Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 33.4s

Alternatives: 41

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -1.2716086709111215e-35
  2. Ec = 6.619398131828537e-261
  3. Vef = -3.01305712658236e+166
  4. EDonor = -2.9366212584914774e+209
  5. mu = 4.1430142648584165e+114
  6. KbT = 3.9710536669587215e+117
  7. NaChar = 3.5837508858222606e-36
  8. Ev = 4.2616058986788554e+40
  9. EAccept = 6.624601979066035e-190

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

   1. div-inv 100.0%

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

   2. +-commutative 100.0%

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

   3. associate-+l- 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 70.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}\\ t_1 := \frac{NdChar}{1 + t\_0}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t\_1\\ t_3 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + t\_1\\ t_4 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.95 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq -1.9 \cdot 10^{+109}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;Vef \leq -36:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq -5.2 \cdot 10^{-279}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;Vef \leq 2.15 \cdot 10^{-190}:\\ \;\;\;\;t\_4 + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;Vef \leq 1.9 \cdot 10^{-99}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;Vef \leq 6 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - t\_0}\\ \mathbf{elif}\;Vef \leq 2 \cdot 10^{+101}:\\ \;\;\;\;t\_4 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- (+ mu Vef) Ec) KbT)))
        (t_1 (/ NdChar (+ 1.0 t_0)))
        (t_2 (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) t_1))
        (t_3 (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) t_1))
        (t_4 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= Vef -1.95e+143)
     t_2
     (if (<= Vef -1.9e+109)
       t_3
       (if (<= Vef -36.0)
         t_2
         (if (<= Vef -5.2e-279)
           t_3
           (if (<= Vef 2.15e-190)
             (+
              t_4
              (/
               NdChar
               (*
                mu
                (+
                 (/ 1.0 KbT)
                 (/
                  (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT))
                  mu)))))
             (if (<= Vef 1.9e-99)
               t_3
               (if (<= Vef 6e+87)
                 (-
                  (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
                  (/ NdChar (- -1.0 t_0)))
                 (if (<= Vef 2e+101)
                   (+
                    t_4
                    (/
                     NdChar
                     (*
                      EDonor
                      (+
                       (/ 1.0 KbT)
                       (/
                        (- (+ 2.0 (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))
                        EDonor)))))
                   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 = exp((((mu + Vef) - Ec) / KbT));
	double t_1 = NdChar / (1.0 + t_0);
	double t_2 = (NaChar / (1.0 + exp((Vef / KbT)))) + t_1;
	double t_3 = (NaChar / (1.0 + exp((EAccept / KbT)))) + t_1;
	double t_4 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (Vef <= -1.95e+143) {
		tmp = t_2;
	} else if (Vef <= -1.9e+109) {
		tmp = t_3;
	} else if (Vef <= -36.0) {
		tmp = t_2;
	} else if (Vef <= -5.2e-279) {
		tmp = t_3;
	} else if (Vef <= 2.15e-190) {
		tmp = t_4 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (Vef <= 1.9e-99) {
		tmp = t_3;
	} else if (Vef <= 6e+87) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - (NdChar / (-1.0 - t_0));
	} else if (Vef <= 2e+101) {
		tmp = t_4 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = exp((((mu + vef) - ec) / kbt))
    t_1 = ndchar / (1.0d0 + t_0)
    t_2 = (nachar / (1.0d0 + exp((vef / kbt)))) + t_1
    t_3 = (nachar / (1.0d0 + exp((eaccept / kbt)))) + t_1
    t_4 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (vef <= (-1.95d+143)) then
        tmp = t_2
    else if (vef <= (-1.9d+109)) then
        tmp = t_3
    else if (vef <= (-36.0d0)) then
        tmp = t_2
    else if (vef <= (-5.2d-279)) then
        tmp = t_3
    else if (vef <= 2.15d-190) then
        tmp = t_4 + (ndchar / (mu * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu))))
    else if (vef <= 1.9d-99) then
        tmp = t_3
    else if (vef <= 6d+87) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) - (ndchar / ((-1.0d0) - t_0))
    else if (vef <= 2d+101) then
        tmp = t_4 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (mu / kbt))) - (ec / kbt)) / edonor))))
    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 = Math.exp((((mu + Vef) - Ec) / KbT));
	double t_1 = NdChar / (1.0 + t_0);
	double t_2 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + t_1;
	double t_3 = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + t_1;
	double t_4 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (Vef <= -1.95e+143) {
		tmp = t_2;
	} else if (Vef <= -1.9e+109) {
		tmp = t_3;
	} else if (Vef <= -36.0) {
		tmp = t_2;
	} else if (Vef <= -5.2e-279) {
		tmp = t_3;
	} else if (Vef <= 2.15e-190) {
		tmp = t_4 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (Vef <= 1.9e-99) {
		tmp = t_3;
	} else if (Vef <= 6e+87) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) - (NdChar / (-1.0 - t_0));
	} else if (Vef <= 2e+101) {
		tmp = t_4 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp((((mu + Vef) - Ec) / KbT))
	t_1 = NdChar / (1.0 + t_0)
	t_2 = (NaChar / (1.0 + math.exp((Vef / KbT)))) + t_1
	t_3 = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + t_1
	t_4 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if Vef <= -1.95e+143:
		tmp = t_2
	elif Vef <= -1.9e+109:
		tmp = t_3
	elif Vef <= -36.0:
		tmp = t_2
	elif Vef <= -5.2e-279:
		tmp = t_3
	elif Vef <= 2.15e-190:
		tmp = t_4 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))))
	elif Vef <= 1.9e-99:
		tmp = t_3
	elif Vef <= 6e+87:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) - (NdChar / (-1.0 - t_0))
	elif Vef <= 2e+101:
		tmp = t_4 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))))
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))
	t_1 = Float64(NdChar / Float64(1.0 + t_0))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + t_1)
	t_3 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + t_1)
	t_4 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (Vef <= -1.95e+143)
		tmp = t_2;
	elseif (Vef <= -1.9e+109)
		tmp = t_3;
	elseif (Vef <= -36.0)
		tmp = t_2;
	elseif (Vef <= -5.2e-279)
		tmp = t_3;
	elseif (Vef <= 2.15e-190)
		tmp = Float64(t_4 + Float64(NdChar / Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu)))));
	elseif (Vef <= 1.9e-99)
		tmp = t_3;
	elseif (Vef <= 6e+87)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) - Float64(NdChar / Float64(-1.0 - t_0)));
	elseif (Vef <= 2e+101)
		tmp = Float64(t_4 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)) / EDonor)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp((((mu + Vef) - Ec) / KbT));
	t_1 = NdChar / (1.0 + t_0);
	t_2 = (NaChar / (1.0 + exp((Vef / KbT)))) + t_1;
	t_3 = (NaChar / (1.0 + exp((EAccept / KbT)))) + t_1;
	t_4 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (Vef <= -1.95e+143)
		tmp = t_2;
	elseif (Vef <= -1.9e+109)
		tmp = t_3;
	elseif (Vef <= -36.0)
		tmp = t_2;
	elseif (Vef <= -5.2e-279)
		tmp = t_3;
	elseif (Vef <= 2.15e-190)
		tmp = t_4 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	elseif (Vef <= 1.9e-99)
		tmp = t_3;
	elseif (Vef <= 6e+87)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - (NdChar / (-1.0 - t_0));
	elseif (Vef <= 2e+101)
		tmp = t_4 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	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[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -1.95e+143], t$95$2, If[LessEqual[Vef, -1.9e+109], t$95$3, If[LessEqual[Vef, -36.0], t$95$2, If[LessEqual[Vef, -5.2e-279], t$95$3, If[LessEqual[Vef, 2.15e-190], N[(t$95$4 + N[(NdChar / N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.9e-99], t$95$3, If[LessEqual[Vef, 6e+87], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 2e+101], N[(t$95$4 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if Vef < -1.9499999999999999e143 or -1.90000000000000019e109 < Vef < -36 or 2e101 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 88.0%

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

   6. Taylor expanded in EDonor around 0 85.8%

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

   if -1.9499999999999999e143 < Vef < -1.90000000000000019e109 or -36 < Vef < -5.2000000000000004e-279 or 2.15e-190 < Vef < 1.8999999999999998e-99

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 79.3%

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

   6. Taylor expanded in EDonor around 0 75.9%

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

   if -5.2000000000000004e-279 < Vef < 2.15e-190

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 68.3%

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

   6. Taylor expanded in mu around -inf 82.0%

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

   if 1.8999999999999998e-99 < Vef < 5.9999999999999998e87

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 84.6%

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

   6. Taylor expanded in EDonor around 0 78.2%

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

   if 5.9999999999999998e87 < Vef < 2e101

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.7%

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

   6. Taylor expanded in EDonor around -inf 100.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1.95 \cdot 10^{+143}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.9 \cdot 10^{+109}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq -36:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq -5.2 \cdot 10^{-279}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.15 \cdot 10^{-190}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;Vef \leq 1.9 \cdot 10^{-99}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq 6 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2 \cdot 10^{+101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} - t\_1\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - t\_1\\ \mathbf{if}\;Vef \leq -1.05 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq -6.8 \cdot 10^{+108}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq -1.7 \cdot 10^{-112}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;Vef \leq 3 \cdot 10^{-222}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq 3.3 \cdot 10^{-99}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{EAccept}{KbT}}} - t\_1\\ \mathbf{elif}\;Vef \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))))
        (t_1 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_2 (- (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) t_1))
        (t_3 (- (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_1)))
   (if (<= Vef -1.05e+147)
     t_2
     (if (<= Vef -6.8e+108)
       t_0
       (if (<= Vef -1.7e-112)
         t_3
         (if (<= Vef 3e-222)
           t_0
           (if (<= Vef 3.3e-99)
             (- (* NaChar (/ 1.0 (+ 1.0 (exp (/ EAccept KbT))))) t_1)
             (if (<= Vef 3.2e+87) t_3 t_2))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	double t_1 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = (NaChar / (1.0 + exp((Vef / KbT)))) - t_1;
	double t_3 = (NaChar / (1.0 + exp((Ev / KbT)))) - t_1;
	double tmp;
	if (Vef <= -1.05e+147) {
		tmp = t_2;
	} else if (Vef <= -6.8e+108) {
		tmp = t_0;
	} else if (Vef <= -1.7e-112) {
		tmp = t_3;
	} else if (Vef <= 3e-222) {
		tmp = t_0;
	} else if (Vef <= 3.3e-99) {
		tmp = (NaChar * (1.0 / (1.0 + exp((EAccept / KbT))))) - t_1;
	} else if (Vef <= 3.2e+87) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    t_1 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_2 = (nachar / (1.0d0 + exp((vef / kbt)))) - t_1
    t_3 = (nachar / (1.0d0 + exp((ev / kbt)))) - t_1
    if (vef <= (-1.05d+147)) then
        tmp = t_2
    else if (vef <= (-6.8d+108)) then
        tmp = t_0
    else if (vef <= (-1.7d-112)) then
        tmp = t_3
    else if (vef <= 3d-222) then
        tmp = t_0
    else if (vef <= 3.3d-99) then
        tmp = (nachar * (1.0d0 / (1.0d0 + exp((eaccept / kbt))))) - t_1
    else if (vef <= 3.2d+87) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double t_1 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) - t_1;
	double t_3 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) - t_1;
	double tmp;
	if (Vef <= -1.05e+147) {
		tmp = t_2;
	} else if (Vef <= -6.8e+108) {
		tmp = t_0;
	} else if (Vef <= -1.7e-112) {
		tmp = t_3;
	} else if (Vef <= 3e-222) {
		tmp = t_0;
	} else if (Vef <= 3.3e-99) {
		tmp = (NaChar * (1.0 / (1.0 + Math.exp((EAccept / KbT))))) - t_1;
	} else if (Vef <= 3.2e+87) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	t_1 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_2 = (NaChar / (1.0 + math.exp((Vef / KbT)))) - t_1
	t_3 = (NaChar / (1.0 + math.exp((Ev / KbT)))) - t_1
	tmp = 0
	if Vef <= -1.05e+147:
		tmp = t_2
	elif Vef <= -6.8e+108:
		tmp = t_0
	elif Vef <= -1.7e-112:
		tmp = t_3
	elif Vef <= 3e-222:
		tmp = t_0
	elif Vef <= 3.3e-99:
		tmp = (NaChar * (1.0 / (1.0 + math.exp((EAccept / KbT))))) - t_1
	elif Vef <= 3.2e+87:
		tmp = t_3
	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(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	t_1 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - t_1)
	t_3 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) - t_1)
	tmp = 0.0
	if (Vef <= -1.05e+147)
		tmp = t_2;
	elseif (Vef <= -6.8e+108)
		tmp = t_0;
	elseif (Vef <= -1.7e-112)
		tmp = t_3;
	elseif (Vef <= 3e-222)
		tmp = t_0;
	elseif (Vef <= 3.3e-99)
		tmp = Float64(Float64(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(EAccept / KbT))))) - t_1);
	elseif (Vef <= 3.2e+87)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	t_1 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_2 = (NaChar / (1.0 + exp((Vef / KbT)))) - t_1;
	t_3 = (NaChar / (1.0 + exp((Ev / KbT)))) - t_1;
	tmp = 0.0;
	if (Vef <= -1.05e+147)
		tmp = t_2;
	elseif (Vef <= -6.8e+108)
		tmp = t_0;
	elseif (Vef <= -1.7e-112)
		tmp = t_3;
	elseif (Vef <= 3e-222)
		tmp = t_0;
	elseif (Vef <= 3.3e-99)
		tmp = (NaChar * (1.0 / (1.0 + exp((EAccept / KbT))))) - t_1;
	elseif (Vef <= 3.2e+87)
		tmp = t_3;
	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[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[Vef, -1.05e+147], t$95$2, If[LessEqual[Vef, -6.8e+108], t$95$0, If[LessEqual[Vef, -1.7e-112], t$95$3, If[LessEqual[Vef, 3e-222], t$95$0, If[LessEqual[Vef, 3.3e-99], N[(N[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[Vef, 3.2e+87], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -1.05000000000000003e147 or 3.2e87 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 85.6%

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

   if -1.05000000000000003e147 < Vef < -6.79999999999999992e108 or -1.6999999999999999e-112 < Vef < 3.0000000000000003e-222

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 91.6%

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

   if -6.79999999999999992e108 < Vef < -1.6999999999999999e-112 or 3.29999999999999986e-99 < Vef < 3.2e87

