Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 26.6s

Alternatives: 27

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -5.156590236815521e+258
  2. Ec = 3.057935016897305e-6
  3. Vef = -4.496176966240639e+297
  4. EDonor = 7.182750713181622e+199
  5. mu = -3.42731865321427e-48
  6. KbT = 1.4225591964399656e-107
  7. NaChar = -7.436423262389271e+258
  8. Ev = 2.1221272539358513e-134
  9. EAccept = -9.052850936567854e+60

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.5× speedup

Math

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

FPCore

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

Java

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

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (math.exp(-math.log1p(math.exp(((EDonor + ((mu + Vef) - Ec)) / KbT)))) * NdChar) + (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(exp(Float64(-log1p(exp(Float64(Float64(EDonor + Float64(Float64(mu + Vef) - Ec)) / KbT))))) * NdChar) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))))
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

   1. clear-num 99.8%

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

   2. associate-/r/ 99.9%

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

   3. add-exp-log 99.9%

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

   4. rec-exp 99.9%

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

   5. log1p-expm1-u 99.9%

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

   6. log1p-define 99.9%

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

   7. expm1-log1p-u 99.9%

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

   8. div-inv 99.9%

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

   9. div-inv 99.9%

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

   10. associate-+r- 99.9%

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

6. Applied egg-rr 99.9%

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

Alternative 2: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ t_2 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_4 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;NdChar \leq -6.2 \cdot 10^{-124}:\\ \;\;\;\;t\_2 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.9 \cdot 10^{-191}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.3 \cdot 10^{-116}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;NdChar \leq 9.6 \cdot 10^{-42}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 0.00062:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 4 \cdot 10^{+32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t\_4\\ \mathbf{elif}\;NdChar \leq 4 \cdot 10^{+69}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;NdChar \leq 1.95 \cdot 10^{+131}:\\ \;\;\;\;t\_1 + t\_4\\ \mathbf{elif}\;NdChar \leq 1.32 \cdot 10^{+147}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))))
        (t_2
         (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_3
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))))
        (t_4 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
   (if (<= NdChar -6.2e-124)
     (+
      t_2
      (/
       NaChar
       (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT))))
     (if (<= NdChar 3.9e-191)
       (+
        t_0
        (/
         NdChar
         (- (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) (/ Ec KbT))))
       (if (<= NdChar 1.3e-116)
         t_3
         (if (<= NdChar 9.6e-42)
           (+ t_0 (/ NdChar (- 2.0 (/ Ec KbT))))
           (if (<= NdChar 0.00062)
             (+ t_1 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))
             (if (<= NdChar 4e+32)
               (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_4)
               (if (<= NdChar 4e+69)
                 t_3
                 (if (<= NdChar 1.95e+131)
                   (+ t_1 t_4)
                   (if (<= NdChar 1.32e+147)
                     t_3
                     (+ t_2 (/ 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 t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + exp((Ec / -KbT)));
	double t_2 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_3 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	double t_4 = NaChar / (1.0 + exp((EAccept / KbT)));
	double tmp;
	if (NdChar <= -6.2e-124) {
		tmp = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 3.9e-191) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 1.3e-116) {
		tmp = t_3;
	} else if (NdChar <= 9.6e-42) {
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	} else if (NdChar <= 0.00062) {
		tmp = t_1 + (NaChar / (1.0 + exp((Vef / KbT))));
	} else if (NdChar <= 4e+32) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_4;
	} else if (NdChar <= 4e+69) {
		tmp = t_3;
	} else if (NdChar <= 1.95e+131) {
		tmp = t_1 + t_4;
	} else if (NdChar <= 1.32e+147) {
		tmp = t_3;
	} else {
		tmp = t_2 + (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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))
    t_1 = ndchar / (1.0d0 + exp((ec / -kbt)))
    t_2 = ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_3 = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    t_4 = nachar / (1.0d0 + exp((eaccept / kbt)))
    if (ndchar <= (-6.2d-124)) then
        tmp = t_2 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (ndchar <= 3.9d-191) then
        tmp = t_0 + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))
    else if (ndchar <= 1.3d-116) then
        tmp = t_3
    else if (ndchar <= 9.6d-42) then
        tmp = t_0 + (ndchar / (2.0d0 - (ec / kbt)))
    else if (ndchar <= 0.00062d0) then
        tmp = t_1 + (nachar / (1.0d0 + exp((vef / kbt))))
    else if (ndchar <= 4d+32) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_4
    else if (ndchar <= 4d+69) then
        tmp = t_3
    else if (ndchar <= 1.95d+131) then
        tmp = t_1 + t_4
    else if (ndchar <= 1.32d+147) then
        tmp = t_3
    else
        tmp = t_2 + (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 t_0 = NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp((Ec / -KbT)));
	double t_2 = NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_3 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double t_4 = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	double tmp;
	if (NdChar <= -6.2e-124) {
		tmp = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 3.9e-191) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 1.3e-116) {
		tmp = t_3;
	} else if (NdChar <= 9.6e-42) {
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	} else if (NdChar <= 0.00062) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	} else if (NdChar <= 4e+32) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_4;
	} else if (NdChar <= 4e+69) {
		tmp = t_3;
	} else if (NdChar <= 1.95e+131) {
		tmp = t_1 + t_4;
	} else if (NdChar <= 1.32e+147) {
		tmp = t_3;
	} else {
		tmp = t_2 + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))
	t_1 = NdChar / (1.0 + math.exp((Ec / -KbT)))
	t_2 = NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_3 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	t_4 = NaChar / (1.0 + math.exp((EAccept / KbT)))
	tmp = 0
	if NdChar <= -6.2e-124:
		tmp = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NdChar <= 3.9e-191:
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	elif NdChar <= 1.3e-116:
		tmp = t_3
	elif NdChar <= 9.6e-42:
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)))
	elif NdChar <= 0.00062:
		tmp = t_1 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	elif NdChar <= 4e+32:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_4
	elif NdChar <= 4e+69:
		tmp = t_3
	elif NdChar <= 1.95e+131:
		tmp = t_1 + t_4
	elif NdChar <= 1.32e+147:
		tmp = t_3
	else:
		tmp = t_2 + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT)))))
	t_2 = Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	t_3 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	t_4 = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))))
	tmp = 0.0
	if (NdChar <= -6.2e-124)
		tmp = Float64(t_2 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NdChar <= 3.9e-191)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))));
	elseif (NdChar <= 1.3e-116)
		tmp = t_3;
	elseif (NdChar <= 9.6e-42)
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))));
	elseif (NdChar <= 0.00062)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	elseif (NdChar <= 4e+32)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_4);
	elseif (NdChar <= 4e+69)
		tmp = t_3;
	elseif (NdChar <= 1.95e+131)
		tmp = Float64(t_1 + t_4);
	elseif (NdChar <= 1.32e+147)
		tmp = t_3;
	else
		tmp = Float64(t_2 + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	t_1 = NdChar / (1.0 + exp((Ec / -KbT)));
	t_2 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_3 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	t_4 = NaChar / (1.0 + exp((EAccept / KbT)));
	tmp = 0.0;
	if (NdChar <= -6.2e-124)
		tmp = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NdChar <= 3.9e-191)
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	elseif (NdChar <= 1.3e-116)
		tmp = t_3;
	elseif (NdChar <= 9.6e-42)
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	elseif (NdChar <= 0.00062)
		tmp = t_1 + (NaChar / (1.0 + exp((Vef / KbT))));
	elseif (NdChar <= 4e+32)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + t_4;
	elseif (NdChar <= 4e+69)
		tmp = t_3;
	elseif (NdChar <= 1.95e+131)
		tmp = t_1 + t_4;
	elseif (NdChar <= 1.32e+147)
		tmp = t_3;
	else
		tmp = t_2 + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar * N[(1.0 / 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$3 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -6.2e-124], N[(t$95$2 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.9e-191], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.3e-116], t$95$3, If[LessEqual[NdChar, 9.6e-42], N[(t$95$0 + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 0.00062], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 4e+32], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[NdChar, 4e+69], t$95$3, If[LessEqual[NdChar, 1.95e+131], N[(t$95$1 + t$95$4), $MachinePrecision], If[LessEqual[NdChar, 1.32e+147], t$95$3, N[(t$95$2 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if NdChar < -6.1999999999999996e-124

