Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 27.3s

Alternatives: 26

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -4.9925244234319265e-20
  2. Ec = -1.1439547564367602e+291
  3. Vef = -2.8620045511461767e+305
  4. EDonor = 1.2986289600330479e+111
  5. mu = 7.119089705277956e-95
  6. KbT = 2.1094562877626004e+102
  7. NaChar = 8.121281458925079e-21
  8. Ev = -1.0759320448517906e+229
  9. EAccept = -4.595032115816588e-300

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + (exp(1) ^ Float64(Float64(Float64(Vef - Ec) + Float64(mu + EDonor)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + (2.71828182845904523536 ^ (((Vef - Ec) + (mu + EDonor)) / KbT)))) + (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

   1. *-un-lft-identity 100.0%

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

   2. exp-prod 100.0%

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

   3. +-commutative 100.0%

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

   4. +-commutative 100.0%

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

   5. associate-+l+ 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := t_0 + t_1\\ t_3 := \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ t_4 := t_3 + t_1\\ t_5 := t_3 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -2.05 \cdot 10^{+166}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq -7.5 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -14000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq -6 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 8.5 \cdot 10^{-297}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 8.8 \cdot 10^{-194}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 7.2 \cdot 10^{+111}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
        (t_2 (+ t_0 t_1))
        (t_3 (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT)))))
        (t_4 (+ t_3 t_1))
        (t_5 (+ t_3 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -2.05e+166)
     t_5
     (if (<= Vef -7.5e+98)
       t_2
       (if (<= Vef -14000.0)
         t_5
         (if (<= Vef -6e-34)
           t_2
           (if (<= Vef 8.5e-297)
             t_4
             (if (<= Vef 8.8e-194)
               (+ t_0 (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
               (if (<= Vef 7.2e+111) t_4 t_5)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((EDonor / KbT)));
	double t_1 = NaChar / (1.0 + exp((Ev / KbT)));
	double t_2 = t_0 + t_1;
	double t_3 = NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)));
	double t_4 = t_3 + t_1;
	double t_5 = t_3 + (NaChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -2.05e+166) {
		tmp = t_5;
	} else if (Vef <= -7.5e+98) {
		tmp = t_2;
	} else if (Vef <= -14000.0) {
		tmp = t_5;
	} else if (Vef <= -6e-34) {
		tmp = t_2;
	} else if (Vef <= 8.5e-297) {
		tmp = t_4;
	} else if (Vef <= 8.8e-194) {
		tmp = t_0 + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (Vef <= 7.2e+111) {
		tmp = t_4;
	} else {
		tmp = t_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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((edonor / kbt)))
    t_1 = nachar / (1.0d0 + exp((ev / kbt)))
    t_2 = t_0 + t_1
    t_3 = ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))
    t_4 = t_3 + t_1
    t_5 = t_3 + (nachar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-2.05d+166)) then
        tmp = t_5
    else if (vef <= (-7.5d+98)) then
        tmp = t_2
    else if (vef <= (-14000.0d0)) then
        tmp = t_5
    else if (vef <= (-6d-34)) then
        tmp = t_2
    else if (vef <= 8.5d-297) then
        tmp = t_4
    else if (vef <= 8.8d-194) then
        tmp = t_0 + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (vef <= 7.2d+111) then
        tmp = t_4
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp((Ev / KbT)));
	double t_2 = t_0 + t_1;
	double t_3 = NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)));
	double t_4 = t_3 + t_1;
	double t_5 = t_3 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -2.05e+166) {
		tmp = t_5;
	} else if (Vef <= -7.5e+98) {
		tmp = t_2;
	} else if (Vef <= -14000.0) {
		tmp = t_5;
	} else if (Vef <= -6e-34) {
		tmp = t_2;
	} else if (Vef <= 8.5e-297) {
		tmp = t_4;
	} else if (Vef <= 8.8e-194) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (Vef <= 7.2e+111) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((EDonor / KbT)))
	t_1 = NaChar / (1.0 + math.exp((Ev / KbT)))
	t_2 = t_0 + t_1
	t_3 = NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))
	t_4 = t_3 + t_1
	t_5 = t_3 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -2.05e+166:
		tmp = t_5
	elif Vef <= -7.5e+98:
		tmp = t_2
	elif Vef <= -14000.0:
		tmp = t_5
	elif Vef <= -6e-34:
		tmp = t_2
	elif Vef <= 8.5e-297:
		tmp = t_4
	elif Vef <= 8.8e-194:
		tmp = t_0 + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif Vef <= 7.2e+111:
		tmp = t_4
	else:
		tmp = t_5
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT))))
	t_2 = Float64(t_0 + t_1)
	t_3 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT))))
	t_4 = Float64(t_3 + t_1)
	t_5 = Float64(t_3 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -2.05e+166)
		tmp = t_5;
	elseif (Vef <= -7.5e+98)
		tmp = t_2;
	elseif (Vef <= -14000.0)
		tmp = t_5;
	elseif (Vef <= -6e-34)
		tmp = t_2;
	elseif (Vef <= 8.5e-297)
		tmp = t_4;
	elseif (Vef <= 8.8e-194)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (Vef <= 7.2e+111)
		tmp = t_4;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((EDonor / KbT)));
	t_1 = NaChar / (1.0 + exp((Ev / KbT)));
	t_2 = t_0 + t_1;
	t_3 = NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)));
	t_4 = t_3 + t_1;
	t_5 = t_3 + (NaChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -2.05e+166)
		tmp = t_5;
	elseif (Vef <= -7.5e+98)
		tmp = t_2;
	elseif (Vef <= -14000.0)
		tmp = t_5;
	elseif (Vef <= -6e-34)
		tmp = t_2;
	elseif (Vef <= 8.5e-297)
		tmp = t_4;
	elseif (Vef <= 8.8e-194)
		tmp = t_0 + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (Vef <= 7.2e+111)
		tmp = t_4;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -2.05e+166], t$95$5, If[LessEqual[Vef, -7.5e+98], t$95$2, If[LessEqual[Vef, -14000.0], t$95$5, If[LessEqual[Vef, -6e-34], t$95$2, If[LessEqual[Vef, 8.5e-297], t$95$4, If[LessEqual[Vef, 8.8e-194], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 7.2e+111], t$95$4, t$95$5]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -2.0500000000000001e166 or -7.50000000000000036e98 < Vef < -14000 or 7.2000000000000004e111 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 90.4%

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

   5. Taylor expanded in EDonor around 0 87.1%

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

      1. +-commutative 87.1%

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

      2. +-commutative 87.1%

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

   7. Simplified 87.1%

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

   if -2.0500000000000001e166 < Vef < -7.50000000000000036e98 or -14000 < Vef < -6e-34

   1. Initial program 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in EDonor around inf 87.4%

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

   5. Taylor expanded in Ev around inf 67.2%

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

   if -6e-34 < Vef < 8.49999999999999991e-297 or 8.8000000000000005e-194 < Vef < 7.2000000000000004e111

   1. Initial program 100.0%

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

   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. Step-by-step derivation

      1. *-un-lft-identity 100.0%

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

      2. exp-prod 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in Ev around inf 72.0%

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

   7. Taylor expanded in EDonor around 0 65.9%

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

      1. +-commutative 65.9%

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

      2. +-commutative 65.9%

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

   9. Simplified 65.9%

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

   if 8.49999999999999991e-297 < Vef < 8.8000000000000005e-194

   1. Initial program 100.0%

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

   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. Taylor expanded in EDonor around inf 86.2%