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 80.2%

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

   if 3.0000000000000003e-222 < Vef < 3.29999999999999986e-99

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. div-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in EAccept around inf 75.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1.05 \cdot 10^{+147}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq -6.8 \cdot 10^{+108}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.7 \cdot 10^{-112}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3 \cdot 10^{-222}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.3 \cdot 10^{-99}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.2 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} - t\_1\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - t\_1\\ \mathbf{if}\;Vef \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq -1.4 \cdot 10^{+109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq -9 \cdot 10^{-113}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;Vef \leq 1.5 \cdot 10^{-222}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq 1.16 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - t\_1\\ \mathbf{elif}\;Vef \leq 8.6 \cdot 10^{+85}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))))
        (t_1 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_2 (- (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) t_1))
        (t_3 (- (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_1)))
   (if (<= Vef -2.4e+142)
     t_2
     (if (<= Vef -1.4e+109)
       t_0
       (if (<= Vef -9e-113)
         t_3
         (if (<= Vef 1.5e-222)
           t_0
           (if (<= Vef 1.16e-101)
             (- (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) t_1)
             (if (<= Vef 8.6e+85) t_3 t_2))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	double t_1 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = (NaChar / (1.0 + exp((Vef / KbT)))) - t_1;
	double t_3 = (NaChar / (1.0 + exp((Ev / KbT)))) - t_1;
	double tmp;
	if (Vef <= -2.4e+142) {
		tmp = t_2;
	} else if (Vef <= -1.4e+109) {
		tmp = t_0;
	} else if (Vef <= -9e-113) {
		tmp = t_3;
	} else if (Vef <= 1.5e-222) {
		tmp = t_0;
	} else if (Vef <= 1.16e-101) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - t_1;
	} else if (Vef <= 8.6e+85) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    t_1 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_2 = (nachar / (1.0d0 + exp((vef / kbt)))) - t_1
    t_3 = (nachar / (1.0d0 + exp((ev / kbt)))) - t_1
    if (vef <= (-2.4d+142)) then
        tmp = t_2
    else if (vef <= (-1.4d+109)) then
        tmp = t_0
    else if (vef <= (-9d-113)) then
        tmp = t_3
    else if (vef <= 1.5d-222) then
        tmp = t_0
    else if (vef <= 1.16d-101) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) - t_1
    else if (vef <= 8.6d+85) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double t_1 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) - t_1;
	double t_3 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) - t_1;
	double tmp;
	if (Vef <= -2.4e+142) {
		tmp = t_2;
	} else if (Vef <= -1.4e+109) {
		tmp = t_0;
	} else if (Vef <= -9e-113) {
		tmp = t_3;
	} else if (Vef <= 1.5e-222) {
		tmp = t_0;
	} else if (Vef <= 1.16e-101) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) - t_1;
	} else if (Vef <= 8.6e+85) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	t_1 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_2 = (NaChar / (1.0 + math.exp((Vef / KbT)))) - t_1
	t_3 = (NaChar / (1.0 + math.exp((Ev / KbT)))) - t_1
	tmp = 0
	if Vef <= -2.4e+142:
		tmp = t_2
	elif Vef <= -1.4e+109:
		tmp = t_0
	elif Vef <= -9e-113:
		tmp = t_3
	elif Vef <= 1.5e-222:
		tmp = t_0
	elif Vef <= 1.16e-101:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) - t_1
	elif Vef <= 8.6e+85:
		tmp = t_3
	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(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	t_1 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - t_1)
	t_3 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) - t_1)
	tmp = 0.0
	if (Vef <= -2.4e+142)
		tmp = t_2;
	elseif (Vef <= -1.4e+109)
		tmp = t_0;
	elseif (Vef <= -9e-113)
		tmp = t_3;
	elseif (Vef <= 1.5e-222)
		tmp = t_0;
	elseif (Vef <= 1.16e-101)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) - t_1);
	elseif (Vef <= 8.6e+85)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	t_1 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_2 = (NaChar / (1.0 + exp((Vef / KbT)))) - t_1;
	t_3 = (NaChar / (1.0 + exp((Ev / KbT)))) - t_1;
	tmp = 0.0;
	if (Vef <= -2.4e+142)
		tmp = t_2;
	elseif (Vef <= -1.4e+109)
		tmp = t_0;
	elseif (Vef <= -9e-113)
		tmp = t_3;
	elseif (Vef <= 1.5e-222)
		tmp = t_0;
	elseif (Vef <= 1.16e-101)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - t_1;
	elseif (Vef <= 8.6e+85)
		tmp = t_3;
	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[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[Vef, -2.4e+142], t$95$2, If[LessEqual[Vef, -1.4e+109], t$95$0, If[LessEqual[Vef, -9e-113], t$95$3, If[LessEqual[Vef, 1.5e-222], t$95$0, If[LessEqual[Vef, 1.16e-101], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[Vef, 8.6e+85], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -2.3999999999999999e142 or 8.5999999999999998e85 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 85.6%

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

   if -2.3999999999999999e142 < Vef < -1.4000000000000001e109 or -9.0000000000000002e-113 < Vef < 1.50000000000000015e-222

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 91.6%

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

   if -1.4000000000000001e109 < Vef < -9.0000000000000002e-113 or 1.15999999999999995e-101 < Vef < 8.5999999999999998e85

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 80.2%

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

   if 1.50000000000000015e-222 < Vef < 1.15999999999999995e-101

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 75.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.4 \cdot 10^{+109}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -9 \cdot 10^{-113}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.5 \cdot 10^{-222}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.16 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.6 \cdot 10^{+85}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -5 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -1.25 \cdot 10^{-179}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq -7.5 \cdot 10^{-253}:\\ \;\;\;\;t\_1 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \mathbf{elif}\;mu \leq 8.3 \cdot 10^{-259}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq 3.1 \cdot 10^{-195}:\\ \;\;\;\;t\_1 + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;mu \leq 5.5 \cdot 10^{+50}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_2 (+ t_1 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))))
   (if (<= mu -5e+149)
     t_2
     (if (<= mu -1.25e-179)
       t_0
       (if (<= mu -7.5e-253)
         (+
          t_1
          (/
           NdChar
           (*
            EDonor
            (+
             (/ 1.0 KbT)
             (/ (- (+ 2.0 (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT)) EDonor)))))
         (if (<= mu 8.3e-259)
           t_0
           (if (<= mu 3.1e-195)
             (+
              t_1
              (/
               NdChar
               (*
                mu
                (+
                 (/ 1.0 KbT)
                 (/
                  (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT))
                  mu)))))
             (if (<= mu 5.5e+50) 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((EAccept / KbT)))) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + exp((mu / KbT))));
	double tmp;
	if (mu <= -5e+149) {
		tmp = t_2;
	} else if (mu <= -1.25e-179) {
		tmp = t_0;
	} else if (mu <= -7.5e-253) {
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	} else if (mu <= 8.3e-259) {
		tmp = t_0;
	} else if (mu <= 3.1e-195) {
		tmp = t_1 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (mu <= 5.5e+50) {
		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((eaccept / kbt)))) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_2 = t_1 + (ndchar / (1.0d0 + exp((mu / kbt))))
    if (mu <= (-5d+149)) then
        tmp = t_2
    else if (mu <= (-1.25d-179)) then
        tmp = t_0
    else if (mu <= (-7.5d-253)) then
        tmp = t_1 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (mu / kbt))) - (ec / kbt)) / edonor))))
    else if (mu <= 8.3d-259) then
        tmp = t_0
    else if (mu <= 3.1d-195) then
        tmp = t_1 + (ndchar / (mu * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu))))
    else if (mu <= 5.5d+50) 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((EAccept / KbT)))) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double tmp;
	if (mu <= -5e+149) {
		tmp = t_2;
	} else if (mu <= -1.25e-179) {
		tmp = t_0;
	} else if (mu <= -7.5e-253) {
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	} else if (mu <= 8.3e-259) {
		tmp = t_0;
	} else if (mu <= 3.1e-195) {
		tmp = t_1 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (mu <= 5.5e+50) {
		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((EAccept / KbT)))) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_2 = t_1 + (NdChar / (1.0 + math.exp((mu / KbT))))
	tmp = 0
	if mu <= -5e+149:
		tmp = t_2
	elif mu <= -1.25e-179:
		tmp = t_0
	elif mu <= -7.5e-253:
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))))
	elif mu <= 8.3e-259:
		tmp = t_0
	elif mu <= 3.1e-195:
		tmp = t_1 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))))
	elif mu <= 5.5e+50:
		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(EAccept / KbT)))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	tmp = 0.0
	if (mu <= -5e+149)
		tmp = t_2;
	elseif (mu <= -1.25e-179)
		tmp = t_0;
	elseif (mu <= -7.5e-253)
		tmp = Float64(t_1 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)) / EDonor)))));
	elseif (mu <= 8.3e-259)
		tmp = t_0;
	elseif (mu <= 3.1e-195)
		tmp = Float64(t_1 + Float64(NdChar / Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu)))));
	elseif (mu <= 5.5e+50)
		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((EAccept / KbT)))) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_2 = t_1 + (NdChar / (1.0 + exp((mu / KbT))));
	tmp = 0.0;
	if (mu <= -5e+149)
		tmp = t_2;
	elseif (mu <= -1.25e-179)
		tmp = t_0;
	elseif (mu <= -7.5e-253)
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	elseif (mu <= 8.3e-259)
		tmp = t_0;
	elseif (mu <= 3.1e-195)
		tmp = t_1 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	elseif (mu <= 5.5e+50)
		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[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -5e+149], t$95$2, If[LessEqual[mu, -1.25e-179], t$95$0, If[LessEqual[mu, -7.5e-253], N[(t$95$1 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 8.3e-259], t$95$0, If[LessEqual[mu, 3.1e-195], N[(t$95$1 + N[(NdChar / N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 5.5e+50], t$95$0, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if mu < -4.9999999999999999e149 or 5.4999999999999998e50 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 90.5%

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

   if -4.9999999999999999e149 < mu < -1.2499999999999999e-179 or -7.49999999999999987e-253 < mu < 8.3000000000000003e-259 or 3.10000000000000002e-195 < mu < 5.4999999999999998e50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 78.3%

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

   if -1.2499999999999999e-179 < mu < -7.49999999999999987e-253

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 70.7%

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

   6. Taylor expanded in EDonor around -inf 85.8%

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

   if 8.3000000000000003e-259 < mu < 3.10000000000000002e-195

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.6%

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

   6. Taylor expanded in mu around -inf 94.3%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -5 \cdot 10^{+149}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.25 \cdot 10^{-179}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq -7.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \mathbf{elif}\;mu \leq 8.3 \cdot 10^{-259}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 3.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;mu \leq 5.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}\\ \mathbf{if}\;EAccept \leq 3.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - t\_1}\\ \mathbf{elif}\;EAccept \leq 5.9 \cdot 10^{-61}:\\ \;\;\;\;t\_0 + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;EAccept \leq 6.5 \cdot 10^{+67}:\\ \;\;\;\;t\_0 + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1 (exp (/ (- (+ mu Vef) Ec) KbT))))
   (if (<= EAccept 3.5e-169)
     (- (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar (- -1.0 t_1)))
     (if (<= EAccept 5.9e-61)
       (+
        t_0
        (/
         NdChar
         (*
          Ec
          (+
           (/ (+ 2.0 (+ (+ (/ Vef KbT) (/ mu KbT)) (/ EDonor KbT))) Ec)
           (/ -1.0 KbT)))))
       (if (<= EAccept 3.2e-18)
         (+
          (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))))
         (if (<= EAccept 6.5e+67)
           (+
            t_0
            (/
             NdChar
             (*
              mu
              (+
               (/ 1.0 KbT)
               (/ (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)) mu)))))
           (+
            (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
            (/ NdChar (+ 1.0 t_1)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = exp((((mu + Vef) - Ec) / KbT));
	double tmp;
	if (EAccept <= 3.5e-169) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - (NdChar / (-1.0 - t_1));
	} else if (EAccept <= 5.9e-61) {
		tmp = t_0 + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	} else if (EAccept <= 3.2e-18) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((Ec / -KbT))));
	} else if (EAccept <= 6.5e+67) {
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + t_1));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = exp((((mu + vef) - ec) / kbt))
    if (eaccept <= 3.5d-169) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) - (ndchar / ((-1.0d0) - t_1))
    else if (eaccept <= 5.9d-61) then
        tmp = t_0 + (ndchar / (ec * (((2.0d0 + (((vef / kbt) + (mu / kbt)) + (edonor / kbt))) / ec) + ((-1.0d0) / kbt))))
    else if (eaccept <= 3.2d-18) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((ec / -kbt))))
    else if (eaccept <= 6.5d+67) then
        tmp = t_0 + (ndchar / (mu * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu))))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / (1.0d0 + t_1))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = Math.exp((((mu + Vef) - Ec) / KbT));
	double tmp;
	if (EAccept <= 3.5e-169) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) - (NdChar / (-1.0 - t_1));
	} else if (EAccept <= 5.9e-61) {
		tmp = t_0 + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	} else if (EAccept <= 3.2e-18) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((Ec / -KbT))));
	} else if (EAccept <= 6.5e+67) {
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (1.0 + t_1));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = math.exp((((mu + Vef) - Ec) / KbT))
	tmp = 0
	if EAccept <= 3.5e-169:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) - (NdChar / (-1.0 - t_1))
	elif EAccept <= 5.9e-61:
		tmp = t_0 + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))))
	elif EAccept <= 3.2e-18:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((Ec / -KbT))))
	elif EAccept <= 6.5e+67:
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (1.0 + t_1))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))
	tmp = 0.0
	if (EAccept <= 3.5e-169)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) - Float64(NdChar / Float64(-1.0 - t_1)));
	elseif (EAccept <= 5.9e-61)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(Float64(Vef / KbT) + Float64(mu / KbT)) + Float64(EDonor / KbT))) / Ec) + Float64(-1.0 / KbT)))));
	elseif (EAccept <= 3.2e-18)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))));
	elseif (EAccept <= 6.5e+67)
		tmp = Float64(t_0 + Float64(NdChar / Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(1.0 + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = exp((((mu + Vef) - Ec) / KbT));
	tmp = 0.0;
	if (EAccept <= 3.5e-169)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - (NdChar / (-1.0 - t_1));
	elseif (EAccept <= 5.9e-61)
		tmp = t_0 + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	elseif (EAccept <= 3.2e-18)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((Ec / -KbT))));
	elseif (EAccept <= 6.5e+67)
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[EAccept, 3.5e-169], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 5.9e-61], N[(t$95$0 + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.2e-18], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 6.5e+67], N[(t$95$0 + N[(NdChar / N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if EAccept < 3.5000000000000003e-169

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 72.7%

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

   6. Taylor expanded in EDonor around 0 66.0%

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

   if 3.5000000000000003e-169 < EAccept < 5.89999999999999972e-61

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 87.3%

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

   6. Taylor expanded in Ec around -inf 96.3%

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

      1. associate-*r* 96.3%

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

      2. mul-1-neg 96.3%

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

      3. +-commutative 96.3%

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

      4. mul-1-neg 96.3%

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

      5. unsub-neg 96.3%

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

      6. +-commutative 96.3%

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

   8. Simplified 96.3%

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

   if 5.89999999999999972e-61 < EAccept < 3.1999999999999999e-18

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.4%

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

   6. Taylor expanded in Ec around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-neg-frac2 71.4%

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

   8. Simplified 71.4%

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

   if 3.1999999999999999e-18 < EAccept < 6.4999999999999995e67

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 37.8%

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

   6. Taylor expanded in mu around -inf 60.9%

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

   if 6.4999999999999995e67 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 87.0%