   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%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. add-exp-log 99.9%

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

      4. rec-exp 99.9%

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

      5. log1p-expm1-u 99.9%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.9%

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

      2. log1p-undefine 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. pow-exp 99.9%

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

      5. add-exp-log 99.9%

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

      6. pow-exp 99.9%

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

      7. *-un-lft-identity 99.9%

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

      8. associate--l+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in KbT around inf 72.5%

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

   if -6.1999999999999996e-124 < NdChar < 3.8999999999999999e-191

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 79.5%

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

   if 3.8999999999999999e-191 < NdChar < 1.3e-116 or 4.00000000000000021e32 < NdChar < 4.0000000000000003e69 or 1.95e131 < NdChar < 1.32000000000000006e147

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 87.3%

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

   6. Taylor expanded in Ev around inf 68.2%

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

   if 1.3e-116 < NdChar < 9.60000000000000011e-42

   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%

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

   5. Taylor expanded in Ec around inf 70.1%

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

      1. mul-1-neg 70.1%

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

      2. distribute-neg-frac2 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in Ec around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. unsub-neg 75.4%

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

   10. Simplified 75.4%

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

   if 9.60000000000000011e-42 < NdChar < 6.2e-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%

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

   5. Taylor expanded in Ec around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. distribute-neg-frac2 86.2%

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

   7. Simplified 86.2%

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

   8. Taylor expanded in Vef around inf 72.1%

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

   if 6.2e-4 < NdChar < 4.00000000000000021e32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 88.4%

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

   6. Taylor expanded in EAccept around inf 74.2%

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

   if 4.0000000000000003e69 < NdChar < 1.95e131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. distribute-neg-frac2 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in EAccept around inf 58.7%

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

   if 1.32000000000000006e147 < NdChar

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

      3. add-exp-log 99.7%

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

      4. rec-exp 99.7%

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

      5. log1p-expm1-u 99.7%

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

      6. log1p-define 99.8%

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

      7. expm1-log1p-u 99.8%

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

      8. div-inv 99.8%

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

      9. div-inv 99.8%

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

      10. associate-+r- 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. exp-neg 99.7%

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

      2. log1p-undefine 99.7%

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

      3. *-un-lft-identity 99.7%

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

      4. pow-exp 99.7%

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

      5. add-exp-log 99.8%

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

      6. pow-exp 99.7%

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

      7. *-un-lft-identity 99.7%

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

      8. associate--l+ 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in KbT around inf 83.2%

      \[\leadsto \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} \cdot NdChar + \frac{NaChar}{\color{blue}{2}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6.2 \cdot 10^{-124}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.9 \cdot 10^{-191}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.3 \cdot 10^{-116}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 9.6 \cdot 10^{-42}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 0.00062:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 4 \cdot 10^{+32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 4 \cdot 10^{+69}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.95 \cdot 10^{+131}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.32 \cdot 10^{+147}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;NdChar \leq -2.6 \cdot 10^{-124}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5.8 \cdot 10^{-192}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.56 \cdot 10^{-116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NdChar \leq 1.75 \cdot 10^{-29}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.45 \cdot 10^{+131}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 9.5 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT)))))
        (t_1
         (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))))
   (if (<= NdChar -2.6e-124)
     (+
      t_1
      (/
       NaChar
       (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT))))
     (if (<= NdChar 5.8e-192)
       (+
        t_0
        (/
         NdChar
         (- (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) (/ Ec KbT))))
       (if (<= NdChar 1.56e-116)
         t_2
         (if (<= NdChar 1.75e-29)
           (+ t_0 (/ NdChar (- 2.0 (/ Ec KbT))))
           (if (<= NdChar 1.45e+131)
             (+
              (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
              (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
             (if (<= NdChar 9.5e+146) t_2 (+ t_1 (/ 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 t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_2 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	double tmp;
	if (NdChar <= -2.6e-124) {
		tmp = t_1 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 5.8e-192) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 1.56e-116) {
		tmp = t_2;
	} else if (NdChar <= 1.75e-29) {
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	} else if (NdChar <= 1.45e+131) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (NdChar <= 9.5e+146) {
		tmp = t_2;
	} else {
		tmp = t_1 + (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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))
    t_1 = ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_2 = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    if (ndchar <= (-2.6d-124)) then
        tmp = t_1 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (ndchar <= 5.8d-192) then
        tmp = t_0 + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))
    else if (ndchar <= 1.56d-116) then
        tmp = t_2
    else if (ndchar <= 1.75d-29) then
        tmp = t_0 + (ndchar / (2.0d0 - (ec / kbt)))
    else if (ndchar <= 1.45d+131) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (ndchar <= 9.5d+146) then
        tmp = t_2
    else
        tmp = t_1 + (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 t_0 = NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_2 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double tmp;
	if (NdChar <= -2.6e-124) {
		tmp = t_1 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 5.8e-192) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 1.56e-116) {
		tmp = t_2;
	} else if (NdChar <= 1.75e-29) {
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	} else if (NdChar <= 1.45e+131) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (NdChar <= 9.5e+146) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))
	t_1 = NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_2 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	tmp = 0
	if NdChar <= -2.6e-124:
		tmp = t_1 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NdChar <= 5.8e-192:
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	elif NdChar <= 1.56e-116:
		tmp = t_2
	elif NdChar <= 1.75e-29:
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)))
	elif NdChar <= 1.45e+131:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif NdChar <= 9.5e+146:
		tmp = t_2
	else:
		tmp = t_1 + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	tmp = 0.0
	if (NdChar <= -2.6e-124)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NdChar <= 5.8e-192)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))));
	elseif (NdChar <= 1.56e-116)
		tmp = t_2;
	elseif (NdChar <= 1.75e-29)
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))));
	elseif (NdChar <= 1.45e+131)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (NdChar <= 9.5e+146)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	t_1 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_2 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	tmp = 0.0;
	if (NdChar <= -2.6e-124)
		tmp = t_1 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NdChar <= 5.8e-192)
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	elseif (NdChar <= 1.56e-116)
		tmp = t_2;
	elseif (NdChar <= 1.75e-29)
		tmp = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	elseif (NdChar <= 1.45e+131)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (NdChar <= 9.5e+146)
		tmp = t_2;
	else
		tmp = t_1 + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar * N[(1.0 / 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$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -2.6e-124], N[(t$95$1 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 5.8e-192], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.56e-116], t$95$2, If[LessEqual[NdChar, 1.75e-29], N[(t$95$0 + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.45e+131], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 9.5e+146], t$95$2, N[(t$95$1 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if NdChar < -2.6e-124

   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%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. add-exp-log 99.9%

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

      4. rec-exp 99.9%

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

      5. log1p-expm1-u 99.9%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.9%

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

      2. log1p-undefine 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. pow-exp 99.9%