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

   5. Taylor expanded in mu around inf 72.5%

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

      1. associate-*r/ 44.0%

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

      2. mul-1-neg 44.0%

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

   7. Simplified 72.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.05 \cdot 10^{+166}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -7.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq -14000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -6 \cdot 10^{-34}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.5 \cdot 10^{-297}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.8 \cdot 10^{-194}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 7.2 \cdot 10^{+111}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 3: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ t_3 := t_2 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -5.5 \cdot 10^{+166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -1.25 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -1.05 \cdot 10^{-204}:\\ \;\;\;\;t_2 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.76 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 3.55 \cdot 10^{-84}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.65 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT)))))
        (t_3 (+ t_2 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -5.5e+166)
     t_3
     (if (<= Vef -1.25e-100)
       t_1
       (if (<= Vef -1.05e-204)
         (+ t_2 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
         (if (<= Vef 1.76e-209)
           t_1
           (if (<= Vef 3.55e-84)
             (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
             (if (<= Vef 1.65e+113) t_1 t_3))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_2 = NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)));
	double t_3 = t_2 + (NaChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -5.5e+166) {
		tmp = t_3;
	} else if (Vef <= -1.25e-100) {
		tmp = t_1;
	} else if (Vef <= -1.05e-204) {
		tmp = t_2 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Vef <= 1.76e-209) {
		tmp = t_1;
	} else if (Vef <= 3.55e-84) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= 1.65e+113) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_2 = ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))
    t_3 = t_2 + (nachar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-5.5d+166)) then
        tmp = t_3
    else if (vef <= (-1.25d-100)) then
        tmp = t_1
    else if (vef <= (-1.05d-204)) then
        tmp = t_2 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (vef <= 1.76d-209) then
        tmp = t_1
    else if (vef <= 3.55d-84) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= 1.65d+113) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_2 = NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)));
	double t_3 = t_2 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -5.5e+166) {
		tmp = t_3;
	} else if (Vef <= -1.25e-100) {
		tmp = t_1;
	} else if (Vef <= -1.05e-204) {
		tmp = t_2 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Vef <= 1.76e-209) {
		tmp = t_1;
	} else if (Vef <= 3.55e-84) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= 1.65e+113) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_2 = NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))
	t_3 = t_2 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -5.5e+166:
		tmp = t_3
	elif Vef <= -1.25e-100:
		tmp = t_1
	elif Vef <= -1.05e-204:
		tmp = t_2 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Vef <= 1.76e-209:
		tmp = t_1
	elif Vef <= 3.55e-84:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= 1.65e+113:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT))))
	t_3 = Float64(t_2 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -5.5e+166)
		tmp = t_3;
	elseif (Vef <= -1.25e-100)
		tmp = t_1;
	elseif (Vef <= -1.05e-204)
		tmp = Float64(t_2 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Vef <= 1.76e-209)
		tmp = t_1;
	elseif (Vef <= 3.55e-84)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= 1.65e+113)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_2 = NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)));
	t_3 = t_2 + (NaChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -5.5e+166)
		tmp = t_3;
	elseif (Vef <= -1.25e-100)
		tmp = t_1;
	elseif (Vef <= -1.05e-204)
		tmp = t_2 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Vef <= 1.76e-209)
		tmp = t_1;
	elseif (Vef <= 3.55e-84)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= 1.65e+113)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -5.5e+166], t$95$3, If[LessEqual[Vef, -1.25e-100], t$95$1, If[LessEqual[Vef, -1.05e-204], N[(t$95$2 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.76e-209], t$95$1, If[LessEqual[Vef, 3.55e-84], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.65e+113], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -5.50000000000000008e166 or 1.6500000000000002e113 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 97.0%

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

   5. Taylor expanded in EDonor around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. +-commutative 97.0%

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

   7. Simplified 97.0%

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

   if -5.50000000000000008e166 < Vef < -1.25e-100 or -1.05000000000000005e-204 < Vef < 1.75999999999999992e-209 or 3.5499999999999998e-84 < Vef < 1.6500000000000002e113

   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. Taylor expanded in EDonor around inf 81.2%

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

   if -1.25e-100 < Vef < -1.05000000000000005e-204

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. exp-prod 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in Ev around inf 81.1%

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

   7. Taylor expanded in EDonor around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. +-commutative 76.8%

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

   9. Simplified 76.8%

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

   if 1.75999999999999992e-209 < Vef < 3.5499999999999998e-84

   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. Taylor expanded in mu around inf 85.8%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -5.5 \cdot 10^{+166}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.25 \cdot 10^{-100}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.05 \cdot 10^{-204}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.76 \cdot 10^{-209}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.55 \cdot 10^{-84}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.65 \cdot 10^{+113}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 4: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ t_3 := t_2 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -7 \cdot 10^{+167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -9.6 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -2.1 \cdot 10^{-199}:\\ \;\;\;\;t_2 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 9.5 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 2.1 \cdot 10^{+109}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4 \cdot 10^{+112}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT)))))
        (t_3 (+ t_2 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -7e+167)
     t_3
     (if (<= Vef -9.6e-102)
       t_1
       (if (<= Vef -2.1e-199)
         (+ t_2 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
         (if (<= Vef 9.5e-209)
           t_1
           (if (<= Vef 2.1e+109)
             (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
             (if (<= Vef 4e+112)
               (+
                (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ (- Vef Ec) mu)) KbT))))
                (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
               t_3))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_2 = NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)));
	double t_3 = t_2 + (NaChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -7e+167) {
		tmp = t_3;
	} else if (Vef <= -9.6e-102) {
		tmp = t_1;
	} else if (Vef <= -2.1e-199) {
		tmp = t_2 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Vef <= 9.5e-209) {
		tmp = t_1;
	} else if (Vef <= 2.1e+109) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= 4e+112) {
		tmp = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_2 = ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))
    t_3 = t_2 + (nachar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-7d+167)) then
        tmp = t_3
    else if (vef <= (-9.6d-102)) then
        tmp = t_1
    else if (vef <= (-2.1d-199)) then
        tmp = t_2 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (vef <= 9.5d-209) then
        tmp = t_1
    else if (vef <= 2.1d+109) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= 4d+112) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + ((vef - ec) + mu)) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_2 = NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)));
	double t_3 = t_2 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -7e+167) {
		tmp = t_3;
	} else if (Vef <= -9.6e-102) {
		tmp = t_1;
	} else if (Vef <= -2.1e-199) {
		tmp = t_2 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Vef <= 9.5e-209) {
		tmp = t_1;
	} else if (Vef <= 2.1e+109) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= 4e+112) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_2 = NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))
	t_3 = t_2 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -7e+167:
		tmp = t_3
	elif Vef <= -9.6e-102:
		tmp = t_1
	elif Vef <= -2.1e-199:
		tmp = t_2 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Vef <= 9.5e-209:
		tmp = t_1
	elif Vef <= 2.1e+109:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= 4e+112:
		tmp = (NdChar / (1.0 + math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT))))
	t_3 = Float64(t_2 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -7e+167)
		tmp = t_3;
	elseif (Vef <= -9.6e-102)
		tmp = t_1;
	elseif (Vef <= -2.1e-199)
		tmp = Float64(t_2 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Vef <= 9.5e-209)
		tmp = t_1;
	elseif (Vef <= 2.1e+109)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= 4e+112)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(Float64(Vef - Ec) + mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_2 = NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)));
	t_3 = t_2 + (NaChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -7e+167)
		tmp = t_3;
	elseif (Vef <= -9.6e-102)
		tmp = t_1;
	elseif (Vef <= -2.1e-199)
		tmp = t_2 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Vef <= 9.5e-209)
		tmp = t_1;
	elseif (Vef <= 2.1e+109)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= 4e+112)
		tmp = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -7e+167], t$95$3, If[LessEqual[Vef, -9.6e-102], t$95$1, If[LessEqual[Vef, -2.1e-199], N[(t$95$2 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 9.5e-209], t$95$1, If[LessEqual[Vef, 2.1e+109], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 4e+112], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(N[(Vef - Ec), $MachinePrecision] + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if Vef < -6.99999999999999975e167 or 3.9999999999999997e112 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 97.0%

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

   5. Taylor expanded in EDonor around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. +-commutative 97.0%

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

   7. Simplified 97.0%

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

   if -6.99999999999999975e167 < Vef < -9.6e-102 or -2.10000000000000002e-199 < Vef < 9.50000000000000028e-209

   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. Taylor expanded in EDonor around inf 82.5%

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

   if -9.6e-102 < Vef < -2.10000000000000002e-199

   1. Initial program 100.0%

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

   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. Step-by-step derivation

      1. *-un-lft-identity 100.0%

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

      2. exp-prod 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in Ev around inf 81.1%

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

   7. Taylor expanded in EDonor around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. +-commutative 76.8%

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

   9. Simplified 76.8%

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

   if 9.50000000000000028e-209 < Vef < 2.1000000000000001e109

   1. Initial program 100.0%

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

   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. Taylor expanded in mu around inf 81.4%