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

   6. Taylor expanded in EDonor around 0 85.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 3.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 5.9 \cdot 10^{-61}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;EAccept \leq 6.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - t\_0\\ \mathbf{if}\;EAccept \leq 3.4 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;EAccept \leq 2.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 4.2 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (- (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_0)))
   (if (<= EAccept 3.4e-169)
     t_1
     (if (<= EAccept 2.2e-59)
       (+
        (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
        (/
         NdChar
         (*
          Ec
          (+
           (/ (+ 2.0 (+ (+ (/ Vef KbT) (/ mu KbT)) (/ EDonor KbT))) Ec)
           (/ -1.0 KbT)))))
       (if (<= EAccept 4.2e+64)
         t_1
         (- (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + exp((Ev / KbT)))) - t_0;
	double tmp;
	if (EAccept <= 3.4e-169) {
		tmp = t_1;
	} else if (EAccept <= 2.2e-59) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	} else if (EAccept <= 4.2e+64) {
		tmp = t_1;
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = (nachar / (1.0d0 + exp((ev / kbt)))) - t_0
    if (eaccept <= 3.4d-169) then
        tmp = t_1
    else if (eaccept <= 2.2d-59) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / (ec * (((2.0d0 + (((vef / kbt) + (mu / kbt)) + (edonor / kbt))) / ec) + ((-1.0d0) / kbt))))
    else if (eaccept <= 4.2d+64) then
        tmp = t_1
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) - t_0;
	double tmp;
	if (EAccept <= 3.4e-169) {
		tmp = t_1;
	} else if (EAccept <= 2.2e-59) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	} else if (EAccept <= 4.2e+64) {
		tmp = t_1;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) - t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp((Ev / KbT)))) - t_0
	tmp = 0
	if EAccept <= 3.4e-169:
		tmp = t_1
	elif EAccept <= 2.2e-59:
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))))
	elif EAccept <= 4.2e+64:
		tmp = t_1
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) - t_0)
	tmp = 0.0
	if (EAccept <= 3.4e-169)
		tmp = t_1;
	elseif (EAccept <= 2.2e-59)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(Float64(Vef / KbT) + Float64(mu / KbT)) + Float64(EDonor / KbT))) / Ec) + Float64(-1.0 / KbT)))));
	elseif (EAccept <= 4.2e+64)
		tmp = t_1;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = (NaChar / (1.0 + exp((Ev / KbT)))) - t_0;
	tmp = 0.0;
	if (EAccept <= 3.4e-169)
		tmp = t_1;
	elseif (EAccept <= 2.2e-59)
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	elseif (EAccept <= 4.2e+64)
		tmp = t_1;
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[EAccept, 3.4e-169], t$95$1, If[LessEqual[EAccept, 2.2e-59], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 4.2e+64], t$95$1, N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 3.4e-169 or 2.1999999999999999e-59 < EAccept < 4.2000000000000001e64

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 72.9%

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

   if 3.4e-169 < EAccept < 2.1999999999999999e-59

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 88.3%

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

   6. Taylor expanded in Ec around -inf 96.6%

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

      1. associate-*r* 96.6%

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

      2. mul-1-neg 96.6%

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

      3. +-commutative 96.6%

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

      4. mul-1-neg 96.6%

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

      5. unsub-neg 96.6%

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

      6. +-commutative 96.6%

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

   8. Simplified 96.6%

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

   if 4.2000000000000001e64 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 87.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 3.4 \cdot 10^{-169}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 2.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 4.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;t\_0 + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 780000:\\ \;\;\;\;t\_0 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} - mu \cdot \left(\frac{\left(\frac{\frac{Ec}{EDonor}}{KbT} - \frac{Vef}{EDonor \cdot KbT}\right) - \frac{2}{EDonor}}{mu} + \frac{-1}{EDonor \cdot KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq 5 \cdot 10^{+38}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -4.6e-20)
     (+
      t_0
      (/
       NdChar
       (*
        mu
        (+
         (/ 1.0 KbT)
         (/ (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)) mu)))))
     (if (<= NaChar 8.5e-96)
       (-
        (/ NaChar (+ (/ EAccept KbT) 2.0))
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (if (<= NaChar 780000.0)
         (+
          t_0
          (/
           NdChar
           (*
            EDonor
            (-
             (/ 1.0 KbT)
             (*
              mu
              (+
               (/
                (-
                 (- (/ (/ Ec EDonor) KbT) (/ Vef (* EDonor KbT)))
                 (/ 2.0 EDonor))
                mu)
               (/ -1.0 (* EDonor KbT))))))))
         (if (<= NaChar 5e+38)
           (+
            (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
            (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
           (+
            t_0
            (/
             NdChar
             (*
              EDonor
              (+
               (/ 1.0 KbT)
               (/
                (- (+ 2.0 (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))
                EDonor)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -4.6e-20) {
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (NaChar <= 8.5e-96) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 780000.0) {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) - (mu * ((((((Ec / EDonor) / KbT) - (Vef / (EDonor * KbT))) - (2.0 / EDonor)) / mu) + (-1.0 / (EDonor * KbT)))))));
	} else if (NaChar <= 5e+38) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	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 - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-4.6d-20)) then
        tmp = t_0 + (ndchar / (mu * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu))))
    else if (nachar <= 8.5d-96) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else if (nachar <= 780000.0d0) then
        tmp = t_0 + (ndchar / (edonor * ((1.0d0 / kbt) - (mu * ((((((ec / edonor) / kbt) - (vef / (edonor * kbt))) - (2.0d0 / edonor)) / mu) + ((-1.0d0) / (edonor * kbt)))))))
    else if (nachar <= 5d+38) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_0 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (mu / kbt))) - (ec / kbt)) / edonor))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -4.6e-20) {
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (NaChar <= 8.5e-96) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 780000.0) {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) - (mu * ((((((Ec / EDonor) / KbT) - (Vef / (EDonor * KbT))) - (2.0 / EDonor)) / mu) + (-1.0 / (EDonor * KbT)))))));
	} else if (NaChar <= 5e+38) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -4.6e-20:
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))))
	elif NaChar <= 8.5e-96:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	elif NaChar <= 780000.0:
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) - (mu * ((((((Ec / EDonor) / KbT) - (Vef / (EDonor * KbT))) - (2.0 / EDonor)) / mu) + (-1.0 / (EDonor * KbT)))))))
	elif NaChar <= 5e+38:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -4.6e-20)
		tmp = Float64(t_0 + Float64(NdChar / Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu)))));
	elseif (NaChar <= 8.5e-96)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	elseif (NaChar <= 780000.0)
		tmp = Float64(t_0 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) - Float64(mu * Float64(Float64(Float64(Float64(Float64(Float64(Ec / EDonor) / KbT) - Float64(Vef / Float64(EDonor * KbT))) - Float64(2.0 / EDonor)) / mu) + Float64(-1.0 / Float64(EDonor * KbT))))))));
	elseif (NaChar <= 5e+38)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)) / EDonor)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -4.6e-20)
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	elseif (NaChar <= 8.5e-96)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	elseif (NaChar <= 780000.0)
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) - (mu * ((((((Ec / EDonor) / KbT) - (Vef / (EDonor * KbT))) - (2.0 / EDonor)) / mu) + (-1.0 / (EDonor * KbT)))))));
	elseif (NaChar <= 5e+38)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.6e-20], N[(t$95$0 + N[(NdChar / N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8.5e-96], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 780000.0], N[(t$95$0 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] - N[(mu * N[(N[(N[(N[(N[(N[(Ec / EDonor), $MachinePrecision] / KbT), $MachinePrecision] - N[(Vef / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 / EDonor), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(-1.0 / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 5e+38], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -4.5999999999999998e-20

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.4%

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

   6. Taylor expanded in mu around -inf 75.2%

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

   if -4.5999999999999998e-20 < NaChar < 8.49999999999999983e-96

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 86.0%

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

   6. Taylor expanded in EAccept around 0 78.6%

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

      1. +-commutative 78.6%

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

   8. Simplified 78.6%

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

   if 8.49999999999999983e-96 < NaChar < 7.8e5

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 42.3%

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

   6. Taylor expanded in EDonor around -inf 60.0%

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

   7. Taylor expanded in mu around -inf 64.6%

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

      1. associate-*r* 64.6%

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

      2. neg-mul-1 64.6%

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

      3. associate-*r/ 64.6%

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

      4. mul-1-neg 64.6%

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

      5. associate--l+ 64.6%

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

      6. associate-*r/ 64.6%

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

      7. metadata-eval 64.6%

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

      8. *-commutative 64.6%

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

      9. associate-/r* 69.1%

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

      10. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   if 7.8e5 < NaChar < 4.9999999999999997e38

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 89.8%

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

   6. Taylor expanded in EDonor around inf 69.5%

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

   if 4.9999999999999997e38 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.3%

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

   6. Taylor expanded in EDonor around -inf 74.2%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 780000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} - mu \cdot \left(\frac{\left(\frac{\frac{Ec}{EDonor}}{KbT} - \frac{Vef}{EDonor \cdot KbT}\right) - \frac{2}{EDonor}}{mu} + \frac{-1}{EDonor \cdot KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq 5 \cdot 10^{+38}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}\\ \mathbf{if}\;Ec \leq -7.6 \cdot 10^{+192}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - t\_1}\\ \mathbf{elif}\;Ec \leq 2.4 \cdot 10^{-10}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ec \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;t\_0 - \frac{NdChar}{\frac{Ec}{KbT} + \left(mu \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{mu \cdot KbT} + \frac{EDonor}{mu \cdot KbT}\right)\right) - 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1 (exp (/ (- (+ mu Vef) Ec) KbT))))
   (if (<= Ec -7.6e+192)
     (- (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar (- -1.0 t_1)))
     (if (<= Ec 2.4e-10)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
       (if (<= Ec 6.5e+52)
         (-
          t_0
          (/
           NdChar
           (+
            (/ Ec KbT)
            (-
             (*
              mu
              (- (/ -1.0 KbT) (+ (/ Vef (* mu KbT)) (/ EDonor (* mu KbT)))))
             2.0))))
         (+
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
          (/ NdChar (+ 1.0 t_1))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = exp((((mu + Vef) - Ec) / KbT));
	double tmp;
	if (Ec <= -7.6e+192) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - (NdChar / (-1.0 - t_1));
	} else if (Ec <= 2.4e-10) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Ec <= 6.5e+52) {
		tmp = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + t_1));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = exp((((mu + vef) - ec) / kbt))
    if (ec <= (-7.6d+192)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) - (ndchar / ((-1.0d0) - t_1))
    else if (ec <= 2.4d-10) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (ec <= 6.5d+52) then
        tmp = t_0 - (ndchar / ((ec / kbt) + ((mu * (((-1.0d0) / kbt) - ((vef / (mu * kbt)) + (edonor / (mu * kbt))))) - 2.0d0)))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / (1.0d0 + t_1))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = Math.exp((((mu + Vef) - Ec) / KbT));
	double tmp;
	if (Ec <= -7.6e+192) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) - (NdChar / (-1.0 - t_1));
	} else if (Ec <= 2.4e-10) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Ec <= 6.5e+52) {
		tmp = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (1.0 + t_1));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = math.exp((((mu + Vef) - Ec) / KbT))
	tmp = 0
	if Ec <= -7.6e+192:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) - (NdChar / (-1.0 - t_1))
	elif Ec <= 2.4e-10:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Ec <= 6.5e+52:
		tmp = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (1.0 + t_1))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))
	tmp = 0.0
	if (Ec <= -7.6e+192)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) - Float64(NdChar / Float64(-1.0 - t_1)));
	elseif (Ec <= 2.4e-10)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Ec <= 6.5e+52)
		tmp = Float64(t_0 - Float64(NdChar / Float64(Float64(Ec / KbT) + Float64(Float64(mu * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(mu * KbT)) + Float64(EDonor / Float64(mu * KbT))))) - 2.0))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(1.0 + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = exp((((mu + Vef) - Ec) / KbT));
	tmp = 0.0;
	if (Ec <= -7.6e+192)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) - (NdChar / (-1.0 - t_1));
	elseif (Ec <= 2.4e-10)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Ec <= 6.5e+52)
		tmp = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[Ec, -7.6e+192], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 2.4e-10], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 6.5e+52], N[(t$95$0 - N[(NdChar / N[(N[(Ec / KbT), $MachinePrecision] + N[(N[(mu * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(Vef / N[(mu * KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ec < -7.5999999999999999e192

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 75.3%

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

   6. Taylor expanded in EDonor around 0 71.5%

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

   if -7.5999999999999999e192 < Ec < 2.4e-10

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 81.1%

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

   if 2.4e-10 < Ec < 6.49999999999999996e52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.7%

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

   6. Taylor expanded in mu around inf 81.4%

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

      1. +-commutative 81.4%

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

      2. *-commutative 81.4%

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

      3. *-commutative 81.4%

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

   8. Simplified 81.4%

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

   if 6.49999999999999996e52 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.2%

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

   6. Taylor expanded in EDonor around 0 69.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -7.6 \cdot 10^{+192}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} - \frac{NdChar}{-1 - e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Ec \leq 2.4 \cdot 10^{-10}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ec \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{\frac{Ec}{KbT} + \left(mu \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{mu \cdot KbT} + \frac{EDonor}{mu \cdot KbT}\right)\right) - 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -7 \cdot 10^{-55}:\\ \;\;\;\;t\_0 + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;NaChar \leq 2.12 \cdot 10^{-47}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -7e-55)
     (+
      t_0
      (/
       NdChar
       (*
        mu
        (+
         (/ 1.0 KbT)
         (/ (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)) mu)))))
     (if (<= NaChar 2.12e-47)
       (+
        (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
       (+
        t_0
        (/
         NdChar
         (*
          EDonor
          (+
           (/ 1.0 KbT)
           (/ (- (+ 2.0 (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT)) EDonor)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -7e-55) {
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (NaChar <= 2.12e-47) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	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 - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-7d-55)) then
        tmp = t_0 + (ndchar / (mu * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu))))
    else if (nachar <= 2.12d-47) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = t_0 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (mu / kbt))) - (ec / kbt)) / edonor))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -7e-55) {
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (NaChar <= 2.12e-47) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -7e-55:
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))))
	elif NaChar <= 2.12e-47:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -7e-55)
		tmp = Float64(t_0 + Float64(NdChar / Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu)))));
	elseif (NaChar <= 2.12e-47)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)) / EDonor)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -7e-55)
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	elseif (NaChar <= 2.12e-47)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -7e-55], N[(t$95$0 + N[(NdChar / N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.12e-47], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -7.00000000000000051e-55

