.pow(Math.exp(((EDonor + (Vef + (mu - Ec))) / KbT)), 3.0)) + 1.0)) + (NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0));
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(cbrt((exp(Float64(Float64(EDonor + Float64(Vef + Float64(mu - Ec))) / KbT)) ^ 3.0)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0)))
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(N[Power[N[Power[N[Exp[N[(N[(EDonor + N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

   1. add-cbrt-cube 99.9%

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

   2. pow3 99.9%

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

   3. *-un-lft-identity 99.9%

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

   4. *-un-lft-identity 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l- 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 2: 70.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_1 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ t_2 := t\_1 + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{if}\;EAccept \leq -6.2 \cdot 10^{-143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 2.5 \cdot 10^{-217}:\\ \;\;\;\;t\_0 + \frac{NdChar}{e^{\frac{-Ec}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 4.5 \cdot 10^{-188}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{elif}\;EAccept \leq 2.35 \cdot 10^{-74}:\\ \;\;\;\;t\_0 + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 1.28 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 6.8 \cdot 10^{+90}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_1 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0)))
        (t_2 (+ t_1 (/ NaChar (+ (exp (/ Ev KbT)) 1.0)))))
   (if (<= EAccept -6.2e-143)
     t_2
     (if (<= EAccept 2.5e-217)
       (+ t_0 (/ NdChar (+ (exp (/ (- Ec) KbT)) 1.0)))
       (if (<= EAccept 4.5e-188)
         (+
          t_1
          (/
           NaChar
           (+
            (-
             (+ (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))) 1.0)
             (/ mu KbT))
            1.0)))
         (if (<= EAccept 2.35e-74)
           (+ t_0 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)))
           (if (<= EAccept 1.28e-20)
             t_2
             (if (<= EAccept 6.8e+90)
               (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
               (+ t_1 (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double t_2 = t_1 + (NaChar / (exp((Ev / KbT)) + 1.0));
	double tmp;
	if (EAccept <= -6.2e-143) {
		tmp = t_2;
	} else if (EAccept <= 2.5e-217) {
		tmp = t_0 + (NdChar / (exp((-Ec / KbT)) + 1.0));
	} else if (EAccept <= 4.5e-188) {
		tmp = t_1 + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	} else if (EAccept <= 2.35e-74) {
		tmp = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	} else if (EAccept <= 1.28e-20) {
		tmp = t_2;
	} else if (EAccept <= 6.8e+90) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = t_1 + (NaChar / (exp((EAccept / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_1 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    t_2 = t_1 + (nachar / (exp((ev / kbt)) + 1.0d0))
    if (eaccept <= (-6.2d-143)) then
        tmp = t_2
    else if (eaccept <= 2.5d-217) then
        tmp = t_0 + (ndchar / (exp((-ec / kbt)) + 1.0d0))
    else if (eaccept <= 4.5d-188) then
        tmp = t_1 + (nachar / (((((eaccept / kbt) + ((ev / kbt) + (vef / kbt))) + 1.0d0) - (mu / kbt)) + 1.0d0))
    else if (eaccept <= 2.35d-74) then
        tmp = t_0 + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    else if (eaccept <= 1.28d-20) then
        tmp = t_2
    else if (eaccept <= 6.8d+90) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = t_1 + (nachar / (exp((eaccept / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double t_2 = t_1 + (NaChar / (Math.exp((Ev / KbT)) + 1.0));
	double tmp;
	if (EAccept <= -6.2e-143) {
		tmp = t_2;
	} else if (EAccept <= 2.5e-217) {
		tmp = t_0 + (NdChar / (Math.exp((-Ec / KbT)) + 1.0));
	} else if (EAccept <= 4.5e-188) {
		tmp = t_1 + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	} else if (EAccept <= 2.35e-74) {
		tmp = t_0 + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	} else if (EAccept <= 1.28e-20) {
		tmp = t_2;
	} else if (EAccept <= 6.8e+90) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = t_1 + (NaChar / (Math.exp((EAccept / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_1 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	t_2 = t_1 + (NaChar / (math.exp((Ev / KbT)) + 1.0))
	tmp = 0
	if EAccept <= -6.2e-143:
		tmp = t_2
	elif EAccept <= 2.5e-217:
		tmp = t_0 + (NdChar / (math.exp((-Ec / KbT)) + 1.0))
	elif EAccept <= 4.5e-188:
		tmp = t_1 + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0))
	elif EAccept <= 2.35e-74:
		tmp = t_0 + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	elif EAccept <= 1.28e-20:
		tmp = t_2
	elif EAccept <= 6.8e+90:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = t_1 + (NaChar / (math.exp((EAccept / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_1 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)))
	tmp = 0.0
	if (EAccept <= -6.2e-143)
		tmp = t_2;
	elseif (EAccept <= 2.5e-217)
		tmp = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(Float64(-Ec) / KbT)) + 1.0)));
	elseif (EAccept <= 4.5e-188)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(Float64(Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT))) + 1.0) - Float64(mu / KbT)) + 1.0)));
	elseif (EAccept <= 2.35e-74)
		tmp = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)));
	elseif (EAccept <= 1.28e-20)
		tmp = t_2;
	elseif (EAccept <= 6.8e+90)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_1 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	t_2 = t_1 + (NaChar / (exp((Ev / KbT)) + 1.0));
	tmp = 0.0;
	if (EAccept <= -6.2e-143)
		tmp = t_2;
	elseif (EAccept <= 2.5e-217)
		tmp = t_0 + (NdChar / (exp((-Ec / KbT)) + 1.0));
	elseif (EAccept <= 4.5e-188)
		tmp = t_1 + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	elseif (EAccept <= 2.35e-74)
		tmp = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	elseif (EAccept <= 1.28e-20)
		tmp = t_2;
	elseif (EAccept <= 6.8e+90)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = t_1 + (NaChar / (exp((EAccept / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -6.2e-143], t$95$2, If[LessEqual[EAccept, 2.5e-217], N[(t$95$0 + N[(NdChar / N[(N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 4.5e-188], N[(t$95$1 + N[(NaChar / N[(N[(N[(N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 2.35e-74], N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.28e-20], t$95$2, If[LessEqual[EAccept, 6.8e+90], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if EAccept < -6.20000000000000015e-143 or 2.35000000000000005e-74 < EAccept < 1.2800000000000001e-20

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 68.8%

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

   if -6.20000000000000015e-143 < EAccept < 2.5000000000000001e-217

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in Ec around inf 75.9%

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

      1. mul-1-neg 37.1%

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

   7. Simplified 75.9%

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

   if 2.5000000000000001e-217 < EAccept < 4.49999999999999993e-188

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 80.9%

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

   if 4.49999999999999993e-188 < EAccept < 2.35000000000000005e-74

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 74.8%

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

   if 1.2800000000000001e-20 < EAccept < 6.80000000000000036e90

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in KbT around inf 57.3%

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

      1. associate-+r+ 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in EDonor around inf 24.9%