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

      5. add-exp-log 99.9%

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

      6. pow-exp 99.9%

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

      7. *-un-lft-identity 99.9%

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

      8. associate--l+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in KbT around inf 72.5%

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

   if -2.6e-124 < NdChar < 5.80000000000000033e-192

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 79.5%

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

   if 5.80000000000000033e-192 < NdChar < 1.55999999999999997e-116 or 1.45000000000000005e131 < NdChar < 9.49999999999999926e146

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 86.4%

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

   6. Taylor expanded in Ev around inf 68.5%

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

   if 1.55999999999999997e-116 < NdChar < 1.7499999999999999e-29

   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%

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

   5. Taylor expanded in Ec around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. distribute-neg-frac2 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in Ec around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

   10. Simplified 68.2%

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

   if 1.7499999999999999e-29 < NdChar < 1.45000000000000005e131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-neg-frac2 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in EAccept around inf 59.5%

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

   if 9.49999999999999926e146 < NdChar

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

      3. add-exp-log 99.7%

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

      4. rec-exp 99.7%

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

      5. log1p-expm1-u 99.7%

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

      6. log1p-define 99.8%

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

      7. expm1-log1p-u 99.8%

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

      8. div-inv 99.8%

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

      9. div-inv 99.8%

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

      10. associate-+r- 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. exp-neg 99.7%

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

      2. log1p-undefine 99.7%

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

      3. *-un-lft-identity 99.7%

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

      4. pow-exp 99.7%

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

      5. add-exp-log 99.8%

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

      6. pow-exp 99.7%

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

      7. *-un-lft-identity 99.7%

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

      8. associate--l+ 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in KbT around inf 83.2%

      \[\leadsto \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} \cdot NdChar + \frac{NaChar}{\color{blue}{2}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.6 \cdot 10^{-124}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5.8 \cdot 10^{-192}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.56 \cdot 10^{-116}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.75 \cdot 10^{-29}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.45 \cdot 10^{+131}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 9.5 \cdot 10^{+146}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ t_2 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -1.22 \cdot 10^{-126}:\\ \;\;\;\;t\_2 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 4.6 \cdot 10^{-192}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.65 \cdot 10^{-116}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 0.00028:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 2.7 \cdot 10^{+32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 4.8 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (- 2.0 (/ Ec KbT)))))
        (t_2
         (*
          NdChar
          (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))))
   (if (<= NdChar -1.22e-126)
     (+
      t_2
      (/
       NaChar
       (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT))))
     (if (<= NdChar 4.6e-192)
       (+
        t_0
        (/
         NdChar
         (- (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) (/ Ec KbT))))
       (if (<= NdChar 1.65e-116)
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
         (if (<= NdChar 3.3e-32)
           t_1
           (if (<= NdChar 0.00028)
             (+
              (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
              (/ NaChar (+ (/ EAccept KbT) 2.0)))
             (if (<= NdChar 2.7e+32)
               (+
                (/ NdChar (+ 1.0 (exp (/ mu KbT))))
                (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
               (if (<= NdChar 4.8e+144) t_1 (+ t_2 (/ 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 t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	double t_2 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NdChar <= -1.22e-126) {
		tmp = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 4.6e-192) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 1.65e-116) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (NdChar <= 3.3e-32) {
		tmp = t_1;
	} else if (NdChar <= 0.00028) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 2.7e+32) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (NdChar <= 4.8e+144) {
		tmp = t_1;
	} else {
		tmp = t_2 + (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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (2.0d0 - (ec / kbt)))
    t_2 = ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))
    if (ndchar <= (-1.22d-126)) then
        tmp = t_2 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (ndchar <= 4.6d-192) then
        tmp = t_0 + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))
    else if (ndchar <= 1.65d-116) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (ndchar <= 3.3d-32) then
        tmp = t_1
    else if (ndchar <= 0.00028d0) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= 2.7d+32) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (ndchar <= 4.8d+144) then
        tmp = t_1
    else
        tmp = t_2 + (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 t_0 = NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	double t_2 = NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double tmp;
	if (NdChar <= -1.22e-126) {
		tmp = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 4.6e-192) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 1.65e-116) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (NdChar <= 3.3e-32) {
		tmp = t_1;
	} else if (NdChar <= 0.00028) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 2.7e+32) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (NdChar <= 4.8e+144) {
		tmp = t_1;
	} else {
		tmp = t_2 + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (2.0 - (Ec / KbT)))
	t_2 = NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	tmp = 0
	if NdChar <= -1.22e-126:
		tmp = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NdChar <= 4.6e-192:
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	elif NdChar <= 1.65e-116:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif NdChar <= 3.3e-32:
		tmp = t_1
	elif NdChar <= 0.00028:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= 2.7e+32:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif NdChar <= 4.8e+144:
		tmp = t_1
	else:
		tmp = t_2 + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))))
	t_2 = Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	tmp = 0.0
	if (NdChar <= -1.22e-126)
		tmp = Float64(t_2 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NdChar <= 4.6e-192)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))));
	elseif (NdChar <= 1.65e-116)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (NdChar <= 3.3e-32)
		tmp = t_1;
	elseif (NdChar <= 0.00028)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= 2.7e+32)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (NdChar <= 4.8e+144)
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	t_2 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	tmp = 0.0;
	if (NdChar <= -1.22e-126)
		tmp = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NdChar <= 4.6e-192)
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	elseif (NdChar <= 1.65e-116)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (NdChar <= 3.3e-32)
		tmp = t_1;
	elseif (NdChar <= 0.00028)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= 2.7e+32)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (NdChar <= 4.8e+144)
		tmp = t_1;
	else
		tmp = t_2 + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.22e-126], N[(t$95$2 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 4.6e-192], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.65e-116], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.3e-32], t$95$1, If[LessEqual[NdChar, 0.00028], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.7e+32], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 4.8e+144], t$95$1, N[(t$95$2 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if NdChar < -1.21999999999999996e-126

   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%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. add-exp-log 99.9%

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

      4. rec-exp 99.9%

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

      5. log1p-expm1-u 99.9%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.9%

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

      2. log1p-undefine 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. pow-exp 99.9%

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

      5. add-exp-log 99.9%

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

      6. pow-exp 99.9%

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

      7. *-un-lft-identity 99.9%

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

      8. associate--l+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in KbT around inf 72.5%

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

   if -1.21999999999999996e-126 < NdChar < 4.60000000000000037e-192

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 79.5%

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

   if 4.60000000000000037e-192 < NdChar < 1.65e-116

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 83.0%

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

   6. Taylor expanded in Ev around inf 65.6%

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

   if 1.65e-116 < NdChar < 3.30000000000000025e-32 or 2.70000000000000013e32 < NdChar < 4.8000000000000001e144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. distribute-neg-frac2 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in Ec around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

   10. Simplified 65.9%

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

   if 3.30000000000000025e-32 < NdChar < 2.7999999999999998e-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%

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

   5. Taylor expanded in Ec around inf 83.9%

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

      1. mul-1-neg 83.9%

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

      2. distribute-neg-frac2 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in EAccept around inf 67.5%

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

   9. Taylor expanded in EAccept around 0 68.3%

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

   if 2.7999999999999998e-4 < NdChar < 2.70000000000000013e32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 88.4%

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

   6. Taylor expanded in EAccept around inf 74.2%

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

   if 4.8000000000000001e144 < NdChar

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

      3. add-exp-log 99.7%

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

      4. rec-exp 99.7%

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

      5. log1p-expm1-u 99.7%

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

      6. log1p-define 99.8%

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

      7. expm1-log1p-u 99.8%

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

      8. div-inv 99.8%

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

      9. div-inv 99.8%

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

      10. associate-+r- 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. exp-neg 99.7%