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.0%

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

   6. Taylor expanded in mu around -inf 75.2%

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

   if -7.00000000000000051e-55 < NaChar < 2.12e-47

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 84.9%

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

   6. Taylor expanded in EDonor around 0 79.0%

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

   if 2.12e-47 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 58.6%

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

   6. Taylor expanded in EDonor around -inf 70.5%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7 \cdot 10^{-55}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;NaChar \leq 2.12 \cdot 10^{-47}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / 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[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 12: 64.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := t\_0 - \frac{NdChar}{\frac{Ec}{KbT} + \left(mu \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{mu \cdot KbT} + \frac{EDonor}{mu \cdot KbT}\right)\right) - 2\right)}\\ t_2 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -3.2 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 3600000:\\ \;\;\;\;t\_0 + \frac{NdChar}{\frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 7.6 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 5 \cdot 10^{+110} \lor \neg \left(NaChar \leq 2.4 \cdot 10^{+245}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1
         (-
          t_0
          (/
           NdChar
           (+
            (/ Ec KbT)
            (-
             (*
              mu
              (- (/ -1.0 KbT) (+ (/ Vef (* mu KbT)) (/ EDonor (* mu KbT)))))
             2.0)))))
        (t_2
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))
   (if (<= NaChar -3.2e-17)
     t_1
     (if (<= NaChar 1.85e-51)
       t_2
       (if (<= NaChar 3600000.0)
         (+
          t_0
          (/ NdChar (/ (* EDonor (+ 1.0 (/ (- (+ mu Vef) Ec) EDonor))) KbT)))
         (if (<= NaChar 7.6e+25)
           t_2
           (if (or (<= NaChar 5e+110) (not (<= NaChar 2.4e+245)))
             t_1
             (+
              t_0
              (/
               NdChar
               (*
                Ec
                (+
                 (/ (+ 2.0 (+ (+ (/ Vef KbT) (/ mu KbT)) (/ EDonor KbT))) Ec)
                 (/ -1.0 KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)));
	double t_2 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NaChar <= -3.2e-17) {
		tmp = t_1;
	} else if (NaChar <= 1.85e-51) {
		tmp = t_2;
	} else if (NaChar <= 3600000.0) {
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	} else if (NaChar <= 7.6e+25) {
		tmp = t_2;
	} else if ((NaChar <= 5e+110) || !(NaChar <= 2.4e+245)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / 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) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = t_0 - (ndchar / ((ec / kbt) + ((mu * (((-1.0d0) / kbt) - ((vef / (mu * kbt)) + (edonor / (mu * kbt))))) - 2.0d0)))
    t_2 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    if (nachar <= (-3.2d-17)) then
        tmp = t_1
    else if (nachar <= 1.85d-51) then
        tmp = t_2
    else if (nachar <= 3600000.0d0) then
        tmp = t_0 + (ndchar / ((edonor * (1.0d0 + (((mu + vef) - ec) / edonor))) / kbt))
    else if (nachar <= 7.6d+25) then
        tmp = t_2
    else if ((nachar <= 5d+110) .or. (.not. (nachar <= 2.4d+245))) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (ec * (((2.0d0 + (((vef / kbt) + (mu / kbt)) + (edonor / kbt))) / ec) + ((-1.0d0) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)));
	double t_2 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NaChar <= -3.2e-17) {
		tmp = t_1;
	} else if (NaChar <= 1.85e-51) {
		tmp = t_2;
	} else if (NaChar <= 3600000.0) {
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	} else if (NaChar <= 7.6e+25) {
		tmp = t_2;
	} else if ((NaChar <= 5e+110) || !(NaChar <= 2.4e+245)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)))
	t_2 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	tmp = 0
	if NaChar <= -3.2e-17:
		tmp = t_1
	elif NaChar <= 1.85e-51:
		tmp = t_2
	elif NaChar <= 3600000.0:
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT))
	elif NaChar <= 7.6e+25:
		tmp = t_2
	elif (NaChar <= 5e+110) or not (NaChar <= 2.4e+245):
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(t_0 - Float64(NdChar / Float64(Float64(Ec / KbT) + Float64(Float64(mu * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(mu * KbT)) + Float64(EDonor / Float64(mu * KbT))))) - 2.0))))
	t_2 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	tmp = 0.0
	if (NaChar <= -3.2e-17)
		tmp = t_1;
	elseif (NaChar <= 1.85e-51)
		tmp = t_2;
	elseif (NaChar <= 3600000.0)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(EDonor * Float64(1.0 + Float64(Float64(Float64(mu + Vef) - Ec) / EDonor))) / KbT)));
	elseif (NaChar <= 7.6e+25)
		tmp = t_2;
	elseif ((NaChar <= 5e+110) || !(NaChar <= 2.4e+245))
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(Float64(Vef / KbT) + Float64(mu / KbT)) + Float64(EDonor / KbT))) / Ec) + Float64(-1.0 / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)));
	t_2 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	tmp = 0.0;
	if (NaChar <= -3.2e-17)
		tmp = t_1;
	elseif (NaChar <= 1.85e-51)
		tmp = t_2;
	elseif (NaChar <= 3600000.0)
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	elseif (NaChar <= 7.6e+25)
		tmp = t_2;
	elseif ((NaChar <= 5e+110) || ~((NaChar <= 2.4e+245)))
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - N[(NdChar / N[(N[(Ec / KbT), $MachinePrecision] + N[(N[(mu * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(Vef / N[(mu * KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -3.2e-17], t$95$1, If[LessEqual[NaChar, 1.85e-51], t$95$2, If[LessEqual[NaChar, 3600000.0], N[(t$95$0 + N[(NdChar / N[(N[(EDonor * N[(1.0 + N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 7.6e+25], t$95$2, If[Or[LessEqual[NaChar, 5e+110], N[Not[LessEqual[NaChar, 2.4e+245]], $MachinePrecision]], t$95$1, N[(t$95$0 + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -3.2000000000000002e-17 or 7.6000000000000001e25 < NaChar < 4.99999999999999978e110 or 2.3999999999999998e245 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.6%

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

   6. Taylor expanded in mu around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. *-commutative 73.0%

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

      3. *-commutative 73.0%

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

   8. Simplified 73.0%

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

   if -3.2000000000000002e-17 < NaChar < 1.84999999999999987e-51 or 3.6e6 < NaChar < 7.6000000000000001e25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 84.6%

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

   6. Taylor expanded in EAccept around 0 75.7%

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

      1. +-commutative 75.7%

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

   8. Simplified 75.7%

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

   if 1.84999999999999987e-51 < NaChar < 3.6e6

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 47.9%

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

   6. Taylor expanded in EDonor around -inf 69.2%

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

   7. Taylor expanded in KbT around 0 69.8%

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

   if 4.99999999999999978e110 < NaChar < 2.3999999999999998e245

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 73.9%

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

   6. Taylor expanded in Ec around -inf 81.6%

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

      1. associate-*r* 81.6%

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

      2. mul-1-neg 81.6%

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

      3. +-commutative 81.6%

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

      4. mul-1-neg 81.6%

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

      5. unsub-neg 81.6%

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

      6. +-commutative 81.6%

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

   8. Simplified 81.6%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{\frac{Ec}{KbT} + \left(mu \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{mu \cdot KbT} + \frac{EDonor}{mu \cdot KbT}\right)\right) - 2\right)}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-51}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 3600000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 7.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 5 \cdot 10^{+110} \lor \neg \left(NaChar \leq 2.4 \cdot 10^{+245}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{\frac{Ec}{KbT} + \left(mu \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{mu \cdot KbT} + \frac{EDonor}{mu \cdot KbT}\right)\right) - 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.65 \cdot 10^{-20}:\\ \;\;\;\;t\_1 + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;NaChar \leq 6.5 \cdot 10^{-96}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 54000000:\\ \;\;\;\;t\_1 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} - mu \cdot \left(\frac{\left(\frac{\frac{Ec}{EDonor}}{KbT} - \frac{Vef}{EDonor \cdot KbT}\right) - \frac{2}{EDonor}}{mu} + \frac{-1}{EDonor \cdot KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq 4.2 \cdot 10^{+31}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ (/ EAccept KbT) 2.0))
          (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -1.65e-20)
     (+
      t_1
      (/
       NdChar
       (*
        mu
        (+
         (/ 1.0 KbT)
         (/ (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)) mu)))))
     (if (<= NaChar 6.5e-96)
       t_0
       (if (<= NaChar 54000000.0)
         (+
          t_1
          (/
           NdChar
           (*
            EDonor
            (-
             (/ 1.0 KbT)
             (*
              mu
              (+
               (/
                (-
                 (- (/ (/ Ec EDonor) KbT) (/ Vef (* EDonor KbT)))
                 (/ 2.0 EDonor))
                mu)
               (/ -1.0 (* EDonor KbT))))))))
         (if (<= NaChar 4.2e+31)
           t_0
           (+
            t_1
            (/
             NdChar
             (*
              EDonor
              (+
               (/ 1.0 KbT)
               (/
                (- (+ 2.0 (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))
                EDonor)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -1.65e-20) {
		tmp = t_1 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (NaChar <= 6.5e-96) {
		tmp = t_0;
	} else if (NaChar <= 54000000.0) {
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) - (mu * ((((((Ec / EDonor) / KbT) - (Vef / (EDonor * KbT))) - (2.0 / EDonor)) / mu) + (-1.0 / (EDonor * KbT)))))));
	} else if (NaChar <= 4.2e+31) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-1.65d-20)) then
        tmp = t_1 + (ndchar / (mu * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu))))
    else if (nachar <= 6.5d-96) then
        tmp = t_0
    else if (nachar <= 54000000.0d0) then
        tmp = t_1 + (ndchar / (edonor * ((1.0d0 / kbt) - (mu * ((((((ec / edonor) / kbt) - (vef / (edonor * kbt))) - (2.0d0 / edonor)) / mu) + ((-1.0d0) / (edonor * kbt)))))))
    else if (nachar <= 4.2d+31) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (mu / kbt))) - (ec / kbt)) / edonor))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -1.65e-20) {
		tmp = t_1 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (NaChar <= 6.5e-96) {
		tmp = t_0;
	} else if (NaChar <= 54000000.0) {
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) - (mu * ((((((Ec / EDonor) / KbT) - (Vef / (EDonor * KbT))) - (2.0 / EDonor)) / mu) + (-1.0 / (EDonor * KbT)))))));
	} else if (NaChar <= 4.2e+31) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -1.65e-20:
		tmp = t_1 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))))
	elif NaChar <= 6.5e-96:
		tmp = t_0
	elif NaChar <= 54000000.0:
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) - (mu * ((((((Ec / EDonor) / KbT) - (Vef / (EDonor * KbT))) - (2.0 / EDonor)) / mu) + (-1.0 / (EDonor * KbT)))))))
	elif NaChar <= 4.2e+31:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.65e-20)
		tmp = Float64(t_1 + Float64(NdChar / Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu)))));
	elseif (NaChar <= 6.5e-96)
		tmp = t_0;
	elseif (NaChar <= 54000000.0)
		tmp = Float64(t_1 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) - Float64(mu * Float64(Float64(Float64(Float64(Float64(Float64(Ec / EDonor) / KbT) - Float64(Vef / Float64(EDonor * KbT))) - Float64(2.0 / EDonor)) / mu) + Float64(-1.0 / Float64(EDonor * KbT))))))));
	elseif (NaChar <= 4.2e+31)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)) / EDonor)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.65e-20)
		tmp = t_1 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	elseif (NaChar <= 6.5e-96)
		tmp = t_0;
	elseif (NaChar <= 54000000.0)
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) - (mu * ((((((Ec / EDonor) / KbT) - (Vef / (EDonor * KbT))) - (2.0 / EDonor)) / mu) + (-1.0 / (EDonor * KbT)))))));
	elseif (NaChar <= 4.2e+31)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.65e-20], N[(t$95$1 + N[(NdChar / N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 6.5e-96], t$95$0, If[LessEqual[NaChar, 54000000.0], N[(t$95$1 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] - N[(mu * N[(N[(N[(N[(N[(N[(Ec / EDonor), $MachinePrecision] / KbT), $MachinePrecision] - N[(Vef / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 / EDonor), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(-1.0 / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.2e+31], t$95$0, N[(t$95$1 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.65e-20

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.4%

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

   6. Taylor expanded in mu around -inf 75.2%

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

   if -1.65e-20 < NaChar < 6.50000000000000001e-96 or 5.4e7 < NaChar < 4.19999999999999958e31

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 85.1%

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

   6. Taylor expanded in EAccept around 0 78.2%

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

      1. +-commutative 78.2%

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

   8. Simplified 78.2%

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

   if 6.50000000000000001e-96 < NaChar < 5.4e7

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 42.9%

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

   6. Taylor expanded in EDonor around -inf 59.9%

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

   7. Taylor expanded in mu around -inf 64.3%

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

      1. associate-*r* 64.3%

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

      2. neg-mul-1 64.3%

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

      3. associate-*r/ 64.3%

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

      4. mul-1-neg 64.3%

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

      5. associate--l+ 64.3%

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

      6. associate-*r/ 64.3%

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

      7. metadata-eval 64.3%

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

      8. *-commutative 64.3%

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

      9. associate-/r* 68.6%

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

      10. *-commutative 68.6%

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

   9. Simplified 68.6%

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

   if 4.19999999999999958e31 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.3%

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

   6. Taylor expanded in EDonor around -inf 74.2%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.65 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;NaChar \leq 6.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 54000000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} - mu \cdot \left(\frac{\left(\frac{\frac{Ec}{EDonor}}{KbT} - \frac{Vef}{EDonor \cdot KbT}\right) - \frac{2}{EDonor}}{mu} + \frac{-1}{EDonor \cdot KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq 4.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -4.6 \cdot 10^{-20} \lor \neg \left(NaChar \leq 3.9 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -4.6e-20) (not (<= NaChar 3.9e-95)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/
     NdChar
     (*
      Ec
      (+
       (/ (+ 2.0 (+ (+ (/ Vef KbT) (/ mu KbT)) (/ EDonor KbT))) Ec)
       (/ -1.0 KbT)))))
   (-
    (/ NaChar (+ (/ EAccept KbT) 2.0))
    (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -4.6e-20) || !(NaChar <= 3.9e-95)) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	} else {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-4.6d-20)) .or. (.not. (nachar <= 3.9d-95))) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / (ec * (((2.0d0 + (((vef / kbt) + (mu / kbt)) + (edonor / kbt))) / ec) + ((-1.0d0) / kbt))))
    else
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -4.6e-20) || !(NaChar <= 3.9e-95)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	} else {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -4.6e-20) or not (NaChar <= 3.9e-95):
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))))
	else:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -4.6e-20) || !(NaChar <= 3.9e-95))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(Ec * Float64(Float64(Float64(2.0 + Float64(Float64(Float64(Vef / KbT) + Float64(mu / KbT)) + Float64(EDonor / KbT))) / Ec) + Float64(-1.0 / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -4.6e-20) || ~((NaChar <= 3.9e-95)))
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (Ec * (((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) / Ec) + (-1.0 / KbT))));
	else
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -4.6e-20], N[Not[LessEqual[NaChar, 3.9e-95]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(Ec * N[(N[(N[(2.0 + N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.5999999999999998e-20 or 3.9e-95 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.0%