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

   if 2.1000000000000001e109 < Vef < 3.9999999999999997e112

   1. Initial program 100.0%

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

   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. Taylor expanded in EAccept around inf 100.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -7 \cdot 10^{+167}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -9.6 \cdot 10^{-102}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq -2.1 \cdot 10^{-199}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 9.5 \cdot 10^{-209}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.1 \cdot 10^{+109}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4 \cdot 10^{+112}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 5: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -3.4 \cdot 10^{+173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -1.95 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -6 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 2.05 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 1.25 \cdot 10^{+100}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.6 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ (- Vef Ec) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))))
        (t_3
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT))))
          (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -3.4e+173)
     t_3
     (if (<= Vef -1.95e+20)
       t_1
       (if (<= Vef -6e-257)
         t_2
         (if (<= Vef 2.05e-204)
           t_1
           (if (<= Vef 1.25e+100)
             (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
             (if (<= Vef 1.6e+113) t_2 t_3))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_2 = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	double t_3 = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -3.4e+173) {
		tmp = t_3;
	} else if (Vef <= -1.95e+20) {
		tmp = t_1;
	} else if (Vef <= -6e-257) {
		tmp = t_2;
	} else if (Vef <= 2.05e-204) {
		tmp = t_1;
	} else if (Vef <= 1.25e+100) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= 1.6e+113) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_2 = (ndchar / (1.0d0 + exp(((edonor + ((vef - ec) + mu)) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    t_3 = (ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))) + (nachar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-3.4d+173)) then
        tmp = t_3
    else if (vef <= (-1.95d+20)) then
        tmp = t_1
    else if (vef <= (-6d-257)) then
        tmp = t_2
    else if (vef <= 2.05d-204) then
        tmp = t_1
    else if (vef <= 1.25d+100) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= 1.6d+113) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_2 = (NdChar / (1.0 + Math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double t_3 = (NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -3.4e+173) {
		tmp = t_3;
	} else if (Vef <= -1.95e+20) {
		tmp = t_1;
	} else if (Vef <= -6e-257) {
		tmp = t_2;
	} else if (Vef <= 2.05e-204) {
		tmp = t_1;
	} else if (Vef <= 1.25e+100) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= 1.6e+113) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_2 = (NdChar / (1.0 + math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	t_3 = (NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -3.4e+173:
		tmp = t_3
	elif Vef <= -1.95e+20:
		tmp = t_1
	elif Vef <= -6e-257:
		tmp = t_2
	elif Vef <= 2.05e-204:
		tmp = t_1
	elif Vef <= 1.25e+100:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= 1.6e+113:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(Float64(Vef - Ec) + mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	t_3 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -3.4e+173)
		tmp = t_3;
	elseif (Vef <= -1.95e+20)
		tmp = t_1;
	elseif (Vef <= -6e-257)
		tmp = t_2;
	elseif (Vef <= 2.05e-204)
		tmp = t_1;
	elseif (Vef <= 1.25e+100)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= 1.6e+113)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_2 = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	t_3 = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -3.4e+173)
		tmp = t_3;
	elseif (Vef <= -1.95e+20)
		tmp = t_1;
	elseif (Vef <= -6e-257)
		tmp = t_2;
	elseif (Vef <= 2.05e-204)
		tmp = t_1;
	elseif (Vef <= 1.25e+100)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= 1.6e+113)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(N[(Vef - Ec), $MachinePrecision] + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -3.4e+173], t$95$3, If[LessEqual[Vef, -1.95e+20], t$95$1, If[LessEqual[Vef, -6e-257], t$95$2, If[LessEqual[Vef, 2.05e-204], t$95$1, If[LessEqual[Vef, 1.25e+100], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.6e+113], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -3.40000000000000021e173 or 1.5999999999999999e113 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 97.0%

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

   5. Taylor expanded in EDonor around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. +-commutative 97.0%

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

   7. Simplified 97.0%

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

   if -3.40000000000000021e173 < Vef < -1.95e20 or -5.9999999999999999e-257 < Vef < 2.05e-204

   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. Taylor expanded in EDonor around inf 83.0%

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

   if -1.95e20 < Vef < -5.9999999999999999e-257 or 1.25e100 < Vef < 1.5999999999999999e113

   1. Initial program 100.0%

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

   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. Taylor expanded in Ev around inf 74.8%

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

   if 2.05e-204 < Vef < 1.25e100

   1. Initial program 100.0%

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

   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. Taylor expanded in mu around inf 80.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.4 \cdot 10^{+173}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.95 \cdot 10^{+20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq -6 \cdot 10^{-257}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.05 \cdot 10^{-204}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.25 \cdot 10^{+100}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 6: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -4.5 \cdot 10^{+170}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + t_3\\ \mathbf{elif}\;Vef \leq -8 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -5.5 \cdot 10^{-257}:\\ \;\;\;\;t_2 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.75 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ (- Vef Ec) mu)) KbT)))))
        (t_3 (/ NaChar (+ 1.0 (exp (/ Vef KbT))))))
   (if (<= Vef -4.5e+170)
     (+ (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT)))) t_3)
     (if (<= Vef -8e+19)
       t_1
       (if (<= Vef -5.5e-257)
         (+ t_2 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
         (if (<= Vef 2.75e-204)
           t_1
           (if (<= Vef 2.6e+106)
             (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
             (+ t_2 t_3))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_2 = NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)));
	double t_3 = NaChar / (1.0 + exp((Vef / KbT)));
	double tmp;
	if (Vef <= -4.5e+170) {
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + t_3;
	} else if (Vef <= -8e+19) {
		tmp = t_1;
	} else if (Vef <= -5.5e-257) {
		tmp = t_2 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Vef <= 2.75e-204) {
		tmp = t_1;
	} else if (Vef <= 2.6e+106) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_2 = ndchar / (1.0d0 + exp(((edonor + ((vef - ec) + mu)) / kbt)))
    t_3 = nachar / (1.0d0 + exp((vef / kbt)))
    if (vef <= (-4.5d+170)) then
        tmp = (ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))) + t_3
    else if (vef <= (-8d+19)) then
        tmp = t_1
    else if (vef <= (-5.5d-257)) then
        tmp = t_2 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (vef <= 2.75d-204) then
        tmp = t_1
    else if (vef <= 2.6d+106) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else
        tmp = t_2 + t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_2 = NdChar / (1.0 + Math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)));
	double t_3 = NaChar / (1.0 + Math.exp((Vef / KbT)));
	double tmp;
	if (Vef <= -4.5e+170) {
		tmp = (NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)))) + t_3;
	} else if (Vef <= -8e+19) {
		tmp = t_1;
	} else if (Vef <= -5.5e-257) {
		tmp = t_2 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Vef <= 2.75e-204) {
		tmp = t_1;
	} else if (Vef <= 2.6e+106) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_2 = NdChar / (1.0 + math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))
	t_3 = NaChar / (1.0 + math.exp((Vef / KbT)))
	tmp = 0
	if Vef <= -4.5e+170:
		tmp = (NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))) + t_3
	elif Vef <= -8e+19:
		tmp = t_1
	elif Vef <= -5.5e-257:
		tmp = t_2 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Vef <= 2.75e-204:
		tmp = t_1
	elif Vef <= 2.6e+106:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = t_2 + t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(Float64(Vef - Ec) + mu)) / KbT))))
	t_3 = Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	tmp = 0.0
	if (Vef <= -4.5e+170)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)))) + t_3);
	elseif (Vef <= -8e+19)
		tmp = t_1;
	elseif (Vef <= -5.5e-257)
		tmp = Float64(t_2 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Vef <= 2.75e-204)
		tmp = t_1;
	elseif (Vef <= 2.6e+106)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	else
		tmp = Float64(t_2 + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_2 = NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)));
	t_3 = NaChar / (1.0 + exp((Vef / KbT)));
	tmp = 0.0;
	if (Vef <= -4.5e+170)
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + t_3;
	elseif (Vef <= -8e+19)
		tmp = t_1;
	elseif (Vef <= -5.5e-257)
		tmp = t_2 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Vef <= 2.75e-204)
		tmp = t_1;
	elseif (Vef <= 2.6e+106)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	else
		tmp = t_2 + t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(N[(Vef - Ec), $MachinePrecision] + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -4.5e+170], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[Vef, -8e+19], t$95$1, If[LessEqual[Vef, -5.5e-257], N[(t$95$2 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 2.75e-204], t$95$1, If[LessEqual[Vef, 2.6e+106], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$3), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if Vef < -4.50000000000000022e170

   1. Initial program 100.0%

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

   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. Taylor expanded in Vef around inf 95.9%

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

   5. Taylor expanded in EDonor around 0 95.9%

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

      1. +-commutative 95.9%

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

      2. +-commutative 95.9%

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

   7. Simplified 95.9%

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

   if -4.50000000000000022e170 < Vef < -8e19 or -5.50000000000000025e-257 < Vef < 2.75e-204

   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. Taylor expanded in EDonor around inf 83.0%

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

   if -8e19 < Vef < -5.50000000000000025e-257

   1. Initial program 100.0%

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

   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. Taylor expanded in Ev around inf 74.3%

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

   if 2.75e-204 < Vef < 2.6000000000000002e106

   1. Initial program 100.0%

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

   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. Taylor expanded in mu around inf 81.4%