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

      1. associate-/l* 29.8%

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

   10. Simplified 29.8%

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

   11. Taylor expanded in KbT around 0 83.6%

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

   if 6.80000000000000036e90 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 93.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -6.2 \cdot 10^{-143}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 2.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{-Ec}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 4.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{elif}\;EAccept \leq 2.35 \cdot 10^{-74}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 1.28 \cdot 10^{-20}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 6.8 \cdot 10^{+90}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_1 := t\_0 + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ t_2 := t\_0 + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;EDonor \leq -3.9 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EDonor \leq 2.7 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;EDonor \leq 2.1 \cdot 10^{+19}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 5.2 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_1 (+ t_0 (/ NdChar (+ (exp (/ mu KbT)) 1.0))))
        (t_2 (+ t_0 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)))))
   (if (<= EDonor -3.9e+64)
     t_2
     (if (<= EDonor 2.7e-84)
       t_1
       (if (<= EDonor 2.1e+19)
         (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
         (if (<= EDonor 5.2e+165) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (exp((mu / KbT)) + 1.0));
	double t_2 = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -3.9e+64) {
		tmp = t_2;
	} else if (EDonor <= 2.7e-84) {
		tmp = t_1;
	} else if (EDonor <= 2.1e+19) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else if (EDonor <= 5.2e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_1 = t_0 + (ndchar / (exp((mu / kbt)) + 1.0d0))
    t_2 = t_0 + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    if (edonor <= (-3.9d+64)) then
        tmp = t_2
    else if (edonor <= 2.7d-84) then
        tmp = t_1
    else if (edonor <= 2.1d+19) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else if (edonor <= 5.2d+165) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (Math.exp((mu / KbT)) + 1.0));
	double t_2 = t_0 + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -3.9e+64) {
		tmp = t_2;
	} else if (EDonor <= 2.7e-84) {
		tmp = t_1;
	} else if (EDonor <= 2.1e+19) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else if (EDonor <= 5.2e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_1 = t_0 + (NdChar / (math.exp((mu / KbT)) + 1.0))
	t_2 = t_0 + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	tmp = 0
	if EDonor <= -3.9e+64:
		tmp = t_2
	elif EDonor <= 2.7e-84:
		tmp = t_1
	elif EDonor <= 2.1e+19:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	elif EDonor <= 5.2e+165:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)))
	t_2 = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)))
	tmp = 0.0
	if (EDonor <= -3.9e+64)
		tmp = t_2;
	elseif (EDonor <= 2.7e-84)
		tmp = t_1;
	elseif (EDonor <= 2.1e+19)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	elseif (EDonor <= 5.2e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_1 = t_0 + (NdChar / (exp((mu / KbT)) + 1.0));
	t_2 = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	tmp = 0.0;
	if (EDonor <= -3.9e+64)
		tmp = t_2;
	elseif (EDonor <= 2.7e-84)
		tmp = t_1;
	elseif (EDonor <= 2.1e+19)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	elseif (EDonor <= 5.2e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -3.9e+64], t$95$2, If[LessEqual[EDonor, 2.7e-84], t$95$1, If[LessEqual[EDonor, 2.1e+19], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 5.2e+165], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if EDonor < -3.8999999999999998e64 or 5.2000000000000002e165 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 88.7%

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

   if -3.8999999999999998e64 < EDonor < 2.6999999999999999e-84 or 2.1e19 < EDonor < 5.2000000000000002e165

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 82.3%

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

   if 2.6999999999999999e-84 < EDonor < 2.1e19

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.9%

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

      1. associate-+r+ 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in EDonor around inf 36.2%

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

      1. associate-/l* 36.2%

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

   10. Simplified 36.2%

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

   11. Taylor expanded in KbT around 0 85.5%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -3.9 \cdot 10^{+64}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 2.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 2.1 \cdot 10^{+19}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 5.2 \cdot 10^{+165}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Ev \leq -5.5 \cdot 10^{+132}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -8 \cdot 10^{-99}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Ev \leq -9 \cdot 10^{-176}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{elif}\;Ev \leq 1.05 \cdot 10^{-28}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{-Ec}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))))
   (if (<= Ev -5.5e+132)
     (+
      (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
      (/ NdChar (+ (exp (/ Vef KbT)) 1.0)))
     (if (<= Ev -8e-99)
       t_0
       (if (<= Ev -9e-176)
         (+
          (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))
          (/
           NaChar
           (+
            (-
             (+ (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))) 1.0)
             (/ mu KbT))
            1.0)))
         (if (<= Ev 1.05e-28)
           t_0
           (+
            (/ NdChar (+ (exp (/ (- Ec) KbT)) 1.0))
            (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	double tmp;
	if (Ev <= -5.5e+132) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	} else if (Ev <= -8e-99) {
		tmp = t_0;
	} else if (Ev <= -9e-176) {
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	} else if (Ev <= 1.05e-28) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (exp((-Ec / KbT)) + 1.0)) + (NaChar / (exp((EAccept / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    if (ev <= (-5.5d+132)) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / (exp((vef / kbt)) + 1.0d0))
    else if (ev <= (-8d-99)) then
        tmp = t_0
    else if (ev <= (-9d-176)) then
        tmp = (ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (((((eaccept / kbt) + ((ev / kbt) + (vef / kbt))) + 1.0d0) - (mu / kbt)) + 1.0d0))
    else if (ev <= 1.05d-28) then
        tmp = t_0
    else
        tmp = (ndchar / (exp((-ec / kbt)) + 1.0d0)) + (nachar / (exp((eaccept / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	double tmp;
	if (Ev <= -5.5e+132) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / (Math.exp((Vef / KbT)) + 1.0));
	} else if (Ev <= -8e-99) {
		tmp = t_0;
	} else if (Ev <= -9e-176) {
		tmp = (NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	} else if (Ev <= 1.05e-28) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (Math.exp((-Ec / KbT)) + 1.0)) + (NaChar / (Math.exp((EAccept / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	tmp = 0
	if Ev <= -5.5e+132:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / (math.exp((Vef / KbT)) + 1.0))
	elif Ev <= -8e-99:
		tmp = t_0
	elif Ev <= -9e-176:
		tmp = (NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0))
	elif Ev <= 1.05e-28:
		tmp = t_0
	else:
		tmp = (NdChar / (math.exp((-Ec / KbT)) + 1.0)) + (NaChar / (math.exp((EAccept / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0))
	tmp = 0.0
	if (Ev <= -5.5e+132)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)));
	elseif (Ev <= -8e-99)
		tmp = t_0;
	elseif (Ev <= -9e-176)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(Float64(Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT))) + 1.0) - Float64(mu / KbT)) + 1.0)));
	elseif (Ev <= 1.05e-28)
		tmp = t_0;
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(-Ec) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	tmp = 0.0;
	if (Ev <= -5.5e+132)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	elseif (Ev <= -8e-99)
		tmp = t_0;
	elseif (Ev <= -9e-176)
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	elseif (Ev <= 1.05e-28)
		tmp = t_0;
	else
		tmp = (NdChar / (exp((-Ec / KbT)) + 1.0)) + (NaChar / (exp((EAccept / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -5.5e+132], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -8e-99], t$95$0, If[LessEqual[Ev, -9e-176], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(N[(N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 1.05e-28], t$95$0, N[(N[(NdChar / N[(N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -5.5e132