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

   6. Taylor expanded in Ec around -inf 65.8%

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

      1. associate-*r* 65.8%

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

      2. mul-1-neg 65.8%

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

      3. +-commutative 65.8%

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

      4. mul-1-neg 65.8%

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

      5. unsub-neg 65.8%

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

      6. +-commutative 65.8%

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

   8. Simplified 65.8%

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

   if -4.5999999999999998e-20 < NaChar < 3.9e-95

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 86.2%

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

   6. Taylor expanded in EAccept around 0 78.1%

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

      1. +-commutative 78.1%

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

   8. Simplified 78.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.6 \cdot 10^{-20} \lor \neg \left(NaChar \leq 3.9 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{Ec \cdot \left(\frac{2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -5.4 \cdot 10^{-21}:\\ \;\;\;\;t\_0 + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;NaChar \leq 3.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -5.4e-21)
     (+
      t_0
      (/
       NdChar
       (*
        mu
        (+
         (/ 1.0 KbT)
         (/ (- (+ 2.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)) mu)))))
     (if (<= NaChar 3.7e-95)
       (-
        (/ NaChar (+ (/ EAccept KbT) 2.0))
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (+
        t_0
        (/
         NdChar
         (*
          EDonor
          (+
           (/ 1.0 KbT)
           (/ (- (+ 2.0 (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT)) EDonor)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -5.4e-21) {
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (NaChar <= 3.7e-95) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	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 - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-5.4d-21)) then
        tmp = t_0 + (ndchar / (mu * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu))))
    else if (nachar <= 3.7d-95) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else
        tmp = t_0 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (mu / kbt))) - (ec / kbt)) / edonor))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -5.4e-21) {
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	} else if (NaChar <= 3.7e-95) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -5.4e-21:
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))))
	elif NaChar <= 3.7e-95:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	else:
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -5.4e-21)
		tmp = Float64(t_0 + Float64(NdChar / Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu)))));
	elseif (NaChar <= 3.7e-95)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)) / EDonor)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -5.4e-21)
		tmp = t_0 + (NdChar / (mu * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu))));
	elseif (NaChar <= 3.7e-95)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	else
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -5.4e-21], N[(t$95$0 + N[(NdChar / N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.7e-95], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -5.4000000000000002e-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. Add Preprocessing

   5. Taylor expanded in KbT around inf 64.4%

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

   6. Taylor expanded in mu around -inf 75.2%

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

   if -5.4000000000000002e-21 < NaChar < 3.69999999999999994e-95

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 86.2%

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

   6. Taylor expanded in EAccept around 0 78.1%

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

      1. +-commutative 78.1%

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

   8. Simplified 78.1%

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

   if 3.69999999999999994e-95 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.0%

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

   6. Taylor expanded in EDonor around -inf 68.8%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.4 \cdot 10^{-21}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{mu \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu}\right)}\\ \mathbf{elif}\;NaChar \leq 3.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 65.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -7 \cdot 10^{-12}:\\ \;\;\;\;t\_0 - \frac{NdChar}{\frac{Ec}{KbT} + \left(mu \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{mu \cdot KbT} + \frac{EDonor}{mu \cdot KbT}\right)\right) - 2\right)}\\ \mathbf{elif}\;NaChar \leq 3.1 \cdot 10^{-95}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -7e-12)
     (-
      t_0
      (/
       NdChar
       (+
        (/ Ec KbT)
        (-
         (* mu (- (/ -1.0 KbT) (+ (/ Vef (* mu KbT)) (/ EDonor (* mu KbT)))))
         2.0))))
     (if (<= NaChar 3.1e-95)
       (-
        (/ NaChar (+ (/ EAccept KbT) 2.0))
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (+
        t_0
        (/
         NdChar
         (*
          EDonor
          (+
           (/ 1.0 KbT)
           (/ (- (+ 2.0 (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT)) EDonor)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -7e-12) {
		tmp = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)));
	} else if (NaChar <= 3.1e-95) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	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 - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-7d-12)) then
        tmp = t_0 - (ndchar / ((ec / kbt) + ((mu * (((-1.0d0) / kbt) - ((vef / (mu * kbt)) + (edonor / (mu * kbt))))) - 2.0d0)))
    else if (nachar <= 3.1d-95) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else
        tmp = t_0 + (ndchar / (edonor * ((1.0d0 / kbt) + (((2.0d0 + ((vef / kbt) + (mu / kbt))) - (ec / kbt)) / edonor))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -7e-12) {
		tmp = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)));
	} else if (NaChar <= 3.1e-95) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -7e-12:
		tmp = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)))
	elif NaChar <= 3.1e-95:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	else:
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -7e-12)
		tmp = Float64(t_0 - Float64(NdChar / Float64(Float64(Ec / KbT) + Float64(Float64(mu * Float64(Float64(-1.0 / KbT) - Float64(Float64(Vef / Float64(mu * KbT)) + Float64(EDonor / Float64(mu * KbT))))) - 2.0))));
	elseif (NaChar <= 3.1e-95)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)) / EDonor)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -7e-12)
		tmp = t_0 - (NdChar / ((Ec / KbT) + ((mu * ((-1.0 / KbT) - ((Vef / (mu * KbT)) + (EDonor / (mu * KbT))))) - 2.0)));
	elseif (NaChar <= 3.1e-95)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	else
		tmp = t_0 + (NdChar / (EDonor * ((1.0 / KbT) + (((2.0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)) / EDonor))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -7e-12], N[(t$95$0 - N[(NdChar / N[(N[(Ec / KbT), $MachinePrecision] + N[(N[(mu * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(N[(Vef / N[(mu * KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.1e-95], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -7.0000000000000001e-12

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.8%

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

   6. Taylor expanded in mu around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. *-commutative 73.0%

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

      3. *-commutative 73.0%

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

   8. Simplified 73.0%

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

   if -7.0000000000000001e-12 < NaChar < 3.09999999999999992e-95

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 86.4%

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

   6. Taylor expanded in EAccept around 0 77.4%

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

      1. +-commutative 77.4%

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

   8. Simplified 77.4%

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

   if 3.09999999999999992e-95 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.0%

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

   6. Taylor expanded in EDonor around -inf 68.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7 \cdot 10^{-12}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{\frac{Ec}{KbT} + \left(mu \cdot \left(\frac{-1}{KbT} - \left(\frac{Vef}{mu \cdot KbT} + \frac{EDonor}{mu \cdot KbT}\right)\right) - 2\right)}\\ \mathbf{elif}\;NaChar \leq 3.1 \cdot 10^{-95}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{EDonor \cdot \left(\frac{1}{KbT} + \frac{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}{EDonor}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 64.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2 \cdot 10^{-14}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} - mu \cdot \left(\frac{-1}{KbT} - \frac{Vef}{mu \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-51}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -2e-14)
     (+
      t_0
      (/
       NdChar
       (-
        (+ 2.0 (- (/ EDonor KbT) (* mu (- (/ -1.0 KbT) (/ Vef (* mu KbT))))))
        (/ Ec KbT))))
     (if (<= NaChar 1.85e-51)
       (-
        (/ NaChar (+ (/ EAccept KbT) 2.0))
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (+
        t_0
        (/ NdChar (/ (* EDonor (+ 1.0 (/ (- (+ mu Vef) Ec) EDonor))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2e-14) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) - (mu * ((-1.0 / KbT) - (Vef / (mu * KbT)))))) - (Ec / KbT)));
	} else if (NaChar <= 1.85e-51) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-2d-14)) then
        tmp = t_0 + (ndchar / ((2.0d0 + ((edonor / kbt) - (mu * (((-1.0d0) / kbt) - (vef / (mu * kbt)))))) - (ec / kbt)))
    else if (nachar <= 1.85d-51) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else
        tmp = t_0 + (ndchar / ((edonor * (1.0d0 + (((mu + vef) - ec) / edonor))) / kbt))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2e-14) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) - (mu * ((-1.0 / KbT) - (Vef / (mu * KbT)))))) - (Ec / KbT)));
	} else if (NaChar <= 1.85e-51) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -2e-14:
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) - (mu * ((-1.0 / KbT) - (Vef / (mu * KbT)))))) - (Ec / KbT)))
	elif NaChar <= 1.85e-51:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	else:
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -2e-14)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) - Float64(mu * Float64(Float64(-1.0 / KbT) - Float64(Vef / Float64(mu * KbT)))))) - Float64(Ec / KbT))));
	elseif (NaChar <= 1.85e-51)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(EDonor * Float64(1.0 + Float64(Float64(Float64(mu + Vef) - Ec) / EDonor))) / KbT)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2e-14)
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) - (mu * ((-1.0 / KbT) - (Vef / (mu * KbT)))))) - (Ec / KbT)));
	elseif (NaChar <= 1.85e-51)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	else
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2e-14], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] - N[(mu * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(Vef / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.85e-51], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(N[(EDonor * N[(1.0 + N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2e-14

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.8%

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

   6. Taylor expanded in mu around inf 70.0%

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

      1. *-commutative 70.0%

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

   8. Simplified 70.0%

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

   if -2e-14 < NaChar < 1.84999999999999987e-51

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 84.8%

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

   6. Taylor expanded in EAccept around 0 75.4%

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

      1. +-commutative 75.4%

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

   8. Simplified 75.4%

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

   if 1.84999999999999987e-51 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.9%

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

   6. Taylor expanded in EDonor around -inf 69.7%

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

   7. Taylor expanded in KbT around 0 62.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} - mu \cdot \left(\frac{-1}{KbT} - \frac{Vef}{mu \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-51}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.08 \cdot 10^{-44}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00037:\\ \;\;\;\;t\_0 + \frac{NdChar}{\frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 9.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -7.5e-14)
     (+ t_0 (/ NdChar 2.0))
     (if (<= NaChar 1.08e-44)
       (-
        (* NaChar 0.5)
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (if (<= NaChar 0.00037)
         (+ t_0 (/ NdChar (/ EDonor KbT)))
         (if (<= NaChar 9.2e+48)
           (-
            (/ NaChar (+ (/ Vef KbT) 2.0))
            (/ NdChar (- -1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
           (-
            (/ NdChar 2.0)
            (*
             NaChar
             (/
              1.0
              (- -1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -7.5e-14) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 1.08e-44) {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 0.00037) {
		tmp = t_0 + (NdChar / (EDonor / KbT));
	} else if (NaChar <= 9.2e+48) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - 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) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-7.5d-14)) then
        tmp = t_0 + (ndchar / 2.0d0)
    else if (nachar <= 1.08d-44) then
        tmp = (nachar * 0.5d0) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else if (nachar <= 0.00037d0) then
        tmp = t_0 + (ndchar / (edonor / kbt))
    else if (nachar <= 9.2d+48) then
        tmp = (nachar / ((vef / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp((((mu + vef) - ec) / kbt))))
    else
        tmp = (ndchar / 2.0d0) - (nachar * (1.0d0 / ((-1.0d0) - exp(((vef + (eaccept + (ev - 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 t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -7.5e-14) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 1.08e-44) {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 0.00037) {
		tmp = t_0 + (NdChar / (EDonor / KbT));
	} else if (NaChar <= 9.2e+48) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -7.5e-14:
		tmp = t_0 + (NdChar / 2.0)
	elif NaChar <= 1.08e-44:
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	elif NaChar <= 0.00037:
		tmp = t_0 + (NdChar / (EDonor / KbT))
	elif NaChar <= 9.2e+48:
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -7.5e-14)
		tmp = Float64(t_0 + Float64(NdChar / 2.0));
	elseif (NaChar <= 1.08e-44)
		tmp = Float64(Float64(NaChar * 0.5) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	elseif (NaChar <= 0.00037)
		tmp = Float64(t_0 + Float64(NdChar / Float64(EDonor / KbT)));
	elseif (NaChar <= 9.2e+48)
		tmp = Float64(Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar * Float64(1.0 / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -7.5e-14)
		tmp = t_0 + (NdChar / 2.0);
	elseif (NaChar <= 1.08e-44)
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	elseif (NaChar <= 0.00037)
		tmp = t_0 + (NdChar / (EDonor / KbT));
	elseif (NaChar <= 9.2e+48)
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -7.5e-14], N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.08e-44], N[(N[(NaChar * 0.5), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 0.00037], N[(t$95$0 + N[(NdChar / N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 9.2e+48], N[(N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar * N[(1.0 / N[(-1.0 - N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -7.4999999999999996e-14

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 61.9%

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

   if -7.4999999999999996e-14 < NaChar < 1.07999999999999994e-44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   if 1.07999999999999994e-44 < NaChar < 3.6999999999999999e-4

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.0%

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

   6. Taylor expanded in EDonor around inf 67.7%

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

   if 3.6999999999999999e-4 < NaChar < 9.2000000000000001e48

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 60.8%

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

   6. Taylor expanded in Vef around 0 45.4%

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

      1. +-commutative 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in EDonor around 0 45.4%

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

   if 9.2000000000000001e48 < NaChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. div-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 58.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.08 \cdot 10^{-44}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00037:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 9.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 57.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.09 \cdot 10^{-44}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00037:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{elif}\;NaChar \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -4.5e-11)
     (+ t_0 (/ NdChar 2.0))
     (if (<= NaChar 1.09e-44)
       (-
        (* NaChar 0.5)
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (if (<= NaChar 0.00037)
         (+ t_0 (* KbT (/ NdChar EDonor)))
         (if (<= NaChar 3.8e+49)
           (-
            (/ NaChar (+ (/ Vef KbT) 2.0))
            (/ NdChar (- -1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
           (-
            (/ NdChar 2.0)
            (*
             NaChar
             (/
              1.0
              (- -1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -4.5e-11) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 1.09e-44) {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 0.00037) {
		tmp = t_0 + (KbT * (NdChar / EDonor));
	} else if (NaChar <= 3.8e+49) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - 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) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-4.5d-11)) then
        tmp = t_0 + (ndchar / 2.0d0)
    else if (nachar <= 1.09d-44) then
        tmp = (nachar * 0.5d0) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else if (nachar <= 0.00037d0) then
        tmp = t_0 + (kbt * (ndchar / edonor))
    else if (nachar <= 3.8d+49) then
        tmp = (nachar / ((vef / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp((((mu + vef) - ec) / kbt))))
    else
        tmp = (ndchar / 2.0d0) - (nachar * (1.0d0 / ((-1.0d0) - exp(((vef + (eaccept + (ev - 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 t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -4.5e-11) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 1.09e-44) {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 0.00037) {
		tmp = t_0 + (KbT * (NdChar / EDonor));
	} else if (NaChar <= 3.8e+49) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -4.5e-11:
		tmp = t_0 + (NdChar / 2.0)
	elif NaChar <= 1.09e-44:
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	elif NaChar <= 0.00037:
		tmp = t_0 + (KbT * (NdChar / EDonor))
	elif NaChar <= 3.8e+49:
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -4.5e-11)
		tmp = Float64(t_0 + Float64(NdChar / 2.0));
	elseif (NaChar <= 1.09e-44)
		tmp = Float64(Float64(NaChar * 0.5) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	elseif (NaChar <= 0.00037)
		tmp = Float64(t_0 + Float64(KbT * Float64(NdChar / EDonor)));
	elseif (NaChar <= 3.8e+49)
		tmp = Float64(Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar * Float64(1.0 / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -4.5e-11)
		tmp = t_0 + (NdChar / 2.0);
	elseif (NaChar <= 1.09e-44)
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	elseif (NaChar <= 0.00037)
		tmp = t_0 + (KbT * (NdChar / EDonor));
	elseif (NaChar <= 3.8e+49)
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.5e-11], N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.09e-44], N[(N[(NaChar * 0.5), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 0.00037], N[(t$95$0 + N[(KbT * N[(NdChar / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.8e+49], N[(N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar * N[(1.0 / N[(-1.0 - N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -4.5e-11