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

   if 2.6000000000000002e106 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 95.6%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4.5 \cdot 10^{+170}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -8 \cdot 10^{+19}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq -5.5 \cdot 10^{-257}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.75 \cdot 10^{-204}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 7: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_2 := t_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_3 := \frac{NaChar}{t_0}\\ t_4 := t_3 + NdChar \cdot \frac{1}{t_0}\\ \mathbf{if}\;Vef \leq -3.3 \cdot 10^{+166}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -4.8 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -3.1 \cdot 10^{+78}:\\ \;\;\;\;t_3 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.08 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 4 \cdot 10^{+21}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
        (t_2 (+ t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT))))))
        (t_3 (/ NaChar t_0))
        (t_4 (+ t_3 (* NdChar (/ 1.0 t_0)))))
   (if (<= Vef -3.3e+166)
     t_4
     (if (<= Vef -4.8e+98)
       t_2
       (if (<= Vef -3.1e+78)
         (+ t_3 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         (if (<= Vef -3.2e+20)
           (+ t_1 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
           (if (<= Vef -1.08e-260)
             t_2
             (if (<= Vef 4e+21)
               (+ t_1 (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
               t_4))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + exp((Vef / KbT));
	double t_1 = NdChar / (1.0 + exp((EDonor / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	double t_3 = NaChar / t_0;
	double t_4 = t_3 + (NdChar * (1.0 / t_0));
	double tmp;
	if (Vef <= -3.3e+166) {
		tmp = t_4;
	} else if (Vef <= -4.8e+98) {
		tmp = t_2;
	} else if (Vef <= -3.1e+78) {
		tmp = t_3 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= -3.2e+20) {
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (Vef <= -1.08e-260) {
		tmp = t_2;
	} else if (Vef <= 4e+21) {
		tmp = t_1 + (NaChar / (1.0 + exp((-mu / KbT))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = ndchar / (1.0d0 + exp((edonor / kbt)))
    t_2 = t_1 + (nachar / (1.0d0 + exp((ev / kbt))))
    t_3 = nachar / t_0
    t_4 = t_3 + (ndchar * (1.0d0 / t_0))
    if (vef <= (-3.3d+166)) then
        tmp = t_4
    else if (vef <= (-4.8d+98)) then
        tmp = t_2
    else if (vef <= (-3.1d+78)) then
        tmp = t_3 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= (-3.2d+20)) then
        tmp = t_1 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (vef <= (-1.08d-260)) then
        tmp = t_2
    else if (vef <= 4d+21) then
        tmp = t_1 + (nachar / (1.0d0 + exp((-mu / kbt))))
    else
        tmp = t_4
    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 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double t_3 = NaChar / t_0;
	double t_4 = t_3 + (NdChar * (1.0 / t_0));
	double tmp;
	if (Vef <= -3.3e+166) {
		tmp = t_4;
	} else if (Vef <= -4.8e+98) {
		tmp = t_2;
	} else if (Vef <= -3.1e+78) {
		tmp = t_3 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= -3.2e+20) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (Vef <= -1.08e-260) {
		tmp = t_2;
	} else if (Vef <= 4e+21) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = NdChar / (1.0 + math.exp((EDonor / KbT)))
	t_2 = t_1 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	t_3 = NaChar / t_0
	t_4 = t_3 + (NdChar * (1.0 / t_0))
	tmp = 0
	if Vef <= -3.3e+166:
		tmp = t_4
	elif Vef <= -4.8e+98:
		tmp = t_2
	elif Vef <= -3.1e+78:
		tmp = t_3 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= -3.2e+20:
		tmp = t_1 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif Vef <= -1.08e-260:
		tmp = t_2
	elif Vef <= 4e+21:
		tmp = t_1 + (NaChar / (1.0 + math.exp((-mu / KbT))))
	else:
		tmp = t_4
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	t_3 = Float64(NaChar / t_0)
	t_4 = Float64(t_3 + Float64(NdChar * Float64(1.0 / t_0)))
	tmp = 0.0
	if (Vef <= -3.3e+166)
		tmp = t_4;
	elseif (Vef <= -4.8e+98)
		tmp = t_2;
	elseif (Vef <= -3.1e+78)
		tmp = Float64(t_3 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= -3.2e+20)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (Vef <= -1.08e-260)
		tmp = t_2;
	elseif (Vef <= 4e+21)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = NdChar / (1.0 + exp((EDonor / KbT)));
	t_2 = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	t_3 = NaChar / t_0;
	t_4 = t_3 + (NdChar * (1.0 / t_0));
	tmp = 0.0;
	if (Vef <= -3.3e+166)
		tmp = t_4;
	elseif (Vef <= -4.8e+98)
		tmp = t_2;
	elseif (Vef <= -3.1e+78)
		tmp = t_3 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= -3.2e+20)
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (Vef <= -1.08e-260)
		tmp = t_2;
	elseif (Vef <= 4e+21)
		tmp = t_1 + (NaChar / (1.0 + exp((-mu / KbT))));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NaChar / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(NdChar * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -3.3e+166], t$95$4, If[LessEqual[Vef, -4.8e+98], t$95$2, If[LessEqual[Vef, -3.1e+78], N[(t$95$3 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -3.2e+20], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -1.08e-260], t$95$2, If[LessEqual[Vef, 4e+21], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if Vef < -3.3000000000000002e166 or 4e21 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 93.7%

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

      1. div-inv 93.7%

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

      2. associate-+r+ 93.7%

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

      3. +-commutative 93.7%

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

      4. +-commutative 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in Vef around inf 85.6%

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

   if -3.3000000000000002e166 < Vef < -4.7999999999999997e98 or -3.2e20 < Vef < -1.08e-260

   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. Taylor expanded in EDonor around inf 77.3%

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

   5. Taylor expanded in Ev around inf 59.1%

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

   if -4.7999999999999997e98 < Vef < -3.1e78

   1. Initial program 100.0%

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

   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. Taylor expanded in Vef around inf 70.6%

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

   5. Taylor expanded in mu around inf 70.6%

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

   if -3.1e78 < Vef < -3.2e20

   1. Initial program 100.0%

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

   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. Taylor expanded in EDonor around inf 85.1%

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

   5. Taylor expanded in EAccept around inf 62.0%

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

   if -1.08e-260 < Vef < 4e21

   1. Initial program 100.0%

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

   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. Taylor expanded in EDonor around inf 76.4%

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

   5. Taylor expanded in mu around inf 61.5%

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

      1. associate-*r/ 43.3%

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

      2. mul-1-neg 43.3%

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

   7. Simplified 61.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{-mu}{KbT}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.3 \cdot 10^{+166}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + NdChar \cdot \frac{1}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -4.8 \cdot 10^{+98}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.1 \cdot 10^{+78}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.08 \cdot 10^{-260}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + NdChar \cdot \frac{1}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 8: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\ t_2 := t_1 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.3 \cdot 10^{+168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -9 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -3.4 \cdot 10^{-207}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 7.4 \cdot 10^{+112}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT)))))
        (t_2 (+ t_1 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -1.3e+168)
     t_2
     (if (<= Vef -9e-102)
       t_0
       (if (<= Vef -3.4e-207)
         (+ t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
         (if (<= Vef 7.4e+112) t_0 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_1 = NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -1.3e+168) {
		tmp = t_2;
	} else if (Vef <= -9e-102) {
		tmp = t_0;
	} else if (Vef <= -3.4e-207) {
		tmp = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Vef <= 7.4e+112) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_1 = ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))
    t_2 = t_1 + (nachar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-1.3d+168)) then
        tmp = t_2
    else if (vef <= (-9d-102)) then
        tmp = t_0
    else if (vef <= (-3.4d-207)) then
        tmp = t_1 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (vef <= 7.4d+112) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_1 = NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -1.3e+168) {
		tmp = t_2;
	} else if (Vef <= -9e-102) {
		tmp = t_0;
	} else if (Vef <= -3.4e-207) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Vef <= 7.4e+112) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_1 = NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))
	t_2 = t_1 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -1.3e+168:
		tmp = t_2
	elif Vef <= -9e-102:
		tmp = t_0
	elif Vef <= -3.4e-207:
		tmp = t_1 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Vef <= 7.4e+112:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT))))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -1.3e+168)
		tmp = t_2;
	elseif (Vef <= -9e-102)
		tmp = t_0;
	elseif (Vef <= -3.4e-207)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Vef <= 7.4e+112)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_1 = NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)));
	t_2 = t_1 + (NaChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -1.3e+168)
		tmp = t_2;
	elseif (Vef <= -9e-102)
		tmp = t_0;
	elseif (Vef <= -3.4e-207)
		tmp = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Vef <= 7.4e+112)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -1.3e+168], t$95$2, If[LessEqual[Vef, -9e-102], t$95$0, If[LessEqual[Vef, -3.4e-207], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 7.4e+112], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -1.3e168 or 7.40000000000000008e112 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 97.0%

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

   5. Taylor expanded in EDonor around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. +-commutative 97.0%

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

   7. Simplified 97.0%

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

   if -1.3e168 < Vef < -8.99999999999999999e-102 or -3.39999999999999999e-207 < Vef < 7.40000000000000008e112

   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. Taylor expanded in EDonor around inf 78.8%

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

   if -8.99999999999999999e-102 < Vef < -3.39999999999999999e-207

   1. Initial program 100.0%

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

   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. Step-by-step derivation

      1. *-un-lft-identity 100.0%

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

      2. exp-prod 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in Ev around inf 81.1%