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 77.5%

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

   6. Taylor expanded in Ev around inf 67.0%

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

   if -5.5e132 < Ev < -8.0000000000000002e-99 or -9e-176 < Ev < 1.05000000000000003e-28

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 55.7%

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

      1. associate-+r+ 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in EDonor around inf 33.8%

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

      1. associate-/l* 36.0%

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

   10. Simplified 36.0%

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

   11. Taylor expanded in KbT around 0 69.0%

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

   if -8.0000000000000002e-99 < Ev < -9e-176

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.7%

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

   if 1.05000000000000003e-28 < Ev

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 78.9%

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

   6. Taylor expanded in Ec around inf 60.0%

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

      1. mul-1-neg 42.9%

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

   8. Simplified 60.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -5.5 \cdot 10^{+132}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -8 \cdot 10^{-99}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -9 \cdot 10^{-176}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{elif}\;Ev \leq 1.05 \cdot 10^{-28}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{-Ec}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;EDonor \leq -4.2 \cdot 10^{-213}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;EDonor \leq 3.3 \cdot 10^{-94}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 4.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0))
          (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)))))
   (if (<= EDonor -4.2e-213)
     t_0
     (if (<= EDonor 3.3e-94)
       (+
        (/ NdChar (+ (exp (/ Vef KbT)) 1.0))
        (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0)))
       (if (<= EDonor 4.4e+80)
         (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -4.2e-213) {
		tmp = t_0;
	} else if (EDonor <= 3.3e-94) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else if (EDonor <= 4.4e+80) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)) + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    if (edonor <= (-4.2d-213)) then
        tmp = t_0
    else if (edonor <= 3.3d-94) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0))
    else if (edonor <= 4.4d+80) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -4.2e-213) {
		tmp = t_0;
	} else if (EDonor <= 3.3e-94) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else if (EDonor <= 4.4e+80) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	tmp = 0
	if EDonor <= -4.2e-213:
		tmp = t_0
	elif EDonor <= 3.3e-94:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0))
	elif EDonor <= 4.4e+80:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)))
	tmp = 0.0
	if (EDonor <= -4.2e-213)
		tmp = t_0;
	elseif (EDonor <= 3.3e-94)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)));
	elseif (EDonor <= 4.4e+80)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / (exp((EDonor / KbT)) + 1.0));
	tmp = 0.0;
	if (EDonor <= -4.2e-213)
		tmp = t_0;
	elseif (EDonor <= 3.3e-94)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	elseif (EDonor <= 4.4e+80)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -4.2e-213], t$95$0, If[LessEqual[EDonor, 3.3e-94], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 4.4e+80], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if EDonor < -4.1999999999999997e-213 or 4.40000000000000005e80 < EDonor

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EDonor around inf 81.9%

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

   if -4.1999999999999997e-213 < EDonor < 3.3000000000000001e-94

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 83.3%

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

   6. Taylor expanded in EAccept around 0 80.3%

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

   if 3.3000000000000001e-94 < EDonor < 4.40000000000000005e80

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 58.5%

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

      1. associate-+r+ 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in EDonor around inf 39.0%

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

      1. associate-/l* 39.0%

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

   10. Simplified 39.0%

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

   11. Taylor expanded in KbT around 0 77.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -4.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 3.3 \cdot 10^{-94}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 4.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1}\\ t_1 := t\_0 + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;EDonor \leq -1.1 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;EDonor \leq 3.7 \cdot 10^{-82}:\\ \;\;\;\;t\_0 + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 9.2 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0)))
        (t_1 (+ t_0 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)))))
   (if (<= EDonor -1.1e-28)
     t_1
     (if (<= EDonor 3.7e-82)
       (+ t_0 (/ NdChar (+ (exp (/ Vef KbT)) 1.0)))
       (if (<= EDonor 9.2e+87)
         (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
         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 / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -1.1e-28) {
		tmp = t_1;
	} else if (EDonor <= 3.7e-82) {
		tmp = t_0 + (NdChar / (exp((Vef / KbT)) + 1.0));
	} else if (EDonor <= 9.2e+87) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)
    t_1 = t_0 + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    if (edonor <= (-1.1d-28)) then
        tmp = t_1
    else if (edonor <= 3.7d-82) then
        tmp = t_0 + (ndchar / (exp((vef / kbt)) + 1.0d0))
    else if (edonor <= 9.2d+87) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    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 / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (EDonor <= -1.1e-28) {
		tmp = t_1;
	} else if (EDonor <= 3.7e-82) {
		tmp = t_0 + (NdChar / (Math.exp((Vef / KbT)) + 1.0));
	} else if (EDonor <= 9.2e+87) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)
	t_1 = t_0 + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	tmp = 0
	if EDonor <= -1.1e-28:
		tmp = t_1
	elif EDonor <= 3.7e-82:
		tmp = t_0 + (NdChar / (math.exp((Vef / KbT)) + 1.0))
	elif EDonor <= 9.2e+87:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)))
	tmp = 0.0
	if (EDonor <= -1.1e-28)
		tmp = t_1;
	elseif (EDonor <= 3.7e-82)
		tmp = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)));
	elseif (EDonor <= 9.2e+87)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0);
	t_1 = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	tmp = 0.0;
	if (EDonor <= -1.1e-28)
		tmp = t_1;
	elseif (EDonor <= 3.7e-82)
		tmp = t_0 + (NdChar / (exp((Vef / KbT)) + 1.0));
	elseif (EDonor <= 9.2e+87)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -1.1e-28], t$95$1, If[LessEqual[EDonor, 3.7e-82], N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 9.2e+87], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if EDonor < -1.09999999999999998e-28 or 9.2000000000000007e87 < EDonor