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 61.9%

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

   if -4.5e-11 < NaChar < 1.09e-44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   if 1.09e-44 < NaChar < 3.6999999999999999e-4

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.0%

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

   6. Taylor expanded in EDonor around -inf 78.3%

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

   7. Taylor expanded in EDonor around inf 67.7%

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

      1. associate-/l* 67.7%

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

   9. Simplified 67.7%

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

   if 3.6999999999999999e-4 < NaChar < 3.7999999999999999e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 60.8%

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

   6. Taylor expanded in Vef around 0 45.4%

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

      1. +-commutative 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in EDonor around 0 45.4%

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

   if 3.7999999999999999e49 < NaChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. div-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 58.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.09 \cdot 10^{-44}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00037:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{elif}\;NaChar \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 56.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 8.8 \cdot 10^{-45}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00091:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{elif}\;NaChar \leq 9.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -3.2e-15)
     (+ t_0 (/ NdChar 2.0))
     (if (<= NaChar 8.8e-45)
       (-
        (* NaChar 0.5)
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (if (<= NaChar 0.00091)
         (+ t_0 (* KbT (/ NdChar EDonor)))
         (if (<= NaChar 9.8e+48)
           (-
            (/ NaChar (+ (/ Vef KbT) 2.0))
            (/ NdChar (- -1.0 (exp (/ Vef KbT)))))
           (-
            (/ NdChar 2.0)
            (*
             NaChar
             (/
              1.0
              (- -1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -3.2e-15) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 8.8e-45) {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 0.00091) {
		tmp = t_0 + (KbT * (NdChar / EDonor));
	} else if (NaChar <= 9.8e+48) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - exp((Vef / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - 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) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-3.2d-15)) then
        tmp = t_0 + (ndchar / 2.0d0)
    else if (nachar <= 8.8d-45) then
        tmp = (nachar * 0.5d0) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else if (nachar <= 0.00091d0) then
        tmp = t_0 + (kbt * (ndchar / edonor))
    else if (nachar <= 9.8d+48) then
        tmp = (nachar / ((vef / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp((vef / kbt))))
    else
        tmp = (ndchar / 2.0d0) - (nachar * (1.0d0 / ((-1.0d0) - exp(((vef + (eaccept + (ev - 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 t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -3.2e-15) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 8.8e-45) {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 0.00091) {
		tmp = t_0 + (KbT * (NdChar / EDonor));
	} else if (NaChar <= 9.8e+48) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp((Vef / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -3.2e-15:
		tmp = t_0 + (NdChar / 2.0)
	elif NaChar <= 8.8e-45:
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	elif NaChar <= 0.00091:
		tmp = t_0 + (KbT * (NdChar / EDonor))
	elif NaChar <= 9.8e+48:
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp((Vef / KbT))))
	else:
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -3.2e-15)
		tmp = Float64(t_0 + Float64(NdChar / 2.0));
	elseif (NaChar <= 8.8e-45)
		tmp = Float64(Float64(NaChar * 0.5) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	elseif (NaChar <= 0.00091)
		tmp = Float64(t_0 + Float64(KbT * Float64(NdChar / EDonor)));
	elseif (NaChar <= 9.8e+48)
		tmp = Float64(Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Vef / KbT)))));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar * Float64(1.0 / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -3.2e-15)
		tmp = t_0 + (NdChar / 2.0);
	elseif (NaChar <= 8.8e-45)
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	elseif (NaChar <= 0.00091)
		tmp = t_0 + (KbT * (NdChar / EDonor));
	elseif (NaChar <= 9.8e+48)
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - exp((Vef / KbT))));
	else
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -3.2e-15], N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8.8e-45], N[(N[(NaChar * 0.5), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 0.00091], N[(t$95$0 + N[(KbT * N[(NdChar / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 9.8e+48], N[(N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar * N[(1.0 / N[(-1.0 - N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -3.1999999999999999e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 61.9%

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

   if -3.1999999999999999e-15 < NaChar < 8.79999999999999974e-45

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   if 8.79999999999999974e-45 < NaChar < 9.1e-4

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.0%

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

   6. Taylor expanded in EDonor around -inf 78.3%

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

   7. Taylor expanded in EDonor around inf 67.7%

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

      1. associate-/l* 67.7%

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

   9. Simplified 67.7%

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

   if 9.1e-4 < NaChar < 9.80000000000000059e48

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 60.8%

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

   6. Taylor expanded in Vef around 0 45.4%

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

      1. +-commutative 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in EDonor around 0 45.4%

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

   10. Taylor expanded in Vef around inf 45.2%

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

   if 9.80000000000000059e48 < NaChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. div-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 58.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 8.8 \cdot 10^{-45}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00091:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{elif}\;NaChar \leq 9.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 63.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{-20}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-51}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -6.8e-20)
     (+
      t_0
      (/
       NdChar
       (- (+ 2.0 (+ (+ (/ Vef KbT) (/ mu KbT)) (/ EDonor KbT))) (/ Ec KbT))))
     (if (<= NaChar 1.85e-51)
       (-
        (/ NaChar (+ (/ EAccept KbT) 2.0))
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (+
        t_0
        (/ NdChar (/ (* EDonor (+ 1.0 (/ (- (+ mu Vef) Ec) EDonor))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -6.8e-20) {
		tmp = t_0 + (NdChar / ((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) - (Ec / KbT)));
	} else if (NaChar <= 1.85e-51) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-6.8d-20)) then
        tmp = t_0 + (ndchar / ((2.0d0 + (((vef / kbt) + (mu / kbt)) + (edonor / kbt))) - (ec / kbt)))
    else if (nachar <= 1.85d-51) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else
        tmp = t_0 + (ndchar / ((edonor * (1.0d0 + (((mu + vef) - ec) / edonor))) / kbt))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -6.8e-20) {
		tmp = t_0 + (NdChar / ((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) - (Ec / KbT)));
	} else if (NaChar <= 1.85e-51) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -6.8e-20:
		tmp = t_0 + (NdChar / ((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) - (Ec / KbT)))
	elif NaChar <= 1.85e-51:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	else:
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -6.8e-20)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(Float64(Vef / KbT) + Float64(mu / KbT)) + Float64(EDonor / KbT))) - Float64(Ec / KbT))));
	elseif (NaChar <= 1.85e-51)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(EDonor * Float64(1.0 + Float64(Float64(Float64(mu + Vef) - Ec) / EDonor))) / KbT)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -6.8e-20)
		tmp = t_0 + (NdChar / ((2.0 + (((Vef / KbT) + (mu / KbT)) + (EDonor / KbT))) - (Ec / KbT)));
	elseif (NaChar <= 1.85e-51)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	else
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.8e-20], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.85e-51], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(N[(EDonor * N[(1.0 + N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -6.7999999999999994e-20

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.4%

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

   if -6.7999999999999994e-20 < NaChar < 1.84999999999999987e-51

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 84.6%

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

   6. Taylor expanded in EAccept around 0 76.1%

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

      1. +-commutative 76.1%

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

   8. Simplified 76.1%

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

   if 1.84999999999999987e-51 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.9%

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

   6. Taylor expanded in EDonor around -inf 69.7%

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

   7. Taylor expanded in KbT around 0 62.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right) + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-51}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 62.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -40000000000000:\\ \;\;\;\;t\_0 + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 6.6 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -40000000000000.0)
     (+ t_0 (/ NdChar 2.0))
     (if (<= NaChar 6.6e-52)
       (-
        (/ NaChar (+ (/ EAccept KbT) 2.0))
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (+
        t_0
        (/ NdChar (/ (* EDonor (+ 1.0 (/ (- (+ mu Vef) Ec) EDonor))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -40000000000000.0) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 6.6e-52) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-40000000000000.0d0)) then
        tmp = t_0 + (ndchar / 2.0d0)
    else if (nachar <= 6.6d-52) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else
        tmp = t_0 + (ndchar / ((edonor * (1.0d0 + (((mu + vef) - ec) / edonor))) / kbt))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -40000000000000.0) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 6.6e-52) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -40000000000000.0:
		tmp = t_0 + (NdChar / 2.0)
	elif NaChar <= 6.6e-52:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	else:
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -40000000000000.0)
		tmp = Float64(t_0 + Float64(NdChar / 2.0));
	elseif (NaChar <= 6.6e-52)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(EDonor * Float64(1.0 + Float64(Float64(Float64(mu + Vef) - Ec) / EDonor))) / KbT)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -40000000000000.0)
		tmp = t_0 + (NdChar / 2.0);
	elseif (NaChar <= 6.6e-52)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	else
		tmp = t_0 + (NdChar / ((EDonor * (1.0 + (((mu + Vef) - Ec) / EDonor))) / KbT));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -40000000000000.0], N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 6.6e-52], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(N[(EDonor * N[(1.0 + N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -4e13

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.0%

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

   if -4e13 < NaChar < 6.5999999999999999e-52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 83.1%

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

   6. Taylor expanded in EAccept around 0 73.5%

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

      1. +-commutative 73.5%

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

   8. Simplified 73.5%

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

   if 6.5999999999999999e-52 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.9%

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

   6. Taylor expanded in EDonor around -inf 69.7%

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

   7. Taylor expanded in KbT around 0 62.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -40000000000000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 6.6 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor \cdot \left(1 + \frac{\left(mu + Vef\right) - Ec}{EDonor}\right)}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 56.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 1.09 \cdot 10^{-44}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00037:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1 (+ t_0 (/ NdChar 2.0))))
   (if (<= NaChar -7.2e-14)
     t_1
     (if (<= NaChar 1.09e-44)
       (-
        (* NaChar 0.5)
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (if (<= NaChar 0.00037)
         (+ t_0 (* KbT (/ NdChar EDonor)))
         (if (<= NaChar 1.65e+49)
           (-
            (/ NaChar (+ (/ Vef KbT) 2.0))
            (/ NdChar (- -1.0 (exp (/ Vef KbT)))))
           t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -7.2e-14) {
		tmp = t_1;
	} else if (NaChar <= 1.09e-44) {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 0.00037) {
		tmp = t_0 + (KbT * (NdChar / EDonor));
	} else if (NaChar <= 1.65e+49) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - exp((Vef / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = t_0 + (ndchar / 2.0d0)
    if (nachar <= (-7.2d-14)) then
        tmp = t_1
    else if (nachar <= 1.09d-44) then
        tmp = (nachar * 0.5d0) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else if (nachar <= 0.00037d0) then
        tmp = t_0 + (kbt * (ndchar / edonor))
    else if (nachar <= 1.65d+49) then
        tmp = (nachar / ((vef / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp((vef / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -7.2e-14) {
		tmp = t_1;
	} else if (NaChar <= 1.09e-44) {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else if (NaChar <= 0.00037) {
		tmp = t_0 + (KbT * (NdChar / EDonor));
	} else if (NaChar <= 1.65e+49) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp((Vef / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = t_0 + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -7.2e-14:
		tmp = t_1
	elif NaChar <= 1.09e-44:
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	elif NaChar <= 0.00037:
		tmp = t_0 + (KbT * (NdChar / EDonor))
	elif NaChar <= 1.65e+49:
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp((Vef / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -7.2e-14)
		tmp = t_1;
	elseif (NaChar <= 1.09e-44)
		tmp = Float64(Float64(NaChar * 0.5) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	elseif (NaChar <= 0.00037)
		tmp = Float64(t_0 + Float64(KbT * Float64(NdChar / EDonor)));
	elseif (NaChar <= 1.65e+49)
		tmp = Float64(Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Vef / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = t_0 + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -7.2e-14)
		tmp = t_1;
	elseif (NaChar <= 1.09e-44)
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	elseif (NaChar <= 0.00037)
		tmp = t_0 + (KbT * (NdChar / EDonor));
	elseif (NaChar <= 1.65e+49)
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - exp((Vef / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -7.2e-14], t$95$1, If[LessEqual[NaChar, 1.09e-44], N[(N[(NaChar * 0.5), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 0.00037], N[(t$95$0 + N[(KbT * N[(NdChar / EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.65e+49], N[(N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -7.1999999999999996e-14 or 1.6499999999999999e49 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.0%

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

   if -7.1999999999999996e-14 < NaChar < 1.09e-44

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   if 1.09e-44 < NaChar < 3.6999999999999999e-4

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.0%

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

   6. Taylor expanded in EDonor around -inf 78.3%

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

   7. Taylor expanded in EDonor around inf 67.7%

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

      1. associate-/l* 67.7%

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

   9. Simplified 67.7%

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

   if 3.6999999999999999e-4 < NaChar < 1.6499999999999999e49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 60.8%

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

   6. Taylor expanded in Vef around 0 45.4%

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

      1. +-commutative 45.4%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in EDonor around 0 45.4%

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

   10. Taylor expanded in Vef around inf 45.2%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.09 \cdot 10^{-44}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 0.00037:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{+49}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 61.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1200000000:\\ \;\;\;\;t\_0 + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{-45}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -1200000000.0)
     (+ t_0 (/ NdChar 2.0))
     (if (<= NaChar 1.3e-45)
       (-
        (/ NaChar (+ (/ EAccept KbT) 2.0))
        (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
       (+ t_0 (/ NdChar (/ (- (+ EDonor (+ mu Vef)) Ec) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -1200000000.0) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 1.3e-45) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / (((EDonor + (mu + Vef)) - Ec) / KbT));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-1200000000.0d0)) then
        tmp = t_0 + (ndchar / 2.0d0)
    else if (nachar <= 1.3d-45) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else
        tmp = t_0 + (ndchar / (((edonor + (mu + vef)) - ec) / kbt))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -1200000000.0) {
		tmp = t_0 + (NdChar / 2.0);
	} else if (NaChar <= 1.3e-45) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = t_0 + (NdChar / (((EDonor + (mu + Vef)) - Ec) / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -1200000000.0:
		tmp = t_0 + (NdChar / 2.0)
	elif NaChar <= 1.3e-45:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	else:
		tmp = t_0 + (NdChar / (((EDonor + (mu + Vef)) - 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(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -1200000000.0)
		tmp = Float64(t_0 + Float64(NdChar / 2.0));
	elseif (NaChar <= 1.3e-45)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - 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 - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1200000000.0)
		tmp = t_0 + (NdChar / 2.0);
	elseif (NaChar <= 1.3e-45)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	else
		tmp = t_0 + (NdChar / (((EDonor + (mu + Vef)) - 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[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1200000000.0], N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.3e-45], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.2e9