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

      2. log1p-undefine 99.7%

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

      3. *-un-lft-identity 99.7%

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

      4. pow-exp 99.7%

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

      5. add-exp-log 99.8%

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

      6. pow-exp 99.7%

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

      7. *-un-lft-identity 99.7%

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

      8. associate--l+ 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in KbT around inf 83.2%

      \[\leadsto \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} \cdot NdChar + \frac{NaChar}{\color{blue}{2}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.22 \cdot 10^{-126}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 4.6 \cdot 10^{-192}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.65 \cdot 10^{-116}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 0.00028:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 2.7 \cdot 10^{+32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 4.8 \cdot 10^{+144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ t_2 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_3 := t\_2 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ t_4 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;NdChar \leq -5.8 \cdot 10^{-126}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;NdChar \leq 1.4 \cdot 10^{-191}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.35 \cdot 10^{-116}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;NdChar \leq 1.16 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 4.3 \cdot 10^{+30}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;NdChar \leq 3.9 \cdot 10^{+46}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;NdChar \leq 6.8 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (- 2.0 (/ Ec KbT)))))
        (t_2
         (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_3
         (+
          t_2
          (/
           NaChar
           (-
            (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
            (/ mu KbT)))))
        (t_4
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))))
   (if (<= NdChar -5.8e-126)
     t_3
     (if (<= NdChar 1.4e-191)
       (+
        t_0
        (/
         NdChar
         (- (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) (/ Ec KbT))))
       (if (<= NdChar 1.35e-116)
         t_4
         (if (<= NdChar 1.16e-32)
           t_1
           (if (<= NdChar 4.3e+30)
             t_3
             (if (<= NdChar 3.9e+46)
               t_4
               (if (<= NdChar 6.8e+144) t_1 (+ t_2 (/ 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 t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	double t_2 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_3 = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	double t_4 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	double tmp;
	if (NdChar <= -5.8e-126) {
		tmp = t_3;
	} else if (NdChar <= 1.4e-191) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 1.35e-116) {
		tmp = t_4;
	} else if (NdChar <= 1.16e-32) {
		tmp = t_1;
	} else if (NdChar <= 4.3e+30) {
		tmp = t_3;
	} else if (NdChar <= 3.9e+46) {
		tmp = t_4;
	} else if (NdChar <= 6.8e+144) {
		tmp = t_1;
	} else {
		tmp = t_2 + (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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (2.0d0 - (ec / kbt)))
    t_2 = ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_3 = t_2 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    t_4 = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    if (ndchar <= (-5.8d-126)) then
        tmp = t_3
    else if (ndchar <= 1.4d-191) then
        tmp = t_0 + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))
    else if (ndchar <= 1.35d-116) then
        tmp = t_4
    else if (ndchar <= 1.16d-32) then
        tmp = t_1
    else if (ndchar <= 4.3d+30) then
        tmp = t_3
    else if (ndchar <= 3.9d+46) then
        tmp = t_4
    else if (ndchar <= 6.8d+144) then
        tmp = t_1
    else
        tmp = t_2 + (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 t_0 = NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	double t_2 = NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_3 = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	double t_4 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double tmp;
	if (NdChar <= -5.8e-126) {
		tmp = t_3;
	} else if (NdChar <= 1.4e-191) {
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 1.35e-116) {
		tmp = t_4;
	} else if (NdChar <= 1.16e-32) {
		tmp = t_1;
	} else if (NdChar <= 4.3e+30) {
		tmp = t_3;
	} else if (NdChar <= 3.9e+46) {
		tmp = t_4;
	} else if (NdChar <= 6.8e+144) {
		tmp = t_1;
	} else {
		tmp = t_2 + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (2.0 - (Ec / KbT)))
	t_2 = NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_3 = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	t_4 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	tmp = 0
	if NdChar <= -5.8e-126:
		tmp = t_3
	elif NdChar <= 1.4e-191:
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	elif NdChar <= 1.35e-116:
		tmp = t_4
	elif NdChar <= 1.16e-32:
		tmp = t_1
	elif NdChar <= 4.3e+30:
		tmp = t_3
	elif NdChar <= 3.9e+46:
		tmp = t_4
	elif NdChar <= 6.8e+144:
		tmp = t_1
	else:
		tmp = t_2 + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))))
	t_2 = Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	t_3 = Float64(t_2 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))))
	t_4 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	tmp = 0.0
	if (NdChar <= -5.8e-126)
		tmp = t_3;
	elseif (NdChar <= 1.4e-191)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))));
	elseif (NdChar <= 1.35e-116)
		tmp = t_4;
	elseif (NdChar <= 1.16e-32)
		tmp = t_1;
	elseif (NdChar <= 4.3e+30)
		tmp = t_3;
	elseif (NdChar <= 3.9e+46)
		tmp = t_4;
	elseif (NdChar <= 6.8e+144)
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (2.0 - (Ec / KbT)));
	t_2 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_3 = t_2 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	t_4 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	tmp = 0.0;
	if (NdChar <= -5.8e-126)
		tmp = t_3;
	elseif (NdChar <= 1.4e-191)
		tmp = t_0 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	elseif (NdChar <= 1.35e-116)
		tmp = t_4;
	elseif (NdChar <= 1.16e-32)
		tmp = t_1;
	elseif (NdChar <= 4.3e+30)
		tmp = t_3;
	elseif (NdChar <= 3.9e+46)
		tmp = t_4;
	elseif (NdChar <= 6.8e+144)
		tmp = t_1;
	else
		tmp = t_2 + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar * N[(1.0 / 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$3 = N[(t$95$2 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -5.8e-126], t$95$3, If[LessEqual[NdChar, 1.4e-191], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.35e-116], t$95$4, If[LessEqual[NdChar, 1.16e-32], t$95$1, If[LessEqual[NdChar, 4.3e+30], t$95$3, If[LessEqual[NdChar, 3.9e+46], t$95$4, If[LessEqual[NdChar, 6.8e+144], t$95$1, N[(t$95$2 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -5.79999999999999975e-126 or 1.16000000000000001e-32 < NdChar < 4.3e30

   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%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. add-exp-log 99.9%

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

      4. rec-exp 99.9%

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

      5. log1p-expm1-u 99.9%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.9%

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

      2. log1p-undefine 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. pow-exp 99.9%

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

      5. add-exp-log 99.9%

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

      6. pow-exp 99.9%

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

      7. *-un-lft-identity 99.9%

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

      8. associate--l+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in KbT around inf 70.8%

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

   if -5.79999999999999975e-126 < NdChar < 1.40000000000000006e-191

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 79.5%

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

   if 1.40000000000000006e-191 < NdChar < 1.35e-116 or 4.3e30 < NdChar < 3.89999999999999995e46

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 81.6%

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

   6. Taylor expanded in Ev around inf 58.0%

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

   if 1.35e-116 < NdChar < 1.16000000000000001e-32 or 3.89999999999999995e46 < NdChar < 6.7999999999999998e144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-neg-frac2 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in Ec around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. unsub-neg 68.3%

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

   10. Simplified 68.3%

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

   if 6.7999999999999998e144 < NdChar

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

      3. add-exp-log 99.7%

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

      4. rec-exp 99.7%

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

      5. log1p-expm1-u 99.7%

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

      6. log1p-define 99.8%

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

      7. expm1-log1p-u 99.8%

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

      8. div-inv 99.8%

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

      9. div-inv 99.8%

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

      10. associate-+r- 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. exp-neg 99.7%