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EDonor around inf 83.8%

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

   if -1.09999999999999998e-28 < EDonor < 3.7000000000000001e-82

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 83.2%

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

   if 3.7000000000000001e-82 < EDonor < 9.2000000000000007e87

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 58.2%

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

      1. associate-+r+ 58.2%

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

   7. Simplified 58.2%

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

   8. Taylor expanded in EDonor around inf 41.6%

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

      1. associate-/l* 41.5%

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

   10. Simplified 41.5%

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

   11. Taylor expanded in KbT around 0 80.7%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -1.1 \cdot 10^{-28}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 3.7 \cdot 10^{-82}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;EDonor \leq 9.2 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Ev \leq -7 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.4 \cdot 10^{-99}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Ev \leq -8.8 \cdot 10^{-176}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{elif}\;Ev \leq 6.5 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))))
   (if (<= Ev -7e+133)
     (+
      (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
      (/ NdChar (+ (exp (/ Vef KbT)) 1.0)))
     (if (<= Ev -1.4e-99)
       t_0
       (if (<= Ev -8.8e-176)
         (+
          (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))
          (/
           NaChar
           (+
            (-
             (+ (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))) 1.0)
             (/ mu KbT))
            1.0)))
         (if (<= Ev 6.5e-33)
           t_0
           (+
            (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))
            (/ NdChar (+ (exp (/ mu KbT)) 1.0)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	double tmp;
	if (Ev <= -7e+133) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	} else if (Ev <= -1.4e-99) {
		tmp = t_0;
	} else if (Ev <= -8.8e-176) {
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	} else if (Ev <= 6.5e-33) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    if (ev <= (-7d+133)) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / (exp((vef / kbt)) + 1.0d0))
    else if (ev <= (-1.4d-99)) then
        tmp = t_0
    else if (ev <= (-8.8d-176)) then
        tmp = (ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (((((eaccept / kbt) + ((ev / kbt) + (vef / kbt))) + 1.0d0) - (mu / kbt)) + 1.0d0))
    else if (ev <= 6.5d-33) then
        tmp = t_0
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / (exp((mu / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	double tmp;
	if (Ev <= -7e+133) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / (Math.exp((Vef / KbT)) + 1.0));
	} else if (Ev <= -1.4e-99) {
		tmp = t_0;
	} else if (Ev <= -8.8e-176) {
		tmp = (NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	} else if (Ev <= 6.5e-33) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / (Math.exp((mu / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	tmp = 0
	if Ev <= -7e+133:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / (math.exp((Vef / KbT)) + 1.0))
	elif Ev <= -1.4e-99:
		tmp = t_0
	elif Ev <= -8.8e-176:
		tmp = (NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0))
	elif Ev <= 6.5e-33:
		tmp = t_0
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / (math.exp((mu / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0))
	tmp = 0.0
	if (Ev <= -7e+133)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)));
	elseif (Ev <= -1.4e-99)
		tmp = t_0;
	elseif (Ev <= -8.8e-176)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(Float64(Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT))) + 1.0) - Float64(mu / KbT)) + 1.0)));
	elseif (Ev <= 6.5e-33)
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	tmp = 0.0;
	if (Ev <= -7e+133)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	elseif (Ev <= -1.4e-99)
		tmp = t_0;
	elseif (Ev <= -8.8e-176)
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	elseif (Ev <= 6.5e-33)
		tmp = t_0;
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -7e+133], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.4e-99], t$95$0, If[LessEqual[Ev, -8.8e-176], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(N[(N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 6.5e-33], t$95$0, N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -6.9999999999999997e133

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 77.5%

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

   6. Taylor expanded in Ev around inf 67.0%

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

   if -6.9999999999999997e133 < Ev < -1.4e-99 or -8.7999999999999994e-176 < Ev < 6.4999999999999993e-33

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 56.4%

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

      1. associate-+r+ 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in EDonor around inf 34.2%

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

      1. associate-/l* 36.4%

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

   10. Simplified 36.4%

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

   11. Taylor expanded in KbT around 0 69.2%

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

   if -1.4e-99 < Ev < -8.7999999999999994e-176

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.7%

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

   if 6.4999999999999993e-33 < Ev

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 79.6%

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

   6. Taylor expanded in mu around inf 62.4%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -7 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.4 \cdot 10^{-99}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -8.8 \cdot 10^{-176}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{elif}\;Ev \leq 6.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 9: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 9.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 10^{+204}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 9.5e-11)
   (+
    (/ NdChar (+ (exp (/ Vef KbT)) 1.0))
    (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0)))
   (if (<= EAccept 1e+204)
     (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
     (+
      (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))
      (/ NdChar (+ (exp (/ mu KbT)) 1.0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 9.5e-11) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else if (EAccept <= 1e+204) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= 9.5d-11) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0))
    else if (eaccept <= 1d+204) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / (exp((mu / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 9.5e-11) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else if (EAccept <= 1e+204) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / (Math.exp((mu / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 9.5e-11:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0))
	elif EAccept <= 1e+204:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / (math.exp((mu / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 9.5e-11)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)));
	elseif (EAccept <= 1e+204)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 9.5e-11)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	elseif (EAccept <= 1e+204)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / (exp((mu / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 9.5e-11], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1e+204], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 9.49999999999999951e-11

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 71.7%

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

   6. Taylor expanded in EAccept around 0 68.3%

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

   if 9.49999999999999951e-11 < EAccept < 9.99999999999999989e203

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 54.5%

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

      1. associate-+r+ 54.5%

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

   7. Simplified 54.5%

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

   8. Taylor expanded in EDonor around inf 20.4%

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

      1. associate-/l* 20.1%

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

   10. Simplified 20.1%

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

   11. Taylor expanded in KbT around 0 74.2%

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

   if 9.99999999999999989e203 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 99.9%

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

   6. Taylor expanded in mu around inf 79.3%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 9.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 10^{+204}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -1.85 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -3.6 \cdot 10^{-101} \lor \neg \left(Ev \leq -9.5 \cdot 10^{-176}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -1.85e+133)
   (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (/ NdChar (+ (exp (/ Vef KbT)) 1.0)))
   (if (or (<= Ev -3.6e-101) (not (<= Ev -9.5e-176)))
     (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
     (+
      (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))
      (/
       NaChar
       (+
        (- (+ (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))) 1.0) (/ mu KbT))
        1.0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -1.85e+133) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	} else if ((Ev <= -3.6e-101) || !(Ev <= -9.5e-176)) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-1.85d+133)) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / (exp((vef / kbt)) + 1.0d0))
    else if ((ev <= (-3.6d-101)) .or. (.not. (ev <= (-9.5d-176)))) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = (ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (((((eaccept / kbt) + ((ev / kbt) + (vef / kbt))) + 1.0d0) - (mu / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -1.85e+133) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / (Math.exp((Vef / KbT)) + 1.0));
	} else if ((Ev <= -3.6e-101) || !(Ev <= -9.5e-176)) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -1.85e+133:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / (math.exp((Vef / KbT)) + 1.0))
	elif (Ev <= -3.6e-101) or not (Ev <= -9.5e-176):
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = (NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -1.85e+133)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)));
	elseif ((Ev <= -3.6e-101) || !(Ev <= -9.5e-176))
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(Float64(Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT))) + 1.0) - Float64(mu / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -1.85e+133)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / (exp((Vef / KbT)) + 1.0));
	elseif ((Ev <= -3.6e-101) || ~((Ev <= -9.5e-176)))
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -1.85e+133], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[Ev, -3.6e-101], N[Not[LessEqual[Ev, -9.5e-176]], $MachinePrecision]], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(N[(N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -1.85000000000000012e133