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

   7. Taylor expanded in EDonor around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. +-commutative 76.8%

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

   9. Simplified 76.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1.3 \cdot 10^{+168}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -9 \cdot 10^{-102}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.4 \cdot 10^{-207}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 7.4 \cdot 10^{+112}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 9: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := \frac{NaChar}{t_0} + NdChar \cdot \frac{1}{t_0}\\ \mathbf{if}\;Vef \leq -7.2 \cdot 10^{+230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 7.5 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 1.05 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.5 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT))))
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))))
        (t_2 (+ (/ NaChar t_0) (* NdChar (/ 1.0 t_0)))))
   (if (<= Vef -7.2e+230)
     t_2
     (if (<= Vef 7.5e-297)
       t_1
       (if (<= Vef 1.05e-193)
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
         (if (<= Vef 4.5e+111) 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 = 1.0 + exp((Vef / KbT));
	double t_1 = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	double t_2 = (NaChar / t_0) + (NdChar * (1.0 / t_0));
	double tmp;
	if (Vef <= -7.2e+230) {
		tmp = t_2;
	} else if (Vef <= 7.5e-297) {
		tmp = t_1;
	} else if (Vef <= 1.05e-193) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (Vef <= 4.5e+111) {
		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 = 1.0d0 + exp((vef / kbt))
    t_1 = (ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    t_2 = (nachar / t_0) + (ndchar * (1.0d0 / t_0))
    if (vef <= (-7.2d+230)) then
        tmp = t_2
    else if (vef <= 7.5d-297) then
        tmp = t_1
    else if (vef <= 1.05d-193) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (vef <= 4.5d+111) 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 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = (NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double t_2 = (NaChar / t_0) + (NdChar * (1.0 / t_0));
	double tmp;
	if (Vef <= -7.2e+230) {
		tmp = t_2;
	} else if (Vef <= 7.5e-297) {
		tmp = t_1;
	} else if (Vef <= 1.05e-193) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (Vef <= 4.5e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = (NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	t_2 = (NaChar / t_0) + (NdChar * (1.0 / t_0))
	tmp = 0
	if Vef <= -7.2e+230:
		tmp = t_2
	elif Vef <= 7.5e-297:
		tmp = t_1
	elif Vef <= 1.05e-193:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif Vef <= 4.5e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	t_2 = Float64(Float64(NaChar / t_0) + Float64(NdChar * Float64(1.0 / t_0)))
	tmp = 0.0
	if (Vef <= -7.2e+230)
		tmp = t_2;
	elseif (Vef <= 7.5e-297)
		tmp = t_1;
	elseif (Vef <= 1.05e-193)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (Vef <= 4.5e+111)
		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 = 1.0 + exp((Vef / KbT));
	t_1 = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	t_2 = (NaChar / t_0) + (NdChar * (1.0 / t_0));
	tmp = 0.0;
	if (Vef <= -7.2e+230)
		tmp = t_2;
	elseif (Vef <= 7.5e-297)
		tmp = t_1;
	elseif (Vef <= 1.05e-193)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (Vef <= 4.5e+111)
		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[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / t$95$0), $MachinePrecision] + N[(NdChar * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -7.2e+230], t$95$2, If[LessEqual[Vef, 7.5e-297], t$95$1, If[LessEqual[Vef, 1.05e-193], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 4.5e+111], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -7.20000000000000037e230 or 4.50000000000000001e111 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 98.3%

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

      1. div-inv 98.3%

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

      2. associate-+r+ 98.3%

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

      3. +-commutative 98.3%

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

      4. +-commutative 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in Vef around inf 91.8%

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

   if -7.20000000000000037e230 < Vef < 7.4999999999999994e-297 or 1.05e-193 < Vef < 4.50000000000000001e111

   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. Step-by-step derivation

      1. *-un-lft-identity 99.9%

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

      2. exp-prod 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in Ev around inf 70.5%

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

   7. Taylor expanded in EDonor around 0 63.0%

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

      1. +-commutative 63.0%

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

      2. +-commutative 63.0%

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

   9. Simplified 63.0%

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

   if 7.4999999999999994e-297 < Vef < 1.05e-193

   1. Initial program 100.0%

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

   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. Taylor expanded in EDonor around inf 86.2%

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

   5. Taylor expanded in mu around inf 72.5%

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

      1. associate-*r/ 44.0%

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

      2. mul-1-neg 44.0%

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

   7. Simplified 72.5%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -7.2 \cdot 10^{+230}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + NdChar \cdot \frac{1}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 7.5 \cdot 10^{-297}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.05 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + NdChar \cdot \frac{1}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + 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 = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar / (1.0d0 + exp(((edonor + ((vef - ec) + 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 (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 11: 59.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -5.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -2.1 \cdot 10^{-21}:\\ \;\;\;\;t_0 + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -3.5 \cdot 10^{-113} \lor \neg \left(NdChar \leq 4.8 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
   (if (<= NdChar -5.8e+54)
     (+
      (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
      (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
     (if (<= NdChar -2.1e-21)
       (+ t_0 (/ NdChar (+ (/ EDonor KbT) 2.0)))
       (if (or (<= NdChar -3.5e-113) (not (<= NdChar 4.8e-17)))
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ (- Vef Ec) mu)) KbT))))
          (/ NaChar (+ 1.0 (+ 1.0 (/ EAccept KbT)))))
         (+
          t_0
          (/
           NdChar
           (-
            (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
            (/ Ec KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double tmp;
	if (NdChar <= -5.8e+54) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (NdChar <= -2.1e-21) {
		tmp = t_0 + (NdChar / ((EDonor / KbT) + 2.0));
	} else if ((NdChar <= -3.5e-113) || !(NdChar <= 4.8e-17)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    if (ndchar <= (-5.8d+54)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (ndchar <= (-2.1d-21)) then
        tmp = t_0 + (ndchar / ((edonor / kbt) + 2.0d0))
    else if ((ndchar <= (-3.5d-113)) .or. (.not. (ndchar <= 4.8d-17))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + ((vef - ec) + mu)) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (eaccept / kbt))))
    else
        tmp = t_0 + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double tmp;
	if (NdChar <= -5.8e+54) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (NdChar <= -2.1e-21) {
		tmp = t_0 + (NdChar / ((EDonor / KbT) + 2.0));
	} else if ((NdChar <= -3.5e-113) || !(NdChar <= 4.8e-17)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	tmp = 0
	if NdChar <= -5.8e+54:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif NdChar <= -2.1e-21:
		tmp = t_0 + (NdChar / ((EDonor / KbT) + 2.0))
	elif (NdChar <= -3.5e-113) or not (NdChar <= 4.8e-17):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))))
	else:
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	tmp = 0.0
	if (NdChar <= -5.8e+54)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (NdChar <= -2.1e-21)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(EDonor / KbT) + 2.0)));
	elseif ((NdChar <= -3.5e-113) || !(NdChar <= 4.8e-17))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(Float64(Vef - Ec) + mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(EAccept / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -5.8e+54)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (NdChar <= -2.1e-21)
		tmp = t_0 + (NdChar / ((EDonor / KbT) + 2.0));
	elseif ((NdChar <= -3.5e-113) || ~((NdChar <= 4.8e-17)))
		tmp = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	else
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -5.8e+54], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -2.1e-21], N[(t$95$0 + N[(NdChar / N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NdChar, -3.5e-113], N[Not[LessEqual[NdChar, 4.8e-17]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(N[(Vef - Ec), $MachinePrecision] + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -5.7999999999999997e54

   1. Initial program 100.0%

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

   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. Taylor expanded in EDonor around inf 71.2%

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

   5. Taylor expanded in mu around inf 61.8%

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

      1. associate-*r/ 38.5%

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

      2. mul-1-neg 38.5%

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

   7. Simplified 61.8%

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

   if -5.7999999999999997e54 < NdChar < -2.10000000000000013e-21

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EDonor around inf 69.9%

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

   5. Taylor expanded in EDonor around 0 65.5%

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

   if -2.10000000000000013e-21 < NdChar < -3.50000000000000029e-113 or 4.79999999999999973e-17 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 76.8%

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

   5. Taylor expanded in EAccept around 0 62.0%

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

   if -3.50000000000000029e-113 < NdChar < 4.79999999999999973e-17

   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. Taylor expanded in KbT around inf 73.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -5.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -2.1 \cdot 10^{-21}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -3.5 \cdot 10^{-113} \lor \neg \left(NdChar \leq 4.8 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]

Alternative 12: 59.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -4 \cdot 10^{+27}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -1.32 \cdot 10^{-21}:\\ \;\;\;\;t_0 + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq -2.9 \cdot 10^{-114} \lor \neg \left(NdChar \leq 9.5 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
   (if (<= NdChar -4e+27)
     (+
      (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
      (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= NdChar -1.32e-21)
       (+ t_0 (/ NdChar 2.0))
       (if (or (<= NdChar -2.9e-114) (not (<= NdChar 9.5e-16)))
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ (- Vef Ec) mu)) KbT))))
          (/ NaChar (+ 1.0 (+ 1.0 (/ EAccept KbT)))))
         (+
          t_0
          (/
           NdChar
           (-
            (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
            (/ Ec KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double tmp;
	if (NdChar <= -4e+27) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (NdChar <= -1.32e-21) {
		tmp = t_0 + (NdChar / 2.0);
	} else if ((NdChar <= -2.9e-114) || !(NdChar <= 9.5e-16)) {
		tmp = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    if (ndchar <= (-4d+27)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (ndchar <= (-1.32d-21)) then
        tmp = t_0 + (ndchar / 2.0d0)
    else if ((ndchar <= (-2.9d-114)) .or. (.not. (ndchar <= 9.5d-16))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + ((vef - ec) + mu)) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (eaccept / kbt))))
    else
        tmp = t_0 + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double tmp;
	if (NdChar <= -4e+27) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (NdChar <= -1.32e-21) {
		tmp = t_0 + (NdChar / 2.0);
	} else if ((NdChar <= -2.9e-114) || !(NdChar <= 9.5e-16)) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	tmp = 0
	if NdChar <= -4e+27:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif NdChar <= -1.32e-21:
		tmp = t_0 + (NdChar / 2.0)
	elif (NdChar <= -2.9e-114) or not (NdChar <= 9.5e-16):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))))
	else:
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	tmp = 0.0
	if (NdChar <= -4e+27)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (NdChar <= -1.32e-21)
		tmp = Float64(t_0 + Float64(NdChar / 2.0));
	elseif ((NdChar <= -2.9e-114) || !(NdChar <= 9.5e-16))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(Float64(Vef - Ec) + mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(EAccept / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -4e+27)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (NdChar <= -1.32e-21)
		tmp = t_0 + (NdChar / 2.0);
	elseif ((NdChar <= -2.9e-114) || ~((NdChar <= 9.5e-16)))
		tmp = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	else
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -4e+27], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -1.32e-21], N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NdChar, -2.9e-114], N[Not[LessEqual[NdChar, 9.5e-16]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(N[(Vef - Ec), $MachinePrecision] + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -4.0000000000000001e27