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

      2. log1p-undefine 99.7%

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

      3. *-un-lft-identity 99.7%

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

      4. pow-exp 99.7%

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

      5. add-exp-log 99.8%

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

      6. pow-exp 99.7%

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

      7. *-un-lft-identity 99.7%

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

      8. associate--l+ 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in KbT around inf 83.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -5.8 \cdot 10^{-126}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.4 \cdot 10^{-191}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.35 \cdot 10^{-116}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.16 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 4.3 \cdot 10^{+30}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 6.8 \cdot 10^{+144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{if}\;Ec \leq -7.5 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Ec \leq -1.25 \cdot 10^{-217}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ec \leq 1.8 \cdot 10^{-64}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))))))
   (if (<= Ec -7.5e+155)
     t_1
     (if (<= Ec -1.25e-217)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
       (if (<= Ec 1.8e-64)
         (+ t_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(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((Ec / -KbT))));
	double tmp;
	if (Ec <= -7.5e+155) {
		tmp = t_1;
	} else if (Ec <= -1.25e-217) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (Ec <= 1.8e-64) {
		tmp = t_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(((ev + (vef + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((ec / -kbt))))
    if (ec <= (-7.5d+155)) then
        tmp = t_1
    else if (ec <= (-1.25d-217)) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (ec <= 1.8d-64) then
        tmp = t_0 + (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(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((Ec / -KbT))));
	double tmp;
	if (Ec <= -7.5e+155) {
		tmp = t_1;
	} else if (Ec <= -1.25e-217) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (Ec <= 1.8e-64) {
		tmp = t_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(((Ev + (Vef + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((Ec / -KbT))))
	tmp = 0
	if Ec <= -7.5e+155:
		tmp = t_1
	elif Ec <= -1.25e-217:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif Ec <= 1.8e-64:
		tmp = t_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(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))))
	tmp = 0.0
	if (Ec <= -7.5e+155)
		tmp = t_1;
	elseif (Ec <= -1.25e-217)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (Ec <= 1.8e-64)
		tmp = Float64(t_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(((Ev + (Vef + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((Ec / -KbT))));
	tmp = 0.0;
	if (Ec <= -7.5e+155)
		tmp = t_1;
	elseif (Ec <= -1.25e-217)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (Ec <= 1.8e-64)
		tmp = t_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[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ec, -7.5e+155], t$95$1, If[LessEqual[Ec, -1.25e-217], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 1.8e-64], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if Ec < -7.4999999999999999e155 or 1.7999999999999999e-64 < Ec

   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%

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

   5. Taylor expanded in Ec around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. distribute-neg-frac2 85.4%

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

   7. Simplified 85.4%

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

   if -7.4999999999999999e155 < Ec < -1.2500000000000001e-217

   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%

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

   5. Taylor expanded in EDonor around inf 82.0%

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

   if -1.2500000000000001e-217 < Ec < 1.7999999999999999e-64

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 86.7%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -7.5 \cdot 10^{+155}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;Ec \leq -1.25 \cdot 10^{-217}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ec \leq 1.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -7 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq -2.22 \cdot 10^{+15}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;Vef \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -7e+112)
     t_1
     (if (<= Vef -2.22e+15)
       (+
        (/ NdChar (+ 1.0 (exp (/ mu KbT))))
        (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))
       (if (<= Vef 3.5e+42)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor 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(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -7e+112) {
		tmp = t_1;
	} else if (Vef <= -2.22e+15) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	} else if (Vef <= 3.5e+42) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / 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(((ev + (vef + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-7d+112)) then
        tmp = t_1
    else if (vef <= (-2.22d+15)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    else if (vef <= 3.5d+42) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / 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(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -7e+112) {
		tmp = t_1;
	} else if (Vef <= -2.22e+15) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	} else if (Vef <= 3.5e+42) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / 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(((Ev + (Vef + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -7e+112:
		tmp = t_1
	elif Vef <= -2.22e+15:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	elif Vef <= 3.5e+42:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / 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(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -7e+112)
		tmp = t_1;
	elseif (Vef <= -2.22e+15)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))));
	elseif (Vef <= 3.5e+42)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / 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(((Ev + (Vef + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -7e+112)
		tmp = t_1;
	elseif (Vef <= -2.22e+15)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	elseif (Vef <= 3.5e+42)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / 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[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -7e+112], t$95$1, If[LessEqual[Vef, -2.22e+15], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 3.5e+42], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -6.99999999999999994e112 or 3.50000000000000023e42 < Vef

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 83.4%

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

   if -6.99999999999999994e112 < Vef < -2.22e15

   1. Initial program 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in mu around inf 86.0%

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

   6. Taylor expanded in mu around inf 79.1%

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

      1. associate-*r/ 79.1%

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

      2. mul-1-neg 79.1%

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

   8. Simplified 79.1%

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

   if -2.22e15 < Vef < 3.50000000000000023e42

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 79.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -7 \cdot 10^{+112}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -2.22 \cdot 10^{+15}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;Vef \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -900000 \lor \neg \left(mu \leq 3.5 \cdot 10^{+56}\right):\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))))
   (if (or (<= mu -900000.0) (not (<= mu 3.5e+56)))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double tmp;
	if ((mu <= -900000.0) || !(mu <= 3.5e+56)) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))
    if ((mu <= (-900000.0d0)) .or. (.not. (mu <= 3.5d+56))) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double tmp;
	if ((mu <= -900000.0) || !(mu <= 3.5e+56)) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))
	tmp = 0
	if (mu <= -900000.0) or not (mu <= 3.5e+56):
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = t_0 + (NdChar / (1.0 + math.exp((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(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT))))
	tmp = 0.0
	if ((mu <= -900000.0) || !(mu <= 3.5e+56))
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	tmp = 0.0;
	if ((mu <= -900000.0) || ~((mu <= 3.5e+56)))
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	else
		tmp = t_0 + (NdChar / (1.0 + exp((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[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[mu, -900000.0], N[Not[LessEqual[mu, 3.5e+56]], $MachinePrecision]], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if mu < -9e5 or 3.49999999999999999e56 < mu

   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%

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

   5. Taylor expanded in mu around inf 84.9%

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

   if -9e5 < mu < 3.49999999999999999e56

   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%

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

   5. Taylor expanded in EDonor around inf 79.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -900000 \lor \neg \left(mu \leq 3.5 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq -4.2 \cdot 10^{+181} \lor \neg \left(Ec \leq 7 \cdot 10^{+152}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Ec -4.2e+181) (not (<= Ec 7e+152)))
   (+
    (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
    (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Ec <= -4.2e+181) || !(Ec <= 7e+152)) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ec <= (-4.2d+181)) .or. (.not. (ec <= 7d+152))) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Ec <= -4.2e+181) || !(Ec <= 7e+152)) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Ec <= -4.2e+181) or not (Ec <= 7e+152):
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Ec <= -4.2e+181) || !(Ec <= 7e+152))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Ec <= -4.2e+181) || ~((Ec <= 7e+152)))
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Ec, -4.2e+181], N[Not[LessEqual[Ec, 7e+152]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < -4.19999999999999995e181 or 6.99999999999999963e152 < Ec