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 77.5%

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

   6. Taylor expanded in Ev around inf 67.0%

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

   if -1.85000000000000012e133 < Ev < -3.6e-101 or -9.5e-176 < Ev

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 58.6%

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

      1. associate-+r+ 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in EDonor around inf 33.4%

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

      1. associate-/l* 34.9%

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

   10. Simplified 34.9%

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

   11. Taylor expanded in KbT around 0 67.3%

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

   if -3.6e-101 < Ev < -9.5e-176

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.85 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -3.6 \cdot 10^{-101} \lor \neg \left(Ev \leq -9.5 \cdot 10^{-176}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ t_1 := \frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NaChar \leq -4.2 \cdot 10^{+44}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -65000000000:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{2 - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.85 \cdot 10^{-57}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -8.8 \cdot 10^{-147}:\\ \;\;\;\;t\_1 + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq -1.05 \cdot 10^{-199}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 4.9 \cdot 10^{+23}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0)))
        (t_1 (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))))
   (if (<= NaChar -4.2e+44)
     t_0
     (if (<= NaChar -65000000000.0)
       (+ (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) (/ NaChar (- 2.0 (/ mu KbT))))
       (if (<= NaChar -1.85e-57)
         t_0
         (if (<= NaChar -8.8e-147)
           (+ t_1 (/ NaChar 2.0))
           (if (<= NaChar -1.05e-199)
             t_0
             (if (<= NaChar 4.9e+23)
               (+
                t_1
                (/
                 NaChar
                 (+
                  (-
                   (+ (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))) 1.0)
                   (/ mu KbT))
                  1.0)))
               (+
                (/ NaChar (+ (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 1.0))
                (/ NdChar (+ (/ Vef KbT) 2.0)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	double t_1 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -4.2e+44) {
		tmp = t_0;
	} else if (NaChar <= -65000000000.0) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (2.0 - (mu / KbT)));
	} else if (NaChar <= -1.85e-57) {
		tmp = t_0;
	} else if (NaChar <= -8.8e-147) {
		tmp = t_1 + (NaChar / 2.0);
	} else if (NaChar <= -1.05e-199) {
		tmp = t_0;
	} else if (NaChar <= 4.9e+23) {
		tmp = t_1 + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	} else {
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    t_1 = ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)
    if (nachar <= (-4.2d+44)) then
        tmp = t_0
    else if (nachar <= (-65000000000.0d0)) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (2.0d0 - (mu / kbt)))
    else if (nachar <= (-1.85d-57)) then
        tmp = t_0
    else if (nachar <= (-8.8d-147)) then
        tmp = t_1 + (nachar / 2.0d0)
    else if (nachar <= (-1.05d-199)) then
        tmp = t_0
    else if (nachar <= 4.9d+23) then
        tmp = t_1 + (nachar / (((((eaccept / kbt) + ((ev / kbt) + (vef / kbt))) + 1.0d0) - (mu / kbt)) + 1.0d0))
    else
        tmp = (nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0)) + (ndchar / ((vef / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	double t_1 = NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NaChar <= -4.2e+44) {
		tmp = t_0;
	} else if (NaChar <= -65000000000.0) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (2.0 - (mu / KbT)));
	} else if (NaChar <= -1.85e-57) {
		tmp = t_0;
	} else if (NaChar <= -8.8e-147) {
		tmp = t_1 + (NaChar / 2.0);
	} else if (NaChar <= -1.05e-199) {
		tmp = t_0;
	} else if (NaChar <= 4.9e+23) {
		tmp = t_1 + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	} else {
		tmp = (NaChar / (Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	t_1 = NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)
	tmp = 0
	if NaChar <= -4.2e+44:
		tmp = t_0
	elif NaChar <= -65000000000.0:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (2.0 - (mu / KbT)))
	elif NaChar <= -1.85e-57:
		tmp = t_0
	elif NaChar <= -8.8e-147:
		tmp = t_1 + (NaChar / 2.0)
	elif NaChar <= -1.05e-199:
		tmp = t_0
	elif NaChar <= 4.9e+23:
		tmp = t_1 + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0))
	else:
		tmp = (NaChar / (math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0))
	t_1 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0))
	tmp = 0.0
	if (NaChar <= -4.2e+44)
		tmp = t_0;
	elseif (NaChar <= -65000000000.0)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(2.0 - Float64(mu / KbT))));
	elseif (NaChar <= -1.85e-57)
		tmp = t_0;
	elseif (NaChar <= -8.8e-147)
		tmp = Float64(t_1 + Float64(NaChar / 2.0));
	elseif (NaChar <= -1.05e-199)
		tmp = t_0;
	elseif (NaChar <= 4.9e+23)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(Float64(Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT))) + 1.0) - Float64(mu / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Vef / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	t_1 = NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NaChar <= -4.2e+44)
		tmp = t_0;
	elseif (NaChar <= -65000000000.0)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (2.0 - (mu / KbT)));
	elseif (NaChar <= -1.85e-57)
		tmp = t_0;
	elseif (NaChar <= -8.8e-147)
		tmp = t_1 + (NaChar / 2.0);
	elseif (NaChar <= -1.05e-199)
		tmp = t_0;
	elseif (NaChar <= 4.9e+23)
		tmp = t_1 + (NaChar / (((((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))) + 1.0) - (mu / KbT)) + 1.0));
	else
		tmp = (NaChar / (exp(((Vef + (Ev + (EAccept - mu))) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.2e+44], t$95$0, If[LessEqual[NaChar, -65000000000.0], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(2.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.85e-57], t$95$0, If[LessEqual[NaChar, -8.8e-147], N[(t$95$1 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.05e-199], t$95$0, If[LessEqual[NaChar, 4.9e+23], N[(t$95$1 + N[(NaChar / N[(N[(N[(N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -4.19999999999999974e44 or -6.5e10 < NaChar < -1.85e-57 or -8.8000000000000004e-147 < NaChar < -1.05000000000000001e-199