   1. Initial program 100.0%

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

   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. Taylor expanded in EDonor around inf 70.8%

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

   5. Taylor expanded in Ev around inf 50.5%

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

   if -4.0000000000000001e27 < NdChar < -1.32e-21

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 73.8%

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

   if -1.32e-21 < NdChar < -2.89999999999999997e-114 or 9.5000000000000005e-16 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 76.8%

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

   5. Taylor expanded in EAccept around 0 62.0%

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

   if -2.89999999999999997e-114 < NdChar < 9.5000000000000005e-16

   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. Taylor expanded in KbT around inf 73.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4 \cdot 10^{+27}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -1.32 \cdot 10^{-21}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq -2.9 \cdot 10^{-114} \lor \neg \left(NdChar \leq 9.5 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]

Alternative 13: 62.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{if}\;NdChar \leq -8.2 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -1.3 \cdot 10^{-21}:\\ \;\;\;\;t_0 + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -3.5 \cdot 10^{-113} \lor \neg \left(NdChar \leq 9.2 \cdot 10^{-15}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ (- Vef Ec) mu)) KbT))))
          (/ NaChar (+ 1.0 (+ 1.0 (/ EAccept KbT)))))))
   (if (<= NdChar -8.2e+52)
     t_1
     (if (<= NdChar -1.3e-21)
       (+ t_0 (/ NdChar (+ (/ EDonor KbT) 2.0)))
       (if (or (<= NdChar -3.5e-113) (not (<= NdChar 9.2e-15)))
         t_1
         (+
          t_0
          (/
           NdChar
           (-
            (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
            (/ Ec KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	double tmp;
	if (NdChar <= -8.2e+52) {
		tmp = t_1;
	} else if (NdChar <= -1.3e-21) {
		tmp = t_0 + (NdChar / ((EDonor / KbT) + 2.0));
	} else if ((NdChar <= -3.5e-113) || !(NdChar <= 9.2e-15)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp(((edonor + ((vef - ec) + mu)) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (eaccept / kbt))))
    if (ndchar <= (-8.2d+52)) then
        tmp = t_1
    else if (ndchar <= (-1.3d-21)) then
        tmp = t_0 + (ndchar / ((edonor / kbt) + 2.0d0))
    else if ((ndchar <= (-3.5d-113)) .or. (.not. (ndchar <= 9.2d-15))) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	double tmp;
	if (NdChar <= -8.2e+52) {
		tmp = t_1;
	} else if (NdChar <= -1.3e-21) {
		tmp = t_0 + (NdChar / ((EDonor / KbT) + 2.0));
	} else if ((NdChar <= -3.5e-113) || !(NdChar <= 9.2e-15)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))))
	tmp = 0
	if NdChar <= -8.2e+52:
		tmp = t_1
	elif NdChar <= -1.3e-21:
		tmp = t_0 + (NdChar / ((EDonor / KbT) + 2.0))
	elif (NdChar <= -3.5e-113) or not (NdChar <= 9.2e-15):
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(Float64(Vef - Ec) + mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(EAccept / KbT)))))
	tmp = 0.0
	if (NdChar <= -8.2e+52)
		tmp = t_1;
	elseif (NdChar <= -1.3e-21)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(EDonor / KbT) + 2.0)));
	elseif ((NdChar <= -3.5e-113) || !(NdChar <= 9.2e-15))
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	tmp = 0.0;
	if (NdChar <= -8.2e+52)
		tmp = t_1;
	elseif (NdChar <= -1.3e-21)
		tmp = t_0 + (NdChar / ((EDonor / KbT) + 2.0));
	elseif ((NdChar <= -3.5e-113) || ~((NdChar <= 9.2e-15)))
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(N[(Vef - Ec), $MachinePrecision] + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -8.2e+52], t$95$1, If[LessEqual[NdChar, -1.3e-21], N[(t$95$0 + N[(NdChar / N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NdChar, -3.5e-113], N[Not[LessEqual[NdChar, 9.2e-15]], $MachinePrecision]], t$95$1, N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -8.1999999999999999e52 or -1.30000000000000009e-21 < NdChar < -3.50000000000000029e-113 or 9.19999999999999961e-15 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 73.7%

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

   5. Taylor expanded in EAccept around 0 60.2%

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

   if -8.1999999999999999e52 < NdChar < -1.30000000000000009e-21

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EDonor around inf 69.9%

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

   5. Taylor expanded in EDonor around 0 65.5%

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

   if -3.50000000000000029e-113 < NdChar < 9.19999999999999961e-15

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in KbT around inf 73.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -8.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq -1.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -3.5 \cdot 10^{-113} \lor \neg \left(NdChar \leq 9.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]

Alternative 14: 62.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -1.85 \cdot 10^{+53} \lor \neg \left(NdChar \leq -1.55 \cdot 10^{-21}\right) \land \left(NdChar \leq -2.9 \cdot 10^{-113} \lor \neg \left(NdChar \leq 9.5 \cdot 10^{-16}\right)\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -1.85e+53)
         (and (not (<= NdChar -1.55e-21))
              (or (<= NdChar -2.9e-113) (not (<= NdChar 9.5e-16)))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ (- Vef Ec) mu)) KbT))))
    (/ NaChar (+ 1.0 (+ 1.0 (/ EAccept KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
    (/ NdChar (+ (/ EDonor 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 tmp;
	if ((NdChar <= -1.85e+53) || (!(NdChar <= -1.55e-21) && ((NdChar <= -2.9e-113) || !(NdChar <= 9.5e-16)))) {
		tmp = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / ((EDonor / 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) :: tmp
    if ((ndchar <= (-1.85d+53)) .or. (.not. (ndchar <= (-1.55d-21))) .and. (ndchar <= (-2.9d-113)) .or. (.not. (ndchar <= 9.5d-16))) then
        tmp = (ndchar / (1.0d0 + exp(((edonor + ((vef - ec) + mu)) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (eaccept / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar / ((edonor / 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 tmp;
	if ((NdChar <= -1.85e+53) || (!(NdChar <= -1.55e-21) && ((NdChar <= -2.9e-113) || !(NdChar <= 9.5e-16)))) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -1.85e+53) or (not (NdChar <= -1.55e-21) and ((NdChar <= -2.9e-113) or not (NdChar <= 9.5e-16))):
		tmp = (NdChar / (1.0 + math.exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -1.85e+53) || (!(NdChar <= -1.55e-21) && ((NdChar <= -2.9e-113) || !(NdChar <= 9.5e-16))))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(Float64(Vef - Ec) + mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(EAccept / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(EDonor / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -1.85e+53) || (~((NdChar <= -1.55e-21)) && ((NdChar <= -2.9e-113) || ~((NdChar <= 9.5e-16)))))
		tmp = (NdChar / (1.0 + exp(((EDonor + ((Vef - Ec) + mu)) / KbT)))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -1.85e+53], And[N[Not[LessEqual[NdChar, -1.55e-21]], $MachinePrecision], Or[LessEqual[NdChar, -2.9e-113], N[Not[LessEqual[NdChar, 9.5e-16]], $MachinePrecision]]]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(N[(Vef - Ec), $MachinePrecision] + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -1.85e53 or -1.5499999999999999e-21 < NdChar < -2.90000000000000004e-113 or 9.5000000000000005e-16 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 73.7%

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

   5. Taylor expanded in EAccept around 0 60.2%

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

   if -1.85e53 < NdChar < -1.5499999999999999e-21 or -2.90000000000000004e-113 < NdChar < 9.5000000000000005e-16

   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. Taylor expanded in EDonor around inf 78.3%

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

   5. Taylor expanded in EDonor around 0 70.6%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.85 \cdot 10^{+53} \lor \neg \left(NdChar \leq -1.55 \cdot 10^{-21}\right) \land \left(NdChar \leq -2.9 \cdot 10^{-113} \lor \neg \left(NdChar \leq 9.5 \cdot 10^{-16}\right)\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(\left(Vef - Ec\right) + mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \end{array} \]