   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%

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

   5. Taylor expanded in Ec around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. distribute-neg-frac2 90.1%

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

   7. Simplified 90.1%

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

   8. Taylor expanded in EAccept around inf 69.9%

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

   if -4.19999999999999995e181 < Ec < 6.99999999999999963e152

   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%

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

   5. Taylor expanded in EDonor around inf 78.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -4.2 \cdot 10^{+181} \lor \neg \left(Ec \leq 7 \cdot 10^{+152}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{if}\;mu \leq -1.25 \cdot 10^{+60}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq 6.2 \cdot 10^{-188}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.4 \cdot 10^{+92}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))))
   (if (<= mu -1.25e+60)
     t_0
     (if (<= mu 6.2e-188)
       (+
        (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
        (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
       (if (<= mu 1.4e+92)
         (+
          (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
          (/
           NaChar
           (-
            (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
            (/ 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 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	double tmp;
	if (mu <= -1.25e+60) {
		tmp = t_0;
	} else if (mu <= 6.2e-188) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (mu <= 1.4e+92) {
		tmp = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (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 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    if (mu <= (-1.25d+60)) then
        tmp = t_0
    else if (mu <= 6.2d-188) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (mu <= 1.4d+92) then
        tmp = (ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (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 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	double tmp;
	if (mu <= -1.25e+60) {
		tmp = t_0;
	} else if (mu <= 6.2e-188) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (mu <= 1.4e+92) {
		tmp = (NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	tmp = 0
	if mu <= -1.25e+60:
		tmp = t_0
	elif mu <= 6.2e-188:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif mu <= 1.4e+92:
		tmp = (NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))))
	tmp = 0.0
	if (mu <= -1.25e+60)
		tmp = t_0;
	elseif (mu <= 6.2e-188)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (mu <= 1.4e+92)
		tmp = Float64(Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / 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 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	tmp = 0.0;
	if (mu <= -1.25e+60)
		tmp = t_0;
	elseif (mu <= 6.2e-188)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (mu <= 1.4e+92)
		tmp = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (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[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -1.25e+60], t$95$0, If[LessEqual[mu, 6.2e-188], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.4e+92], N[(N[(NdChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -1.24999999999999994e60 or 1.4e92 < mu

   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%

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

   5. Taylor expanded in mu around inf 88.3%

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

   6. Taylor expanded in mu around inf 75.2%

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

      1. associate-*r/ 75.2%

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

      2. mul-1-neg 75.2%

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

   8. Simplified 75.2%

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

   if -1.24999999999999994e60 < mu < 6.2000000000000004e-188

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in EDonor around inf 73.7%

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

   6. Taylor expanded in Ev around inf 66.5%

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

   if 6.2000000000000004e-188 < mu < 1.4e92

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 100.0%

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

      3. add-exp-log 100.0%

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

      4. rec-exp 100.0%

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

      5. log1p-expm1-u 100.0%

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

      6. log1p-define 100.0%

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

      7. expm1-log1p-u 100.0%

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

      8. div-inv 100.0%

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

      9. div-inv 100.0%

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

      10. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. exp-neg 100.0%

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

      2. log1p-undefine 100.0%

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

      3. *-un-lft-identity 100.0%

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

      4. pow-exp 100.0%

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

      5. add-exp-log 100.0%

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

      6. pow-exp 100.0%

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

      7. *-un-lft-identity 100.0%

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

      8. associate--l+ 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in KbT around inf 67.6%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -1.25 \cdot 10^{+60}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq 6.2 \cdot 10^{-188}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.4 \cdot 10^{+92}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))
  (* NdChar (/ 1.0 (+ 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(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar * (1.0 / (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(((ev + (vef + (eaccept - mu))) / kbt)))) + (ndchar * (1.0d0 / (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(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar * (1.0 / (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(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar * (1.0 / (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(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar * Float64(1.0 / 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(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar * (1.0 / (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[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

   1. clear-num 99.8%

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

   2. associate-/r/ 99.9%

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

   3. add-exp-log 99.9%

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

   4. rec-exp 99.9%

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

   5. log1p-expm1-u 99.9%

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

   6. log1p-define 99.9%

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

   7. expm1-log1p-u 99.9%

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

   8. div-inv 99.9%

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

   9. div-inv 99.9%

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

   10. associate-+r- 99.9%

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

6. Applied egg-rr 99.9%

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

   1. exp-neg 99.9%

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

   2. log1p-undefine 99.9%

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

   3. *-un-lft-identity 99.9%

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

   4. pow-exp 99.9%

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

   5. add-exp-log 99.9%

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

   6. pow-exp 99.9%

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

   7. *-un-lft-identity 99.9%

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

   8. associate--l+ 99.9%

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

8. Applied egg-rr 99.9%

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

9. Final simplification 99.9%

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

Alternative 12: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

Java

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

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + math.pow(math.e, ((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(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + (exp(1) ^ Float64(Float64(EDonor + Float64(Float64(mu + Vef) - Ec)) / KbT)))))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + (2.71828182845904523536 ^ ((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[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Power[E, N[(N[(EDonor + N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

   1. *-un-lft-identity 99.9%

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

   2. exp-prod 99.9%

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

   3. associate-+r- 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 13: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) 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(((Ev + (Vef + (EAccept - mu))) / 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(((ev + (vef + (eaccept - mu))) / 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(((Ev + (Vef + (EAccept - mu))) / 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(((Ev + (Vef + (EAccept - mu))) / 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(Ev + Float64(Vef + Float64(EAccept - mu))) / 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(((Ev + (Vef + (EAccept - mu))) / 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[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $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 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%

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

5. Final simplification 99.9%

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

Alternative 14: 57.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -3.3 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -7.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.05 \cdot 10^{-123}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
          (/ NaChar 2.0))))
   (if (<= NdChar -3.3e+54)
     t_0
     (if (<= NdChar -7.5e-59)
       (+
        (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
        (/ NaChar (+ (/ EAccept KbT) 2.0)))
       (if (<= NdChar -1.05e-123)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/
           NaChar
           (-
            (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
            (/ mu KbT))))
         (if (<= NdChar 1.5e+144)
           (+
            (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))
            (/
             NdChar
             (-
              (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
              (/ Ec 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 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.3e+54) {
		tmp = t_0;
	} else if (NdChar <= -7.5e-59) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -1.05e-123) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 1.5e+144) {
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / 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 = (ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))) + (nachar / 2.0d0)
    if (ndchar <= (-3.3d+54)) then
        tmp = t_0
    else if (ndchar <= (-7.5d-59)) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= (-1.05d-123)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (ndchar <= 1.5d+144) then
        tmp = (nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))) + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / 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 = (NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.3e+54) {
		tmp = t_0;
	} else if (NdChar <= -7.5e-59) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -1.05e-123) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 1.5e+144) {
		tmp = (NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -3.3e+54:
		tmp = t_0
	elif NdChar <= -7.5e-59:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= -1.05e-123:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NdChar <= 1.5e+144:
		tmp = (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -3.3e+54)
		tmp = t_0;
	elseif (NdChar <= -7.5e-59)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= -1.05e-123)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NdChar <= 1.5e+144)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / 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 = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -3.3e+54)
		tmp = t_0;
	elseif (NdChar <= -7.5e-59)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= -1.05e-123)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NdChar <= 1.5e+144)
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / 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[(NdChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.3e+54], t$95$0, If[LessEqual[NdChar, -7.5e-59], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -1.05e-123], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.5e+144], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -3.3e54 or 1.49999999999999995e144 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

      3. add-exp-log 99.9%

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

      4. rec-exp 99.9%

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

      5. log1p-expm1-u 99.9%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.9%

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

      2. log1p-undefine 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. pow-exp 99.9%

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

      5. add-exp-log 99.9%

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

      6. pow-exp 99.9%

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

      7. *-un-lft-identity 99.9%

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

      8. associate--l+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in KbT around inf 74.9%

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

   if -3.3e54 < NdChar < -7.50000000000000019e-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%

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

   5. Taylor expanded in Ec around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-neg-frac2 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in EAccept around inf 63.3%