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 65.4%

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

      1. associate-+r+ 65.4%

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

   7. Simplified 65.4%

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

   8. Taylor expanded in EDonor around inf 40.6%

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

      1. associate-/l* 42.8%

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

   10. Simplified 42.8%

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

   11. Taylor expanded in KbT around 0 79.3%

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

   if -4.19999999999999974e44 < NaChar < -6.5e10

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 100.0%

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

   6. Taylor expanded in mu around inf 91.0%

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

      1. associate-*r/ 91.0%

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

      2. mul-1-neg 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in mu around 0 91.0%

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

       1. mul-1-neg 91.0%

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

       2. unsub-neg 91.0%

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

   11. Simplified 91.0%

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

   if -1.85e-57 < NaChar < -8.8000000000000004e-147

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 74.9%

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

   if -1.05000000000000001e-199 < NaChar < 4.9000000000000003e23

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.5%

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

   if 4.9000000000000003e23 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 91.2%

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

   6. Taylor expanded in Vef around 0 84.0%

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

      1. +-commutative 51.6%

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

   8. Simplified 84.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq -65000000000:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{2 - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.85 \cdot 10^{-57}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq -8.8 \cdot 10^{-147}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq -1.05 \cdot 10^{-199}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq 4.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{\left(\left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right) + 1\right) - \frac{mu}{KbT}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -3.65 \cdot 10^{+118} \lor \neg \left(KbT \leq 1.26 \cdot 10^{+151}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -3.65e+118) (not (<= KbT 1.26e+151)))
   (+
    (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))
    (/ NaChar 2.0))
   (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -3.65e+118) || !(KbT <= 1.26e+151)) {
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((kbt <= (-3.65d+118)) .or. (.not. (kbt <= 1.26d+151))) then
        tmp = (ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -3.65e+118) || !(KbT <= 1.26e+151)) {
		tmp = (NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -3.65e+118) or not (KbT <= 1.26e+151):
		tmp = (NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / 2.0)
	else:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -3.65e+118) || !(KbT <= 1.26e+151))
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -3.65e+118) || ~((KbT <= 1.26e+151)))
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / 2.0);
	else
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -3.65e+118], N[Not[LessEqual[KbT, 1.26e+151]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -3.6500000000000002e118 or 1.26000000000000006e151 < KbT

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 83.1%

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

   if -3.6500000000000002e118 < KbT < 1.26000000000000006e151

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 50.5%

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

      1. associate-+r+ 50.5%

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

   7. Simplified 50.5%

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

   8. Taylor expanded in EDonor around inf 38.4%

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

      1. associate-/l* 38.1%

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

   10. Simplified 38.1%

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

   11. Taylor expanded in KbT around 0 67.2%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.65 \cdot 10^{+118} \lor \neg \left(KbT \leq 1.26 \cdot 10^{+151}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq -2.3 \cdot 10^{-102}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;EAccept \leq 8.6 \cdot 10^{-135}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{e^{\frac{-mu}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 1.7 \cdot 10^{-28}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept -2.3e-102)
   (+ (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) (/ NaChar 2.0))
   (if (<= EAccept 8.6e-135)
     (+ (* NdChar 0.5) (/ NaChar (+ (exp (/ (- mu) KbT)) 1.0)))
     (if (<= EAccept 1.7e-28)
       (+ (/ NdChar (+ (exp (/ mu KbT)) 1.0)) (/ NaChar 2.0))
       (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ 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 (EAccept <= -2.3e-102) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / 2.0);
	} else if (EAccept <= 8.6e-135) {
		tmp = (NdChar * 0.5) + (NaChar / (exp((-mu / KbT)) + 1.0));
	} else if (EAccept <= 1.7e-28) {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (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 (eaccept <= (-2.3d-102)) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else if (eaccept <= 8.6d-135) then
        tmp = (ndchar * 0.5d0) + (nachar / (exp((-mu / kbt)) + 1.0d0))
    else if (eaccept <= 1.7d-28) then
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (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 (EAccept <= -2.3e-102) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / 2.0);
	} else if (EAccept <= 8.6e-135) {
		tmp = (NdChar * 0.5) + (NaChar / (Math.exp((-mu / KbT)) + 1.0));
	} else if (EAccept <= 1.7e-28) {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= -2.3e-102:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / 2.0)
	elif EAccept <= 8.6e-135:
		tmp = (NdChar * 0.5) + (NaChar / (math.exp((-mu / KbT)) + 1.0))
	elif EAccept <= 1.7e-28:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= -2.3e-102)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	elseif (EAccept <= 8.6e-135)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar / Float64(exp(Float64(Float64(-mu) / KbT)) + 1.0)));
	elseif (EAccept <= 1.7e-28)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + 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 (EAccept <= -2.3e-102)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / 2.0);
	elseif (EAccept <= 8.6e-135)
		tmp = (NdChar * 0.5) + (NaChar / (exp((-mu / KbT)) + 1.0));
	elseif (EAccept <= 1.7e-28)
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / 2.0);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, -2.3e-102], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 8.6e-135], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.7e-28], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if EAccept < -2.29999999999999987e-102

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 77.1%

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

   6. Taylor expanded in KbT around inf 46.3%

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

   if -2.29999999999999987e-102 < EAccept < 8.59999999999999997e-135

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 70.2%

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

   6. Taylor expanded in mu around inf 49.4%

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

      1. associate-*r/ 49.4%

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

      2. mul-1-neg 49.4%

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

   8. Simplified 49.4%

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

   9. Taylor expanded in Vef around 0 40.8%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} \]
   10. Step-by-step derivation

       1. +-commutative 40.8%

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

   11. Simplified 40.8%

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

   12. Taylor expanded in Vef around 0 39.6%

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

   if 8.59999999999999997e-135 < EAccept < 1.7e-28

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 53.9%

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

   6. Taylor expanded in mu around inf 38.0%

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

   if 1.7e-28 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 78.4%

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

   6. Taylor expanded in KbT around inf 36.7%

      \[\leadsto \frac{NdChar}{\color{blue}{2}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -2.3 \cdot 10^{-102}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;EAccept \leq 8.6 \cdot 10^{-135}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{e^{\frac{-mu}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 1.7 \cdot 10^{-28}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.25 \cdot 10^{+121} \lor \neg \left(KbT \leq 3.4 \cdot 10^{+161}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{-Ec}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -1.25e+121) (not (<= KbT 3.4e+161)))
   (+ (/ NdChar (+ (exp (/ (- Ec) KbT)) 1.0)) (/ NaChar 2.0))
   (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -1.25e+121) || !(KbT <= 3.4e+161)) {
		tmp = (NdChar / (exp((-Ec / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((kbt <= (-1.25d+121)) .or. (.not. (kbt <= 3.4d+161))) then
        tmp = (ndchar / (exp((-ec / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -1.25e+121) || !(KbT <= 3.4e+161)) {
		tmp = (NdChar / (Math.exp((-Ec / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -1.25e+121) or not (KbT <= 3.4e+161):
		tmp = (NdChar / (math.exp((-Ec / KbT)) + 1.0)) + (NaChar / 2.0)
	else:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -1.25e+121) || !(KbT <= 3.4e+161))
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(-Ec) / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -1.25e+121) || ~((KbT <= 3.4e+161)))
		tmp = (NdChar / (exp((-Ec / KbT)) + 1.0)) + (NaChar / 2.0);
	else
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -1.25e+121], N[Not[LessEqual[KbT, 3.4e+161]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -1.25000000000000002e121 or 3.39999999999999993e161 < KbT