Alternative 15: 39.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NdChar \leq -2.65 \cdot 10^{+51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 10^{-164}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
        (t_1 (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))))
   (if (<= NdChar -2.65e+51)
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (* NaChar 0.5))
     (if (<= NdChar 1.05e-278)
       t_1
       (if (<= NdChar 1e-164)
         (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0)))
         (if (<= NdChar 2.2e-12)
           t_1
           (+ t_0 (/ NaChar (+ (/ EAccept 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 = NdChar / (1.0 + exp((mu / KbT)));
	double t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= -2.65e+51) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else if (NdChar <= 1.05e-278) {
		tmp = t_1;
	} else if (NdChar <= 1e-164) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= 2.2e-12) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NaChar / ((EAccept / 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 = ndchar / (1.0d0 + exp((mu / kbt)))
    t_1 = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    if (ndchar <= (-2.65d+51)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar * 0.5d0)
    else if (ndchar <= 1.05d-278) then
        tmp = t_1
    else if (ndchar <= 1d-164) then
        tmp = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    else if (ndchar <= 2.2d-12) then
        tmp = t_1
    else
        tmp = t_0 + (nachar / ((eaccept / 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 = NdChar / (1.0 + Math.exp((mu / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= -2.65e+51) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else if (NdChar <= 1.05e-278) {
		tmp = t_1;
	} else if (NdChar <= 1e-164) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= 2.2e-12) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((mu / KbT)))
	t_1 = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NdChar <= -2.65e+51:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar * 0.5)
	elif NdChar <= 1.05e-278:
		tmp = t_1
	elif NdChar <= 1e-164:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	elif NdChar <= 2.2e-12:
		tmp = t_1
	else:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NdChar <= -2.65e+51)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar * 0.5));
	elseif (NdChar <= 1.05e-278)
		tmp = t_1;
	elseif (NdChar <= 1e-164)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NdChar <= 2.2e-12)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((mu / KbT)));
	t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -2.65e+51)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	elseif (NdChar <= 1.05e-278)
		tmp = t_1;
	elseif (NdChar <= 1e-164)
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	elseif (NdChar <= 2.2e-12)
		tmp = t_1;
	else
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -2.65e+51], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.05e-278], t$95$1, If[LessEqual[NdChar, 1e-164], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.2e-12], t$95$1, N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -2.6499999999999998e51

   1. Initial program 100.0%

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

   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. Taylor expanded in EDonor around inf 71.7%

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

   5. Taylor expanded in KbT around inf 43.0%

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

   if -2.6499999999999998e51 < NdChar < 1.05000000000000007e-278 or 9.99999999999999962e-165 < NdChar < 2.19999999999999992e-12

   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. Taylor expanded in KbT around inf 56.5%

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

   5. Taylor expanded in Vef around inf 43.5%

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

   if 1.05000000000000007e-278 < NdChar < 9.99999999999999962e-165

   1. Initial program 100.0%

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

   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. Taylor expanded in Vef around inf 58.1%

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

   5. Taylor expanded in mu around inf 44.0%

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

   6. Taylor expanded in Vef around 0 53.1%

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

   if 2.19999999999999992e-12 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 75.3%

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

   5. Taylor expanded in mu around inf 52.5%

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

   6. Taylor expanded in EAccept around 0 44.2%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.65 \cdot 10^{+51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 10^{-164}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]

Alternative 16: 40.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{if}\;NdChar \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 1.75 \cdot 10^{-165}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.18 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NdChar (+ (/ mu KbT) 2.0)))))
   (if (<= NdChar -5.1e+51)
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (* NaChar 0.5))
     (if (<= NdChar 1.05e-278)
       t_1
       (if (<= NdChar 1.75e-165)
         (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0)))
         (if (<= NdChar 1.18e+60)
           t_1
           (+ t_0 (/ NaChar (+ (/ EAccept 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 = NdChar / (1.0 + exp((mu / KbT)));
	double t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	double tmp;
	if (NdChar <= -5.1e+51) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else if (NdChar <= 1.05e-278) {
		tmp = t_1;
	} else if (NdChar <= 1.75e-165) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= 1.18e+60) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NaChar / ((EAccept / 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 = ndchar / (1.0d0 + exp((mu / kbt)))
    t_1 = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    if (ndchar <= (-5.1d+51)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar * 0.5d0)
    else if (ndchar <= 1.05d-278) then
        tmp = t_1
    else if (ndchar <= 1.75d-165) then
        tmp = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    else if (ndchar <= 1.18d+60) then
        tmp = t_1
    else
        tmp = t_0 + (nachar / ((eaccept / 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 = NdChar / (1.0 + Math.exp((mu / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	double tmp;
	if (NdChar <= -5.1e+51) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else if (NdChar <= 1.05e-278) {
		tmp = t_1;
	} else if (NdChar <= 1.75e-165) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= 1.18e+60) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((mu / KbT)))
	t_1 = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	tmp = 0
	if NdChar <= -5.1e+51:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar * 0.5)
	elif NdChar <= 1.05e-278:
		tmp = t_1
	elif NdChar <= 1.75e-165:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	elif NdChar <= 1.18e+60:
		tmp = t_1
	else:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)))
	tmp = 0.0
	if (NdChar <= -5.1e+51)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar * 0.5));
	elseif (NdChar <= 1.05e-278)
		tmp = t_1;
	elseif (NdChar <= 1.75e-165)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NdChar <= 1.18e+60)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((mu / KbT)));
	t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	tmp = 0.0;
	if (NdChar <= -5.1e+51)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	elseif (NdChar <= 1.05e-278)
		tmp = t_1;
	elseif (NdChar <= 1.75e-165)
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	elseif (NdChar <= 1.18e+60)
		tmp = t_1;
	else
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -5.1e+51], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.05e-278], t$95$1, If[LessEqual[NdChar, 1.75e-165], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.18e+60], t$95$1, N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -5.1000000000000001e51

   1. Initial program 100.0%

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

   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. Taylor expanded in EDonor around inf 71.7%

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

   5. Taylor expanded in KbT around inf 43.0%

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

   if -5.1000000000000001e51 < NdChar < 1.05000000000000007e-278 or 1.7500000000000001e-165 < NdChar < 1.18000000000000008e60

   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. Taylor expanded in Vef around inf 65.0%

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

   5. Taylor expanded in mu around inf 50.5%

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

   6. Taylor expanded in mu around 0 45.1%

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

   if 1.05000000000000007e-278 < NdChar < 1.7500000000000001e-165

   1. Initial program 100.0%

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

   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. Taylor expanded in Vef around inf 58.1%

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

   5. Taylor expanded in mu around inf 44.0%

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

   6. Taylor expanded in Vef around 0 53.1%

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

   if 1.18000000000000008e60 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 73.5%

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

   5. Taylor expanded in mu around inf 51.1%

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

   6. Taylor expanded in EAccept around 0 46.8%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.75 \cdot 10^{-165}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.18 \cdot 10^{+60}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]

Alternative 17: 47.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NdChar \leq 6.2 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 1.55 \cdot 10^{-165}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.05 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
          (/ NdChar 2.0))))
   (if (<= NdChar 6.2e-233)
     t_1
     (if (<= NdChar 1.55e-165)
       (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0)))
       (if (<= NdChar 1.05e+39)
         t_1
         (+ t_0 (/ NaChar (+ (/ EAccept 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 = NdChar / (1.0 + exp((mu / KbT)));
	double t_1 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= 6.2e-233) {
		tmp = t_1;
	} else if (NdChar <= 1.55e-165) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= 1.05e+39) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NaChar / ((EAccept / 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 = ndchar / (1.0d0 + exp((mu / kbt)))
    t_1 = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar / 2.0d0)
    if (ndchar <= 6.2d-233) then
        tmp = t_1
    else if (ndchar <= 1.55d-165) then
        tmp = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    else if (ndchar <= 1.05d+39) then
        tmp = t_1
    else
        tmp = t_0 + (nachar / ((eaccept / 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 = NdChar / (1.0 + Math.exp((mu / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= 6.2e-233) {
		tmp = t_1;
	} else if (NdChar <= 1.55e-165) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= 1.05e+39) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((mu / KbT)))
	t_1 = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NdChar <= 6.2e-233:
		tmp = t_1
	elif NdChar <= 1.55e-165:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	elif NdChar <= 1.05e+39:
		tmp = t_1
	else:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NdChar <= 6.2e-233)
		tmp = t_1;
	elseif (NdChar <= 1.55e-165)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NdChar <= 1.05e+39)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((mu / KbT)));
	t_1 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NdChar <= 6.2e-233)
		tmp = t_1;
	elseif (NdChar <= 1.55e-165)
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	elseif (NdChar <= 1.05e+39)
		tmp = t_1;
	else
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, 6.2e-233], t$95$1, If[LessEqual[NdChar, 1.55e-165], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.05e+39], t$95$1, N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < 6.2000000000000003e-233 or 1.54999999999999998e-165 < NdChar < 1.0499999999999999e39