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

   9. Taylor expanded in EAccept around 0 52.3%

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

   if -7.50000000000000019e-59 < NdChar < -1.05e-123

   1. Initial program 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in mu around inf 64.5%

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

   6. Taylor expanded in KbT around inf 57.0%

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

   if -1.05e-123 < NdChar < 1.49999999999999995e144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.6%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.3 \cdot 10^{+54}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -7.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.05 \cdot 10^{-123}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -5.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -8.2 \cdot 10^{-104} \lor \neg \left(NdChar \leq 3.5 \cdot 10^{-156}\right) \land \left(NdChar \leq 1.65 \cdot 10^{-116} \lor \neg \left(NdChar \leq 1.85 \cdot 10^{+144}\right)\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
          (/ NaChar 2.0))))
   (if (<= NdChar -3.4e+54)
     t_0
     (if (<= NdChar -5.2e-68)
       (+
        (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
        (/ NaChar (+ (/ EAccept KbT) 2.0)))
       (if (or (<= NdChar -8.2e-104)
               (and (not (<= NdChar 3.5e-156))
                    (or (<= NdChar 1.65e-116) (not (<= NdChar 1.85e+144)))))
         t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))
          (/ NdChar (- 2.0 (/ 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 = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.4e+54) {
		tmp = t_0;
	} else if (NdChar <= -5.2e-68) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if ((NdChar <= -8.2e-104) || (!(NdChar <= 3.5e-156) && ((NdChar <= 1.65e-116) || !(NdChar <= 1.85e+144)))) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (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 = (ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))) + (nachar / 2.0d0)
    if (ndchar <= (-3.4d+54)) then
        tmp = t_0
    else if (ndchar <= (-5.2d-68)) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else if ((ndchar <= (-8.2d-104)) .or. (.not. (ndchar <= 3.5d-156)) .and. (ndchar <= 1.65d-116) .or. (.not. (ndchar <= 1.85d+144))) then
        tmp = t_0
    else
        tmp = (nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))) + (ndchar / (2.0d0 - (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 = (NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.4e+54) {
		tmp = t_0;
	} else if (NdChar <= -5.2e-68) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if ((NdChar <= -8.2e-104) || (!(NdChar <= 3.5e-156) && ((NdChar <= 1.65e-116) || !(NdChar <= 1.85e+144)))) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -3.4e+54:
		tmp = t_0
	elif NdChar <= -5.2e-68:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	elif (NdChar <= -8.2e-104) or (not (NdChar <= 3.5e-156) and ((NdChar <= 1.65e-116) or not (NdChar <= 1.85e+144))):
		tmp = t_0
	else:
		tmp = (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -3.4e+54)
		tmp = t_0;
	elseif (NdChar <= -5.2e-68)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif ((NdChar <= -8.2e-104) || (!(NdChar <= 3.5e-156) && ((NdChar <= 1.65e-116) || !(NdChar <= 1.85e+144))))
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -3.4e+54)
		tmp = t_0;
	elseif (NdChar <= -5.2e-68)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	elseif ((NdChar <= -8.2e-104) || (~((NdChar <= 3.5e-156)) && ((NdChar <= 1.65e-116) || ~((NdChar <= 1.85e+144)))))
		tmp = t_0;
	else
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.4e+54], t$95$0, If[LessEqual[NdChar, -5.2e-68], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NdChar, -8.2e-104], And[N[Not[LessEqual[NdChar, 3.5e-156]], $MachinePrecision], Or[LessEqual[NdChar, 1.65e-116], N[Not[LessEqual[NdChar, 1.85e+144]], $MachinePrecision]]]], t$95$0, N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -3.4000000000000001e54 or -5.1999999999999996e-68 < NdChar < -8.19999999999999968e-104 or 3.4999999999999999e-156 < NdChar < 1.65e-116 or 1.8499999999999998e144 < NdChar

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

      3. add-exp-log 99.8%

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

      4. rec-exp 99.8%

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

      5. log1p-expm1-u 99.8%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.8%

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

      2. log1p-undefine 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. pow-exp 99.8%

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

      5. add-exp-log 99.8%

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

      6. pow-exp 99.8%

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

      7. *-un-lft-identity 99.8%

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

      8. associate--l+ 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in KbT around inf 73.5%

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

   if -3.4000000000000001e54 < NdChar < -5.1999999999999996e-68

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-neg-frac2 68.3%

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

   7. Simplified 68.3%

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

   8. Taylor expanded in EAccept around inf 61.0%

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

   9. Taylor expanded in EAccept around 0 50.4%

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

   if -8.19999999999999968e-104 < NdChar < 3.4999999999999999e-156 or 1.65e-116 < NdChar < 1.8499999999999998e144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-neg-frac2 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in Ec around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. unsub-neg 65.7%

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

   10. Simplified 65.7%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -5.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -8.2 \cdot 10^{-104} \lor \neg \left(NdChar \leq 3.5 \cdot 10^{-156}\right) \land \left(NdChar \leq 1.65 \cdot 10^{-116} \lor \neg \left(NdChar \leq 1.85 \cdot 10^{+144}\right)\right):\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -1.1 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 4.6 \cdot 10^{-163}:\\ \;\;\;\;t\_2 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5.1 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq 2.7 \cdot 10^{+144}:\\ \;\;\;\;t\_2 + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT))))))
        (t_1
         (+
          t_0
          (/
           NaChar
           (-
            (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
            (/ mu KbT)))))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))))
   (if (<= NdChar -1.1e-124)
     t_1
     (if (<= NdChar 4.6e-163)
       (+
        t_2
        (/
         NdChar
         (- (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) (/ Ec KbT))))
       (if (<= NdChar 5.1e-109)
         t_1
         (if (<= NdChar 2.7e+144)
           (+ t_2 (/ NdChar (- 2.0 (/ Ec KbT))))
           (+ t_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 t_0 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	double t_2 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double tmp;
	if (NdChar <= -1.1e-124) {
		tmp = t_1;
	} else if (NdChar <= 4.6e-163) {
		tmp = t_2 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 5.1e-109) {
		tmp = t_1;
	} else if (NdChar <= 2.7e+144) {
		tmp = t_2 + (NdChar / (2.0 - (Ec / KbT)));
	} else {
		tmp = t_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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))
    t_1 = t_0 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    t_2 = nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))
    if (ndchar <= (-1.1d-124)) then
        tmp = t_1
    else if (ndchar <= 4.6d-163) then
        tmp = t_2 + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))
    else if (ndchar <= 5.1d-109) then
        tmp = t_1
    else if (ndchar <= 2.7d+144) then
        tmp = t_2 + (ndchar / (2.0d0 - (ec / kbt)))
    else
        tmp = t_0 + (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 t_0 = NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	double t_1 = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	double t_2 = NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	double tmp;
	if (NdChar <= -1.1e-124) {
		tmp = t_1;
	} else if (NdChar <= 4.6e-163) {
		tmp = t_2 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else if (NdChar <= 5.1e-109) {
		tmp = t_1;
	} else if (NdChar <= 2.7e+144) {
		tmp = t_2 + (NdChar / (2.0 - (Ec / KbT)));
	} else {
		tmp = t_0 + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))
	t_1 = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	t_2 = NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))
	tmp = 0
	if NdChar <= -1.1e-124:
		tmp = t_1
	elif NdChar <= 4.6e-163:
		tmp = t_2 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	elif NdChar <= 5.1e-109:
		tmp = t_1
	elif NdChar <= 2.7e+144:
		tmp = t_2 + (NdChar / (2.0 - (Ec / KbT)))
	else:
		tmp = t_0 + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT))))
	tmp = 0.0
	if (NdChar <= -1.1e-124)
		tmp = t_1;
	elseif (NdChar <= 4.6e-163)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))));
	elseif (NdChar <= 5.1e-109)
		tmp = t_1;
	elseif (NdChar <= 2.7e+144)
		tmp = Float64(t_2 + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))));
	else
		tmp = Float64(t_0 + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))));
	t_1 = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	t_2 = NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -1.1e-124)
		tmp = t_1;
	elseif (NdChar <= 4.6e-163)
		tmp = t_2 + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	elseif (NdChar <= 5.1e-109)
		tmp = t_1;
	elseif (NdChar <= 2.7e+144)
		tmp = t_2 + (NdChar / (2.0 - (Ec / KbT)));
	else
		tmp = t_0 + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar * N[(1.0 / N[(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[(t$95$0 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.1e-124], t$95$1, If[LessEqual[NdChar, 4.6e-163], N[(t$95$2 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 5.1e-109], t$95$1, If[LessEqual[NdChar, 2.7e+144], N[(t$95$2 + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -1.0999999999999999e-124 or 4.5999999999999999e-163 < NdChar < 5.10000000000000041e-109