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 83.6%

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

   6. Taylor expanded in Ec around inf 78.7%

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

      1. mul-1-neg 78.7%

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

   8. Simplified 78.7%

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

   if -1.25000000000000002e121 < KbT < 3.39999999999999993e161

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 50.8%

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

      1. associate-+r+ 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in EDonor around inf 37.8%

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

      1. associate-/l* 37.5%

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

   10. Simplified 37.5%

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

   11. Taylor expanded in KbT around 0 67.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.25 \cdot 10^{+121} \lor \neg \left(KbT \leq 3.4 \cdot 10^{+161}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{-Ec}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -5.9 \cdot 10^{+128}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;Ev \leq -7.2 \cdot 10^{-134}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{e^{\frac{-mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -5.9e+128)
   (+ (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) (/ NaChar 2.0))
   (if (<= Ev -7.2e-134)
     (+ (* NdChar 0.5) (/ NaChar (+ (exp (/ (- mu) KbT)) 1.0)))
     (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -5.9e+128) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / 2.0);
	} else if (Ev <= -7.2e-134) {
		tmp = (NdChar * 0.5) + (NaChar / (exp((-mu / KbT)) + 1.0));
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-5.9d+128)) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else if (ev <= (-7.2d-134)) then
        tmp = (ndchar * 0.5d0) + (nachar / (exp((-mu / kbt)) + 1.0d0))
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -5.9e+128) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / 2.0);
	} else if (Ev <= -7.2e-134) {
		tmp = (NdChar * 0.5) + (NaChar / (Math.exp((-mu / KbT)) + 1.0));
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -5.9e+128:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / 2.0)
	elif Ev <= -7.2e-134:
		tmp = (NdChar * 0.5) + (NaChar / (math.exp((-mu / KbT)) + 1.0))
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -5.9e+128)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	elseif (Ev <= -7.2e-134)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar / Float64(exp(Float64(Float64(-mu) / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -5.9e+128)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / 2.0);
	elseif (Ev <= -7.2e-134)
		tmp = (NdChar * 0.5) + (NaChar / (exp((-mu / KbT)) + 1.0));
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -5.9e+128], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -7.2e-134], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -5.89999999999999987e128

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.2%

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

   6. Taylor expanded in KbT around inf 44.1%

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

   if -5.89999999999999987e128 < Ev < -7.1999999999999998e-134

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.5%

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

   6. Taylor expanded in mu around inf 52.3%

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

      1. associate-*r/ 52.3%

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

      2. mul-1-neg 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in Vef around 0 37.3%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} \]
   10. Step-by-step derivation

       1. +-commutative 37.3%

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

   11. Simplified 37.3%

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

   12. Taylor expanded in Vef around 0 34.9%

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

   if -7.1999999999999998e-134 < Ev

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 75.9%

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

   6. Taylor expanded in KbT around inf 42.6%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -5.9 \cdot 10^{+128}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;Ev \leq -7.2 \cdot 10^{-134}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{e^{\frac{-mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq 1.9 \cdot 10^{+156}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT 1.9e+156)
   (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
   (+ (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)) (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= 1.9e+156) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= 1.9d+156) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = (ndchar / (exp((edonor / kbt)) + 1.0d0)) + (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 (KbT <= 1.9e+156) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = (NdChar / (Math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= 1.9e+156:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = (NdChar / (math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= 1.9e+156)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)) + 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 (KbT <= 1.9e+156)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, 1.9e+156], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < 1.90000000000000012e156

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 53.5%

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

      1. associate-+r+ 53.5%

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

   7. Simplified 53.5%

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

   8. Taylor expanded in EDonor around inf 34.5%

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

      1. associate-/l* 35.6%

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

   10. Simplified 35.6%

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

   11. Taylor expanded in KbT around 0 65.7%

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

   if 1.90000000000000012e156 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 90.1%

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

   6. Taylor expanded in EDonor around inf 83.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 1.9 \cdot 10^{+156}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 37.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 9 \cdot 10^{+89}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{e^{\frac{-mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 9e+89)
   (+ (* NdChar 0.5) (/ NaChar (+ (exp (/ (- mu) KbT)) 1.0)))
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ 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 (EAccept <= 9e+89) {
		tmp = (NdChar * 0.5) + (NaChar / (exp((-mu / KbT)) + 1.0));
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (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 (eaccept <= 9d+89) then
        tmp = (ndchar * 0.5d0) + (nachar / (exp((-mu / kbt)) + 1.0d0))
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (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 (EAccept <= 9e+89) {
		tmp = (NdChar * 0.5) + (NaChar / (Math.exp((-mu / KbT)) + 1.0));
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 9e+89:
		tmp = (NdChar * 0.5) + (NaChar / (math.exp((-mu / KbT)) + 1.0))
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 9e+89)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar / Float64(exp(Float64(Float64(-mu) / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + 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 (EAccept <= 9e+89)
		tmp = (NdChar * 0.5) + (NaChar / (exp((-mu / KbT)) + 1.0));
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 9e+89], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 9e89

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 69.9%

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

   6. Taylor expanded in mu around inf 51.8%

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

      1. associate-*r/ 51.8%

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

      2. mul-1-neg 51.8%

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

   8. Simplified 51.8%

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

   9. Taylor expanded in Vef around 0 40.1%

      \[\leadsto \frac{NdChar}{\color{blue}{2 + \frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} \]
   10. Step-by-step derivation