   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. Taylor expanded in KbT around inf 51.9%

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

   if 6.2000000000000003e-233 < NdChar < 1.54999999999999998e-165

   1. Initial program 100.0%

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

   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. Taylor expanded in Vef around inf 70.6%

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

   5. Taylor expanded in mu around inf 58.2%

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

   6. Taylor expanded in Vef around 0 70.7%

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

   if 1.0499999999999999e39 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 75.2%

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

   5. Taylor expanded in mu around inf 50.9%

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

   6. Taylor expanded in EAccept around 0 43.7%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq 6.2 \cdot 10^{-233}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 1.55 \cdot 10^{-165}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.05 \cdot 10^{+39}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]

Alternative 18: 53.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq 3.9 \cdot 10^{+119}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar 3.9e+119)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
    (/ NdChar (+ (/ EDonor KbT) 2.0)))
   (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (/ NaChar (+ (/ 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 tmp;
	if (NdChar <= 3.9e+119) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0));
	} else {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((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) :: tmp
    if (ndchar <= 3.9d+119) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar / ((edonor / kbt) + 2.0d0))
    else
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / ((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 tmp;
	if (NdChar <= 3.9e+119) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= 3.9e+119:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0))
	else:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= 3.9e+119)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(EDonor / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= 3.9e+119)
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0));
	else
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, 3.9e+119], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < 3.8999999999999998e119

   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. Taylor expanded in EDonor around inf 73.4%

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

   5. Taylor expanded in EDonor around 0 57.8%

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

   if 3.8999999999999998e119 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in Vef around inf 79.4%

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

   5. Taylor expanded in mu around inf 53.9%

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

   6. Taylor expanded in Vef around 0 48.6%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq 3.9 \cdot 10^{+119}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]

Alternative 19: 40.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 6.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar -2.8e+47)
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (* NaChar 0.5))
   (if (<= NdChar 6.4e-15)
     (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))
     (+
      (/ NdChar (+ 1.0 (exp (/ mu KbT))))
      (/ NaChar (+ (/ EAccept 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 tmp;
	if (NdChar <= -2.8e+47) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else if (NdChar <= 6.4e-15) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((EAccept / 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) :: tmp
    if (ndchar <= (-2.8d+47)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar * 0.5d0)
    else if (ndchar <= 6.4d-15) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / ((eaccept / 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 tmp;
	if (NdChar <= -2.8e+47) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else if (NdChar <= 6.4e-15) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= -2.8e+47:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar * 0.5)
	elif NdChar <= 6.4e-15:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= -2.8e+47)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar * 0.5));
	elseif (NdChar <= 6.4e-15)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= -2.8e+47)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	elseif (NdChar <= 6.4e-15)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, -2.8e+47], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 6.4e-15], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -2.79999999999999988e47

   1. Initial program 100.0%

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

   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. Taylor expanded in EDonor around inf 70.5%

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

   5. Taylor expanded in KbT around inf 42.4%

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

   if -2.79999999999999988e47 < NdChar < 6.3999999999999999e-15

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in KbT around inf 55.4%

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

   5. Taylor expanded in Vef around inf 41.4%

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

   if 6.3999999999999999e-15 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 75.7%

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

   5. Taylor expanded in mu around inf 51.8%

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

   6. Taylor expanded in EAccept around 0 43.6%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 6.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]

Alternative 20: 39.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -3.5 \cdot 10^{+49} \lor \neg \left(NdChar \leq 9.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -3.5e+49) (not (<= NdChar 9.8e-15)))
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (* NaChar 0.5))
   (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -3.5e+49) || !(NdChar <= 9.8e-15)) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-3.5d+49)) .or. (.not. (ndchar <= 9.8d-15))) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar * 0.5d0)
    else
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -3.5e+49) || !(NdChar <= 9.8e-15)) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -3.5e+49) or not (NdChar <= 9.8e-15):
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -3.5e+49) || !(NdChar <= 9.8e-15))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -3.5e+49) || ~((NdChar <= 9.8e-15)))
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	else
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -3.5e+49], N[Not[LessEqual[NdChar, 9.8e-15]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -3.49999999999999975e49 or 9.7999999999999999e-15 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EDonor around inf 70.1%

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

   5. Taylor expanded in KbT around inf 41.3%

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

   if -3.49999999999999975e49 < NdChar < 9.7999999999999999e-15

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in KbT around inf 55.4%

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

   5. Taylor expanded in Vef around inf 41.4%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.5 \cdot 10^{+49} \lor \neg \left(NdChar \leq 9.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 21: 36.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -3.4 \cdot 10^{-224}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -3.4e-224)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -3.4e-224) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-3.4d-224)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -3.4e-224) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -3.4e-224:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -3.4e-224)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -3.4e-224)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -3.4e-224], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -3.39999999999999992e-224

   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. Taylor expanded in KbT around inf 46.0%

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

   5. Taylor expanded in EAccept around inf 34.0%

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

   if -3.39999999999999992e-224 < 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. Taylor expanded in KbT around inf 46.6%

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

   5. Taylor expanded in Ev around inf 31.9%

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

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.4 \cdot 10^{-224}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 22: 36.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -7.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -7.5e+121)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -7.5e+121) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-7.5d+121)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -7.5e+121) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -7.5e+121:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -7.5e+121)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -7.5e+121)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -7.5e+121], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -7.49999999999999965e121

   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. Taylor expanded in KbT around inf 50.2%

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

   5. Taylor expanded in Ev around inf 41.8%

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

   if -7.49999999999999965e121 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 45.7%

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

   5. Taylor expanded in Vef around inf 36.4%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -7.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 23: 36.0% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in KbT around inf 46.4%

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

5. Taylor expanded in EAccept around inf 34.8%

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

6. Final simplification 34.8%

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

Alternative 24: 27.0% accurate, 25.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq 1.06 \cdot 10^{+67}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= mu 1.06e+67) (* 0.5 (+ NdChar NaChar)) (/ NaChar (- 2.0 (/ mu KbT)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (mu <= 1.06e+67) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (2.0 - (mu / KbT));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (mu <= 1.06d+67) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = nachar / (2.0d0 - (mu / kbt))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (mu <= 1.06e+67) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (2.0 - (mu / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if mu <= 1.06e+67:
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NaChar / (2.0 - (mu / KbT))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (mu <= 1.06e+67)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NaChar / Float64(2.0 - Float64(mu / KbT)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (mu <= 1.06e+67)
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NaChar / (2.0 - (mu / KbT));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[mu, 1.06e+67], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(2.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if mu < 1.0599999999999999e67

   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. Taylor expanded in KbT around inf 48.1%

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

   5. Taylor expanded in mu around inf 33.7%

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

      1. associate-*r/ 33.7%

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

      2. mul-1-neg 33.7%

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

   7. Simplified 33.7%

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

   8. Taylor expanded in mu around 0 28.8%

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

      1. mul-1-neg 28.8%

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

      2. unsub-neg 28.8%

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

   10. Simplified 28.8%

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

   11. Taylor expanded in mu around 0 29.7%

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

       1. distribute-lft-out 29.7%

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

   13. Simplified 29.7%

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

   if 1.0599999999999999e67 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 40.0%

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

   5. Taylor expanded in mu around inf 32.9%

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

      1. associate-*r/ 32.9%

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

      2. mul-1-neg 32.9%

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

   7. Simplified 32.9%

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

   8. Taylor expanded in mu around 0 12.8%

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

      1. mul-1-neg 12.8%

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

      2. unsub-neg 12.8%

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

   10. Simplified 12.8%

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

   11. Taylor expanded in NdChar around 0 22.8%

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

4. Final simplification 28.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq 1.06 \cdot 10^{+67}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 - \frac{mu}{KbT}}\\ \end{array} \]

Alternative 25: 28.1% accurate, 45.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in KbT around inf 46.4%

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

5. Taylor expanded in mu around inf 33.5%

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

   1. associate-*r/ 33.5%

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

   2. mul-1-neg 33.5%

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

7. Simplified 33.5%

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

8. Taylor expanded in mu around 0 25.3%

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

   1. mul-1-neg 25.3%

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

   2. unsub-neg 25.3%

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

10. Simplified 25.3%

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

11. Taylor expanded in mu around 0 26.5%

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

    1. distribute-lft-out 26.5%

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

13. Simplified 26.5%

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

14. Final simplification 26.5%

    \[\leadsto 0.5 \cdot \left(NdChar + NaChar\right) \]

Alternative 26: 17.9% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in KbT around inf 46.4%

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

5. Taylor expanded in mu around inf 33.5%

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

   1. associate-*r/ 33.5%

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

   2. mul-1-neg 33.5%

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

7. Simplified 33.5%

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

8. Taylor expanded in mu around 0 25.3%

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

   1. mul-1-neg 25.3%

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

   2. unsub-neg 25.3%

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

10. Simplified 25.3%

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

11. Taylor expanded in NdChar around inf 18.6%

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

12. Final simplification 18.6%

    \[\leadsto NdChar \cdot 0.5 \]

Reproduce

herbie shell --seed 2023318 
(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))))))