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.0%

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

   if -1.2e9 < NaChar < 1.29999999999999993e-45

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 82.6%

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

   6. Taylor expanded in EAccept around 0 72.3%

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

      1. +-commutative 72.3%

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

   8. Simplified 72.3%

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

   if 1.29999999999999993e-45 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 59.3%

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

   6. Taylor expanded in KbT around 0 58.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1200000000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{-45}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 39.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -3.9 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -3.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 6.8 \cdot 10^{+195}:\\ \;\;\;\;\frac{NdChar}{2} + NaChar \cdot \frac{1}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))))
   (if (<= NaChar -3.9e+153)
     t_0
     (if (<= NaChar -3.1e-16)
       (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))
       (if (<= NaChar 2.9e-98)
         (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (* NaChar 0.5))
         (if (<= NaChar 6.8e+195)
           (+ (/ NdChar 2.0) (* NaChar (/ 1.0 (+ 1.0 (exp (/ mu (- KbT)))))))
           t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -3.9e+153) {
		tmp = t_0;
	} else if (NaChar <= -3.1e-16) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 2.9e-98) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	} else if (NaChar <= 6.8e+195) {
		tmp = (NdChar / 2.0) + (NaChar * (1.0 / (1.0 + exp((mu / -KbT)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    if (nachar <= (-3.9d+153)) then
        tmp = t_0
    else if (nachar <= (-3.1d-16)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    else if (nachar <= 2.9d-98) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar * 0.5d0)
    else if (nachar <= 6.8d+195) then
        tmp = (ndchar / 2.0d0) + (nachar * (1.0d0 / (1.0d0 + exp((mu / -kbt)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -3.9e+153) {
		tmp = t_0;
	} else if (NaChar <= -3.1e-16) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 2.9e-98) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar * 0.5);
	} else if (NaChar <= 6.8e+195) {
		tmp = (NdChar / 2.0) + (NaChar * (1.0 / (1.0 + Math.exp((mu / -KbT)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -3.9e+153:
		tmp = t_0
	elif NaChar <= -3.1e-16:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	elif NaChar <= 2.9e-98:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar * 0.5)
	elif NaChar <= 6.8e+195:
		tmp = (NdChar / 2.0) + (NaChar * (1.0 / (1.0 + math.exp((mu / -KbT)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -3.9e+153)
		tmp = t_0;
	elseif (NaChar <= -3.1e-16)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0));
	elseif (NaChar <= 2.9e-98)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar * 0.5));
	elseif (NaChar <= 6.8e+195)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(mu / Float64(-KbT)))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -3.9e+153)
		tmp = t_0;
	elseif (NaChar <= -3.1e-16)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	elseif (NaChar <= 2.9e-98)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	elseif (NaChar <= 6.8e+195)
		tmp = (NdChar / 2.0) + (NaChar * (1.0 / (1.0 + exp((mu / -KbT)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -3.9e+153], t$95$0, If[LessEqual[NaChar, -3.1e-16], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.9e-98], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 6.8e+195], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -3.89999999999999983e153 or 6.80000000000000021e195 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 56.7%

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

   6. Taylor expanded in KbT around inf 38.8%

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

   if -3.89999999999999983e153 < NaChar < -3.1000000000000001e-16

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 83.1%

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

   6. Taylor expanded in KbT around inf 52.2%

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

   if -3.1000000000000001e-16 < NaChar < 2.9e-98

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 70.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 70.7%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 70.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   8. Taylor expanded in Ec around inf 52.4%

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

      1. mul-1-neg 58.1%

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

      2. distribute-neg-frac2 58.1%

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

   10. Simplified 52.4%

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

   if 2.9e-98 < NaChar < 6.80000000000000021e195

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 46.1%

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

   6. Taylor expanded in mu around inf 37.9%

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

      1. associate-*r/ 37.9%

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

      2. mul-1-neg 37.9%

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

   8. Simplified 37.9%

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

      1. div-inv 38.0%

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

      2. distribute-frac-neg 38.0%

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

   10. Applied egg-rr 38.0%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.9 \cdot 10^{+153}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq -3.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 6.8 \cdot 10^{+195}:\\ \;\;\;\;\frac{NdChar}{2} + NaChar \cdot \frac{1}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 40.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -5.2 \cdot 10^{+157}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -9 \cdot 10^{-16}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.04 \cdot 10^{-103}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 2.6 \cdot 10^{+202}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))))
   (if (<= NaChar -5.2e+157)
     t_0
     (if (<= NaChar -9e-16)
       (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))
       (if (<= NaChar 1.04e-103)
         (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (* NaChar 0.5))
         (if (<= NaChar 2.6e+202)
           (+ (/ NdChar 2.0) (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))
           t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -5.2e+157) {
		tmp = t_0;
	} else if (NaChar <= -9e-16) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 1.04e-103) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	} else if (NaChar <= 2.6e+202) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((mu / -KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    if (nachar <= (-5.2d+157)) then
        tmp = t_0
    else if (nachar <= (-9d-16)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    else if (nachar <= 1.04d-103) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar * 0.5d0)
    else if (nachar <= 2.6d+202) then
        tmp = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((mu / -kbt))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -5.2e+157) {
		tmp = t_0;
	} else if (NaChar <= -9e-16) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 1.04e-103) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar * 0.5);
	} else if (NaChar <= 2.6e+202) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -5.2e+157:
		tmp = t_0
	elif NaChar <= -9e-16:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	elif NaChar <= 1.04e-103:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar * 0.5)
	elif NaChar <= 2.6e+202:
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -5.2e+157)
		tmp = t_0;
	elseif (NaChar <= -9e-16)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0));
	elseif (NaChar <= 1.04e-103)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar * 0.5));
	elseif (NaChar <= 2.6e+202)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -5.2e+157)
		tmp = t_0;
	elseif (NaChar <= -9e-16)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	elseif (NaChar <= 1.04e-103)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	elseif (NaChar <= 2.6e+202)
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((mu / -KbT))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -5.2e+157], t$95$0, If[LessEqual[NaChar, -9e-16], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.04e-103], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.6e+202], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -5.20000000000000022e157 or 2.6000000000000002e202 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 56.7%

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

   6. Taylor expanded in KbT around inf 38.8%

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

   if -5.20000000000000022e157 < NaChar < -9.0000000000000003e-16

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 83.1%

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

   6. Taylor expanded in KbT around inf 52.2%

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

   if -9.0000000000000003e-16 < NaChar < 1.04000000000000001e-103

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 70.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 70.7%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 70.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   8. Taylor expanded in Ec around inf 52.4%

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

      1. mul-1-neg 58.1%

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

      2. distribute-neg-frac2 58.1%

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

   10. Simplified 52.4%

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

   if 1.04000000000000001e-103 < NaChar < 2.6000000000000002e202

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 46.1%

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

   6. Taylor expanded in mu around inf 37.9%

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

      1. associate-*r/ 37.9%

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

      2. mul-1-neg 37.9%

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

   8. Simplified 37.9%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq -9 \cdot 10^{-16}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.04 \cdot 10^{-103}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 2.6 \cdot 10^{+202}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 39.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{+157}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.12 \cdot 10^{-95}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 2.35 \cdot 10^{+198}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))))
   (if (<= NaChar -2.7e+157)
     t_0
     (if (<= NaChar -1.15e-10)
       (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))
       (if (<= NaChar 1.12e-95)
         (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (* NaChar 0.5))
         (if (<= NaChar 2.35e+198)
           (+ (/ NdChar 2.0) (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))
           t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -2.7e+157) {
		tmp = t_0;
	} else if (NaChar <= -1.15e-10) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 1.12e-95) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar * 0.5);
	} else if (NaChar <= 2.35e+198) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((mu / -KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    if (nachar <= (-2.7d+157)) then
        tmp = t_0
    else if (nachar <= (-1.15d-10)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    else if (nachar <= 1.12d-95) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar * 0.5d0)
    else if (nachar <= 2.35d+198) then
        tmp = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((mu / -kbt))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -2.7e+157) {
		tmp = t_0;
	} else if (NaChar <= -1.15e-10) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 1.12e-95) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar * 0.5);
	} else if (NaChar <= 2.35e+198) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -2.7e+157:
		tmp = t_0
	elif NaChar <= -1.15e-10:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	elif NaChar <= 1.12e-95:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar * 0.5)
	elif NaChar <= 2.35e+198:
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -2.7e+157)
		tmp = t_0;
	elseif (NaChar <= -1.15e-10)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0));
	elseif (NaChar <= 1.12e-95)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar * 0.5));
	elseif (NaChar <= 2.35e+198)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -2.7e+157)
		tmp = t_0;
	elseif (NaChar <= -1.15e-10)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	elseif (NaChar <= 1.12e-95)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar * 0.5);
	elseif (NaChar <= 2.35e+198)
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((mu / -KbT))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.7e+157], t$95$0, If[LessEqual[NaChar, -1.15e-10], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.12e-95], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.35e+198], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.7e157 or 2.3500000000000001e198 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 56.7%

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

   6. Taylor expanded in KbT around inf 38.8%

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

   if -2.7e157 < NaChar < -1.15000000000000004e-10

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 83.1%

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

   6. Taylor expanded in KbT around inf 52.2%

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

   if -1.15000000000000004e-10 < NaChar < 1.12000000000000006e-95

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 70.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 70.9%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 70.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   8. Taylor expanded in mu around inf 50.1%

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

   if 1.12000000000000006e-95 < NaChar < 2.3500000000000001e198

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 46.2%

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

   6. Taylor expanded in mu around inf 37.9%

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

      1. associate-*r/ 37.9%

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

      2. mul-1-neg 37.9%

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

   8. Simplified 37.9%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{+157}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.12 \cdot 10^{-95}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 2.35 \cdot 10^{+198}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 60.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -3.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - t\_0\\ \mathbf{elif}\;NdChar \leq 5.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 2} - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NdChar -3.6e-9)
     (- (/ NaChar (+ (/ Vef KbT) 2.0)) t_0)
     (if (<= NdChar 5.2e-120)
       (-
        (/ NdChar 2.0)
        (*
         NaChar
         (/ 1.0 (- -1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
       (- (/ NaChar (+ (/ Ev KbT) 2.0)) t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -3.6e-9) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - t_0;
	} else if (NdChar <= 5.2e-120) {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	} else {
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (ndchar <= (-3.6d-9)) then
        tmp = (nachar / ((vef / kbt) + 2.0d0)) - t_0
    else if (ndchar <= 5.2d-120) then
        tmp = (ndchar / 2.0d0) - (nachar * (1.0d0 / ((-1.0d0) - exp(((vef + (eaccept + (ev - mu))) / kbt)))))
    else
        tmp = (nachar / ((ev / kbt) + 2.0d0)) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -3.6e-9) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - t_0;
	} else if (NdChar <= 5.2e-120) {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	} else {
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -3.6e-9:
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - t_0
	elif NdChar <= 5.2e-120:
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))))
	else:
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -3.6e-9)
		tmp = Float64(Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)) - t_0);
	elseif (NdChar <= 5.2e-120)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar * Float64(1.0 / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))));
	else
		tmp = Float64(Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -3.6e-9)
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - t_0;
	elseif (NdChar <= 5.2e-120)
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	else
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.6e-9], N[(N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NdChar, 5.2e-120], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar * N[(1.0 / N[(-1.0 - N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -3.6e-9

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 77.2%

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

   6. Taylor expanded in Vef around 0 66.7%

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

      1. +-commutative 66.7%

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

   8. Simplified 66.7%

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

   if -3.6e-9 < NdChar < 5.2000000000000002e-120

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. div-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 65.4%

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

   if 5.2000000000000002e-120 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 74.0%

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

   6. Taylor expanded in Ev around 0 60.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 5.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 60.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -7.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - t\_0\\ \mathbf{elif}\;NdChar \leq 1.7 \cdot 10^{-121}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 2} - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
   (if (<= NdChar -7.4e-9)
     (- (/ NaChar (+ (/ EAccept KbT) 2.0)) t_0)
     (if (<= NdChar 1.7e-121)
       (-
        (/ NdChar 2.0)
        (*
         NaChar
         (/ 1.0 (- -1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
       (- (/ NaChar (+ (/ Ev KbT) 2.0)) t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -7.4e-9) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - t_0;
	} else if (NdChar <= 1.7e-121) {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	} else {
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt)))
    if (ndchar <= (-7.4d-9)) then
        tmp = (nachar / ((eaccept / kbt) + 2.0d0)) - t_0
    else if (ndchar <= 1.7d-121) then
        tmp = (ndchar / 2.0d0) - (nachar * (1.0d0 / ((-1.0d0) - exp(((vef + (eaccept + (ev - mu))) / kbt)))))
    else
        tmp = (nachar / ((ev / kbt) + 2.0d0)) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -7.4e-9) {
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - t_0;
	} else if (NdChar <= 1.7e-121) {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	} else {
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -7.4e-9:
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - t_0
	elif NdChar <= 1.7e-121:
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))))
	else:
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -7.4e-9)
		tmp = Float64(Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)) - t_0);
	elseif (NdChar <= 1.7e-121)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar * Float64(1.0 / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))));
	else
		tmp = Float64(Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -7.4e-9)
		tmp = (NaChar / ((EAccept / KbT) + 2.0)) - t_0;
	elseif (NdChar <= 1.7e-121)
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	else
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -7.4e-9], N[(N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[NdChar, 1.7e-121], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar * N[(1.0 / N[(-1.0 - N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -7.4e-9

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 80.8%

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

   6. Taylor expanded in EAccept around 0 64.8%

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

      1. +-commutative 64.8%

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

   8. Simplified 64.8%

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

   if -7.4e-9 < NdChar < 1.70000000000000001e-121

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. div-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 65.4%

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

   if 1.70000000000000001e-121 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 74.0%

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

   6. Taylor expanded in Ev around 0 60.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -7.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.7 \cdot 10^{-121}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 61.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -5.7e+18)
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar 2.0))
   (if (<= NaChar 4.8e+48)
     (-
      (/ NaChar (+ (/ Ev KbT) 2.0))
      (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
     (-
      (/ NdChar 2.0)
      (*
       NaChar
       (/ 1.0 (- -1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -5.7e+18) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 4.8e+48) {
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - 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 (nachar <= (-5.7d+18)) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    else if (nachar <= 4.8d+48) then
        tmp = (nachar / ((ev / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    else
        tmp = (ndchar / 2.0d0) - (nachar * (1.0d0 / ((-1.0d0) - exp(((vef + (eaccept + (ev - 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 (NaChar <= -5.7e+18) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 4.8e+48) {
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	} else {
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -5.7e+18:
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	elif NaChar <= 4.8e+48:
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	else:
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -5.7e+18)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0));
	elseif (NaChar <= 4.8e+48)
		tmp = Float64(Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar * Float64(1.0 / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -5.7e+18)
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	elseif (NaChar <= 4.8e+48)
		tmp = (NaChar / ((Ev / KbT) + 2.0)) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	else
		tmp = (NdChar / 2.0) - (NaChar * (1.0 / (-1.0 - exp(((Vef + (EAccept + (Ev - mu))) / KbT)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -5.7e+18], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.8e+48], N[(N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar * N[(1.0 / N[(-1.0 - N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -5.7e18