       1. +-commutative 40.1%

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

   11. Simplified 40.1%

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

   12. Taylor expanded in Vef around 0 38.2%

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

   if 9e89 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 93.0%

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

   6. Taylor expanded in KbT around inf 45.0%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 9 \cdot 10^{+89}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{e^{\frac{-mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq -8 \cdot 10^{+231}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EDonor -8e+231)
   (* KbT (/ NdChar EDonor))
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ 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 (EDonor <= -8e+231) {
		tmp = KbT * (NdChar / EDonor);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (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 (edonor <= (-8d+231)) then
        tmp = kbt * (ndchar / edonor)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (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 (EDonor <= -8e+231) {
		tmp = KbT * (NdChar / EDonor);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EDonor <= -8e+231:
		tmp = KbT * (NdChar / EDonor)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EDonor <= -8e+231)
		tmp = Float64(KbT * Float64(NdChar / EDonor));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + 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 (EDonor <= -8e+231)
		tmp = KbT * (NdChar / EDonor);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EDonor, -8e+231], N[(KbT * N[(NdChar / EDonor), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -8.0000000000000005e231

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 44.8%

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

      1. associate-+r+ 44.8%

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

   7. Simplified 44.8%

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

   8. Taylor expanded in EDonor around inf 55.2%

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

      1. associate-/l* 60.3%

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

   10. Simplified 60.3%

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

   11. Taylor expanded in KbT around inf 7.1%

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

   12. Taylor expanded in NaChar around 0 30.1%

       \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{EDonor}} \]
   13. Step-by-step derivation

       1. associate-*r/ 35.1%

          \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} \]

   14. Simplified 35.1%

       \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} \]

   if -8.0000000000000005e231 < EDonor

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 71.5%

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

   6. Taylor expanded in KbT around inf 39.9%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -8 \cdot 10^{+231}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 1.5 \cdot 10^{+126}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 1.5e+126)
   (+ (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)) (/ NaChar 2.0))
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ 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 (EAccept <= 1.5e+126) {
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (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 (eaccept <= 1.5d+126) then
        tmp = (ndchar / (exp((edonor / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (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 (EAccept <= 1.5e+126) {
		tmp = (NdChar / (Math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 1.5e+126:
		tmp = (NdChar / (math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 1.5e+126)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + 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 (EAccept <= 1.5e+126)
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 1.5e+126], N[(N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 1.5000000000000001e126

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 48.8%

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

   6. Taylor expanded in EDonor around inf 38.1%

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

   if 1.5000000000000001e126 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 94.5%

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

   6. Taylor expanded in KbT around inf 47.2%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 1.5 \cdot 10^{+126}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.8% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq -7.5 \cdot 10^{+229}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EDonor -7.5e+229)
   (* KbT (/ NdChar EDonor))
   (+ (/ NaChar 2.0) (/ 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 (EDonor <= -7.5e+229) {
		tmp = KbT * (NdChar / EDonor);
	} else {
		tmp = (NaChar / 2.0) + (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 (edonor <= (-7.5d+229)) then
        tmp = kbt * (ndchar / edonor)
    else
        tmp = (nachar / 2.0d0) + (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 (EDonor <= -7.5e+229) {
		tmp = KbT * (NdChar / EDonor);
	} else {
		tmp = (NaChar / 2.0) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EDonor <= -7.5e+229:
		tmp = KbT * (NdChar / EDonor)
	else:
		tmp = (NaChar / 2.0) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EDonor <= -7.5e+229)
		tmp = Float64(KbT * Float64(NdChar / EDonor));
	else
		tmp = Float64(Float64(NaChar / 2.0) + 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 (EDonor <= -7.5e+229)
		tmp = KbT * (NdChar / EDonor);
	else
		tmp = (NaChar / 2.0) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EDonor, -7.5e+229], N[(KbT * N[(NdChar / EDonor), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -7.50000000000000021e229

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 44.8%

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

      1. associate-+r+ 44.8%

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

   7. Simplified 44.8%

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

   8. Taylor expanded in EDonor around inf 55.2%

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

      1. associate-/l* 60.3%

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

   10. Simplified 60.3%

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

   11. Taylor expanded in KbT around inf 7.1%

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

   12. Taylor expanded in NaChar around 0 30.1%

       \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{EDonor}} \]
   13. Step-by-step derivation

       1. associate-*r/ 35.1%

          \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} \]

   14. Simplified 35.1%

       \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} \]

   if -7.50000000000000021e229 < EDonor

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 48.5%

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

   6. Taylor expanded in KbT around inf 30.9%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -7.5 \cdot 10^{+229}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 18.0% accurate, 22.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq -3 \cdot 10^{+191}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EDonor -3e+191) (* KbT (/ NdChar EDonor)) (* NaChar 0.5)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EDonor <= -3e+191) {
		tmp = KbT * (NdChar / EDonor);
	} else {
		tmp = NaChar * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (edonor <= (-3d+191)) then
        tmp = kbt * (ndchar / edonor)
    else
        tmp = nachar * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EDonor <= -3e+191) {
		tmp = KbT * (NdChar / EDonor);
	} else {
		tmp = NaChar * 0.5;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EDonor <= -3e+191:
		tmp = KbT * (NdChar / EDonor)
	else:
		tmp = NaChar * 0.5
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EDonor <= -3e+191)
		tmp = Float64(KbT * Float64(NdChar / EDonor));
	else
		tmp = Float64(NaChar * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EDonor <= -3e+191)
		tmp = KbT * (NdChar / EDonor);
	else
		tmp = NaChar * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EDonor, -3e+191], N[(KbT * N[(NdChar / EDonor), $MachinePrecision]), $MachinePrecision], N[(NaChar * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -2.9999999999999997e191

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 40.6%

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

      1. associate-+r+ 40.6%

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

   7. Simplified 40.6%

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

   8. Taylor expanded in EDonor around inf 41.4%

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

      1. associate-/l* 48.6%

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

   10. Simplified 48.6%

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

   11. Taylor expanded in KbT around inf 6.0%

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

   12. Taylor expanded in NaChar around 0 22.8%

       \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{EDonor}} \]
   13. Step-by-step derivation

       1. associate-*r/ 30.0%

          \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} \]

   14. Simplified 30.0%

       \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} \]

   if -2.9999999999999997e191 < EDonor

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 59.2%

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

      1. associate-+r+ 59.2%

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

   7. Simplified 59.2%

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

   8. Taylor expanded in EDonor around inf 31.1%

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

      1. associate-/l* 31.7%

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

   10. Simplified 31.7%

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

   11. Taylor expanded in KbT around inf 10.8%

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

   12. Taylor expanded in NaChar around inf 22.0%

       \[\leadsto \color{blue}{0.5 \cdot NaChar} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -3 \cdot 10^{+191}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 18.7% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in KbT around inf 57.3%

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

   1. associate-+r+ 57.3%

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

7. Simplified 57.3%

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

8. Taylor expanded in EDonor around inf 32.2%

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

   1. associate-/l* 33.4%

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

10. Simplified 33.4%

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

11. Taylor expanded in KbT around inf 10.3%

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

12. Taylor expanded in NaChar around inf 20.4%

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

13. Final simplification 20.4%

    \[\leadsto NaChar \cdot 0.5 \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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))))))