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.2%

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

   if -5.7e18 < NaChar < 4.8000000000000002e48

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 77.3%

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

   6. Taylor expanded in Ev around 0 67.6%

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

   if 4.8000000000000002e48 < NaChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. div-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 58.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - NaChar \cdot \frac{1}{-1 - e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 57.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{-12} \lor \neg \left(NaChar \leq 6.5 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -8.5e-12) (not (<= NaChar 6.5e-45)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar 2.0))
   (-
    (* NaChar 0.5)
    (/ NdChar (- -1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -8.5e-12) || !(NaChar <= 6.5e-45)) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-8.5d-12)) .or. (.not. (nachar <= 6.5d-45))) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar * 0.5d0) - (ndchar / ((-1.0d0) - exp(((edonor + (mu + (vef - ec))) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -8.5e-12) || !(NaChar <= 6.5e-45)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -8.5e-12) or not (NaChar <= 6.5e-45):
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -8.5e-12) || !(NaChar <= 6.5e-45))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar * 0.5) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -8.5e-12) || ~((NaChar <= 6.5e-45)))
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar * 0.5) - (NdChar / (-1.0 - exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -8.5e-12], N[Not[LessEqual[NaChar, 6.5e-45]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar * 0.5), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -8.4999999999999997e-12 or 6.4999999999999995e-45 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.9%

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

   if -8.4999999999999997e-12 < NaChar < 6.4999999999999995e-45

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 68.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{-12} \lor \neg \left(NaChar \leq 6.5 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 - \frac{NdChar}{-1 - e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 55.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -7 \cdot 10^{-11} \lor \neg \left(NaChar \leq 1.22 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -7e-11) (not (<= NaChar 1.22e-45)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar 2.0))
   (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (* NaChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -7e-11) || !(NaChar <= 1.22e-45)) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-7d-11)) .or. (.not. (nachar <= 1.22d-45))) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -7e-11) || !(NaChar <= 1.22e-45)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -7e-11) or not (NaChar <= 1.22e-45):
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -7e-11) || !(NaChar <= 1.22e-45))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -7e-11) || ~((NaChar <= 1.22e-45)))
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -7e-11], N[Not[LessEqual[NaChar, 1.22e-45]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -7.00000000000000038e-11 or 1.22000000000000007e-45 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.9%

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

   if -7.00000000000000038e-11 < NaChar < 1.22000000000000007e-45

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 68.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   8. Taylor expanded in EDonor around 0 63.0%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7 \cdot 10^{-11} \lor \neg \left(NaChar \leq 1.22 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 40.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef}{KbT}}\\ \mathbf{if}\;NdChar \leq -7.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - t\_0}\\ \mathbf{elif}\;NdChar \leq -6.1 \cdot 10^{-289}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 4 \cdot 10^{-120}:\\ \;\;\;\;\frac{NaChar}{1 + t\_0} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ Vef KbT))))
   (if (<= NdChar -7.4e-9)
     (- (/ NaChar (+ (/ Vef KbT) 2.0)) (/ NdChar (- -1.0 t_0)))
     (if (<= NdChar -6.1e-289)
       (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
       (if (<= NdChar 4e-120)
         (+ (/ NaChar (+ 1.0 t_0)) (/ NdChar 2.0))
         (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (* NaChar 0.5)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp((Vef / KbT));
	double tmp;
	if (NdChar <= -7.4e-9) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - t_0));
	} else if (NdChar <= -6.1e-289) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NdChar <= 4e-120) {
		tmp = (NaChar / (1.0 + t_0)) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp((vef / kbt))
    if (ndchar <= (-7.4d-9)) then
        tmp = (nachar / ((vef / kbt) + 2.0d0)) - (ndchar / ((-1.0d0) - t_0))
    else if (ndchar <= (-6.1d-289)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (ndchar <= 4d-120) then
        tmp = (nachar / (1.0d0 + t_0)) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp((Vef / KbT));
	double tmp;
	if (NdChar <= -7.4e-9) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - t_0));
	} else if (NdChar <= -6.1e-289) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NdChar <= 4e-120) {
		tmp = (NaChar / (1.0 + t_0)) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp((Vef / KbT))
	tmp = 0
	if NdChar <= -7.4e-9:
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - t_0))
	elif NdChar <= -6.1e-289:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif NdChar <= 4e-120:
		tmp = (NaChar / (1.0 + t_0)) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Vef / KbT))
	tmp = 0.0
	if (NdChar <= -7.4e-9)
		tmp = Float64(Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)) - Float64(NdChar / Float64(-1.0 - t_0)));
	elseif (NdChar <= -6.1e-289)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (NdChar <= 4e-120)
		tmp = Float64(Float64(NaChar / Float64(1.0 + t_0)) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp((Vef / KbT));
	tmp = 0.0;
	if (NdChar <= -7.4e-9)
		tmp = (NaChar / ((Vef / KbT) + 2.0)) - (NdChar / (-1.0 - t_0));
	elseif (NdChar <= -6.1e-289)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (NdChar <= 4e-120)
		tmp = (NaChar / (1.0 + t_0)) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[NdChar, -7.4e-9], N[(N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -6.1e-289], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 4e-120], N[(N[(NaChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -7.4e-9

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 77.2%

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

   6. Taylor expanded in Vef around 0 66.7%

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

      1. +-commutative 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in EDonor around 0 58.9%

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

   10. Taylor expanded in Vef around inf 49.1%

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

   if -7.4e-9 < NdChar < -6.0999999999999998e-289

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 64.7%

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

   6. Taylor expanded in KbT around inf 43.2%

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

   if -6.0999999999999998e-289 < NdChar < 3.99999999999999991e-120

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.6%

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

   6. Taylor expanded in KbT around inf 54.7%

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

   if 3.99999999999999991e-120 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 53.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 53.2%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 53.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   8. Taylor expanded in Ec around inf 42.8%

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

      1. mul-1-neg 52.2%

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

      2. distribute-neg-frac2 52.2%

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

   10. Simplified 42.8%

       \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{Ec}{-KbT}}}} + NaChar \cdot 0.5 \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -7.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} - \frac{NdChar}{-1 - e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -6.1 \cdot 10^{-289}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 4 \cdot 10^{-120}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 40.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.56 \cdot 10^{-288}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 3 \cdot 10^{-121}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar -1e+25)
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar (+ (/ Vef KbT) 2.0)))
   (if (<= NdChar -1.56e-288)
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
     (if (<= NdChar 3e-121)
       (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))
       (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (* NaChar 0.5))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -1e+25) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= -1.56e-288) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NdChar <= 3e-121) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ndchar <= (-1d+25)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else if (ndchar <= (-1.56d-288)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (ndchar <= 3d-121) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -1e+25) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= -1.56e-288) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NdChar <= 3e-121) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= -1e+25:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	elif NdChar <= -1.56e-288:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif NdChar <= 3e-121:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= -1e+25)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NdChar <= -1.56e-288)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (NdChar <= 3e-121)
		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(Ec / Float64(-KbT))))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= -1e+25)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	elseif (NdChar <= -1.56e-288)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (NdChar <= 3e-121)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, -1e+25], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -1.56e-288], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3e-121], 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[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -1.00000000000000009e25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 78.8%

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

   6. Taylor expanded in EDonor around inf 50.8%

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

   7. Taylor expanded in Vef around 0 46.1%

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

      1. +-commutative 68.7%

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

   9. Simplified 46.1%

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

   if -1.00000000000000009e25 < NdChar < -1.5599999999999999e-288

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 65.3%

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

   6. Taylor expanded in KbT around inf 42.4%

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

   if -1.5599999999999999e-288 < NdChar < 2.9999999999999999e-121

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.6%

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

   6. Taylor expanded in KbT around inf 54.7%

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

   if 2.9999999999999999e-121 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 53.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 53.2%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 53.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   8. Taylor expanded in Ec around inf 42.8%

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

      1. mul-1-neg 52.2%

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

      2. distribute-neg-frac2 52.2%

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

   10. Simplified 42.8%

       \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{Ec}{-KbT}}}} + NaChar \cdot 0.5 \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.56 \cdot 10^{-288}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 3 \cdot 10^{-121}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 39.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -2 \cdot 10^{+156}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -5.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))))
   (if (<= NaChar -2e+156)
     t_0
     (if (<= NaChar -5.8e-13)
       (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))
       (if (<= NaChar 2e+18)
         (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (* NaChar 0.5))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -2e+156) {
		tmp = t_0;
	} else if (NaChar <= -5.8e-13) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 2e+18) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    if (nachar <= (-2d+156)) then
        tmp = t_0
    else if (nachar <= (-5.8d-13)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    else if (nachar <= 2d+18) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar * 0.5d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -2e+156) {
		tmp = t_0;
	} else if (NaChar <= -5.8e-13) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 2e+18) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -2e+156:
		tmp = t_0
	elif NaChar <= -5.8e-13:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	elif NaChar <= 2e+18:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar * 0.5)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -2e+156)
		tmp = t_0;
	elseif (NaChar <= -5.8e-13)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0));
	elseif (NaChar <= 2e+18)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -2e+156)
		tmp = t_0;
	elseif (NaChar <= -5.8e-13)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	elseif (NaChar <= 2e+18)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar * 0.5);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2e+156], t$95$0, If[LessEqual[NaChar, -5.8e-13], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2e+18], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2e156 or 2e18 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 56.2%

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

   6. Taylor expanded in KbT around inf 37.0%

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

   if -2e156 < NaChar < -5.7999999999999995e-13

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 83.1%

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

   6. Taylor expanded in KbT around inf 52.2%

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

   if -5.7999999999999995e-13 < NaChar < 2e18

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 64.5%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 64.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   8. Taylor expanded in mu around inf 46.1%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2 \cdot 10^{+156}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq -5.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 47.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -9 \cdot 10^{+101} \lor \neg \left(NaChar \leq 1.2 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -9e+101) (not (<= NaChar 1.2e+85)))
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (* NaChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -9e+101) || !(NaChar <= 1.2e+85)) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-9d+101)) .or. (.not. (nachar <= 1.2d+85))) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -9e+101) || !(NaChar <= 1.2e+85)) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -9e+101) or not (NaChar <= 1.2e+85):
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -9e+101) || !(NaChar <= 1.2e+85))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -9e+101) || ~((NaChar <= 1.2e+85)))
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -9e+101], N[Not[LessEqual[NaChar, 1.2e+85]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -9.0000000000000004e101 or 1.19999999999999998e85 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 57.7%

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

   6. Taylor expanded in KbT around inf 40.0%

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

   if -9.0000000000000004e101 < NaChar < 1.19999999999999998e85

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 59.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 59.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   8. Taylor expanded in EDonor around 0 55.1%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -9 \cdot 10^{+101} \lor \neg \left(NaChar \leq 1.2 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 36.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2 \cdot 10^{-274}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 4.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2e-274)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (if (<= KbT 4.2e-201)
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (* NaChar 0.5))
     (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ Ev KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -2e-274) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 4.2e-201) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-2d-274)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 4.2d-201) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar * 0.5d0)
    else
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -2e-274) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 4.2e-201) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -2e-274:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= 4.2e-201:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -2e-274)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 4.2e-201)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -2e-274)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 4.2e-201)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	else
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -2e-274], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4.2e-201], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.99999999999999993e-274

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 62.7%

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

   6. Taylor expanded in KbT around inf 37.0%

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

   if -1.99999999999999993e-274 < KbT < 4.20000000000000024e-201

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 41.1%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   7. Simplified 41.1%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]

   8. Taylor expanded in EDonor around inf 37.0%

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

   if 4.20000000000000024e-201 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 48.0%

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

   6. Taylor expanded in Ev around inf 36.2%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2 \cdot 10^{-274}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 4.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 37.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 5.2e+63)
   (- (/ NdChar 2.0) (/ NaChar (- -1.0 (exp (/ Ev KbT)))))
   (+ (/ 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) {
	double tmp;
	if (EAccept <= 5.2e+63) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / 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 (eaccept <= 5.2d+63) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / 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 (EAccept <= 5.2e+63) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 5.2e+63:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 5.2e+63)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / 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 (EAccept <= 5.2e+63)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp((Ev / KbT))));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 5.2e+63], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 5.2000000000000002e63

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 46.3%

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

   6. Taylor expanded in Ev around inf 36.6%

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

   if 5.2000000000000002e63 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 87.0%

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

   6. Taylor expanded in KbT around inf 44.6%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 39: 36.3% 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. Add Preprocessing

5. Taylor expanded in EAccept around inf 69.9%

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

6. Taylor expanded in KbT around inf 35.1%

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

7. Final simplification 35.1%

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

Alternative 40: 28.4% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq 1.05 \cdot 10^{-284}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{mu - Ec}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT 1.05e-284)
   (+
    (/ NaChar (+ (/ Vef KbT) 2.0))
    (/ NdChar (+ 2.0 (+ (/ Vef KbT) (/ (- mu Ec) KbT)))))
   (+ (/ NdChar 2.0) (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= 1.05e-284) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) + (NdChar / (2.0 + ((Vef / KbT) + ((mu - Ec) / KbT))));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= 1.05d-284) then
        tmp = (nachar / ((vef / kbt) + 2.0d0)) + (ndchar / (2.0d0 + ((vef / kbt) + ((mu - ec) / kbt))))
    else
        tmp = (ndchar / 2.0d0) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= 1.05e-284) {
		tmp = (NaChar / ((Vef / KbT) + 2.0)) + (NdChar / (2.0 + ((Vef / KbT) + ((mu - Ec) / KbT))));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= 1.05e-284:
		tmp = (NaChar / ((Vef / KbT) + 2.0)) + (NdChar / (2.0 + ((Vef / KbT) + ((mu - Ec) / KbT))))
	else:
		tmp = (NdChar / 2.0) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= 1.05e-284)
		tmp = Float64(Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)) + Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Float64(mu - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= 1.05e-284)
		tmp = (NaChar / ((Vef / KbT) + 2.0)) + (NdChar / (2.0 + ((Vef / KbT) + ((mu - Ec) / KbT))));
	else
		tmp = (NdChar / 2.0) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, 1.05e-284], N[(N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(mu - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < 1.04999999999999996e-284

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 73.0%

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

   6. Taylor expanded in Vef around 0 55.8%

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

      1. +-commutative 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in EDonor around 0 51.5%

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

   10. Taylor expanded in KbT around inf 32.3%

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

       1. associate-+r- 32.3%

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

       2. associate--l+ 32.3%

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

       3. div-sub 33.1%

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

   12. Simplified 33.1%

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

   if 1.04999999999999996e-284 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.2%

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

   6. Taylor expanded in KbT around inf 28.3%

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

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 1.05 \cdot 10^{-284}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{mu - Ec}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 41: 28.3% accurate, 32.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 47.2%

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

6. Taylor expanded in KbT around inf 29.0%

   \[\leadsto \frac{NdChar}{2} + \frac{NaChar}{\color{blue}{2}} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024102 
(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))))))