   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%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. add-exp-log 99.9%

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

      4. rec-exp 99.9%

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

      5. log1p-expm1-u 99.9%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.9%

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

      2. log1p-undefine 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. pow-exp 99.9%

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

      5. add-exp-log 99.9%

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

      6. pow-exp 99.9%

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

      7. *-un-lft-identity 99.9%

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

      8. associate--l+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in KbT around inf 73.4%

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

   if -1.0999999999999999e-124 < NdChar < 4.5999999999999999e-163

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.7%

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

   if 5.10000000000000041e-109 < NdChar < 2.70000000000000015e144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 72.6%

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

      1. mul-1-neg 72.6%

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

      2. distribute-neg-frac2 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in Ec around 0 57.8%

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

      1. mul-1-neg 57.8%

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

      2. unsub-neg 57.8%

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

   10. Simplified 57.8%

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

   if 2.70000000000000015e144 < NdChar

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

      3. add-exp-log 99.7%

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

      4. rec-exp 99.7%

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

      5. log1p-expm1-u 99.7%

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

      6. log1p-define 99.8%

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

      7. expm1-log1p-u 99.8%

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

      8. div-inv 99.8%

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

      9. div-inv 99.8%

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

      10. associate-+r- 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. exp-neg 99.7%

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

      2. log1p-undefine 99.7%

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

      3. *-un-lft-identity 99.7%

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

      4. pow-exp 99.7%

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

      5. add-exp-log 99.8%

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

      6. pow-exp 99.7%

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

      7. *-un-lft-identity 99.7%

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

      8. associate--l+ 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in KbT around inf 83.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.1 \cdot 10^{-124}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 4.6 \cdot 10^{-163}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NdChar \leq 5.1 \cdot 10^{-109}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 2.7 \cdot 10^{+144}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -3.5 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -9.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -6.1 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 7.6 \cdot 10^{+146}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
          (/ NaChar 2.0))))
   (if (<= NdChar -3.5e+54)
     t_0
     (if (<= NdChar -9.5e-60)
       (+
        (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
        (/ NaChar (+ (/ EAccept KbT) 2.0)))
       (if (<= NdChar -6.1e-99)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/
           NaChar
           (-
            (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
            (/ mu KbT))))
         (if (<= NdChar 7.6e+146)
           (+
            (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))
            (/ NdChar (- 2.0 (/ Ec 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 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.5e+54) {
		tmp = t_0;
	} else if (NdChar <= -9.5e-60) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -6.1e-99) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 7.6e+146) {
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / 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 = (ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))) + (nachar / 2.0d0)
    if (ndchar <= (-3.5d+54)) then
        tmp = t_0
    else if (ndchar <= (-9.5d-60)) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= (-6.1d-99)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (ndchar <= 7.6d+146) then
        tmp = (nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))) + (ndchar / (2.0d0 - (ec / 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 = (NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.5e+54) {
		tmp = t_0;
	} else if (NdChar <= -9.5e-60) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -6.1e-99) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 7.6e+146) {
		tmp = (NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -3.5e+54:
		tmp = t_0
	elif NdChar <= -9.5e-60:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= -6.1e-99:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NdChar <= 7.6e+146:
		tmp = (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -3.5e+54)
		tmp = t_0;
	elseif (NdChar <= -9.5e-60)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= -6.1e-99)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NdChar <= 7.6e+146)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(2.0 - Float64(Ec / 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 = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -3.5e+54)
		tmp = t_0;
	elseif (NdChar <= -9.5e-60)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= -6.1e-99)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NdChar <= 7.6e+146)
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / 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[(NdChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.5e+54], t$95$0, If[LessEqual[NdChar, -9.5e-60], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -6.1e-99], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 7.6e+146], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -3.5000000000000001e54 or 7.59999999999999958e146 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

      3. add-exp-log 99.9%

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

      4. rec-exp 99.9%

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

      5. log1p-expm1-u 99.9%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.9%

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

      2. log1p-undefine 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. pow-exp 99.9%

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

      5. add-exp-log 99.9%

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

      6. pow-exp 99.9%

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

      7. *-un-lft-identity 99.9%

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

      8. associate--l+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in KbT around inf 74.9%

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

   if -3.5000000000000001e54 < NdChar < -9.49999999999999958e-60

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-neg-frac2 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in EAccept around inf 63.3%

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

   9. Taylor expanded in EAccept around 0 52.3%

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

   if -9.49999999999999958e-60 < NdChar < -6.1000000000000003e-99

   1. Initial program 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in mu around inf 63.4%

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

   6. Taylor expanded in KbT around inf 63.3%

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

   if -6.1000000000000003e-99 < NdChar < 7.59999999999999958e146

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. distribute-neg-frac2 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in Ec around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   10. Simplified 63.2%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.5 \cdot 10^{+54}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -9.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -6.1 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 7.6 \cdot 10^{+146}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -3.3 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -2.6 \cdot 10^{-58}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -6 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
          (/ NaChar 2.0))))
   (if (<= NdChar -3.3e+54)
     t_0
     (if (<= NdChar -2.6e-58)
       (+
        (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
        (/ NaChar (+ (/ EAccept KbT) 2.0)))
       (if (<= NdChar -6e-99)
         (+
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/
           NaChar
           (-
            (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
            (/ mu KbT))))
         (if (<= NdChar 3.2e+145)
           (+
            (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))
            (/ NdChar (- 2.0 (/ Ec 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 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.3e+54) {
		tmp = t_0;
	} else if (NdChar <= -2.6e-58) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -6e-99) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 3.2e+145) {
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / 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 = (ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))) + (nachar / 2.0d0)
    if (ndchar <= (-3.3d+54)) then
        tmp = t_0
    else if (ndchar <= (-2.6d-58)) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= (-6d-99)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    else if (ndchar <= 3.2d+145) then
        tmp = (nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))) + (ndchar / (2.0d0 - (ec / 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 = (NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.3e+54) {
		tmp = t_0;
	} else if (NdChar <= -2.6e-58) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -6e-99) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	} else if (NdChar <= 3.2e+145) {
		tmp = (NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -3.3e+54:
		tmp = t_0
	elif NdChar <= -2.6e-58:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= -6e-99:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	elif NdChar <= 3.2e+145:
		tmp = (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -3.3e+54)
		tmp = t_0;
	elseif (NdChar <= -2.6e-58)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= -6e-99)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))));
	elseif (NdChar <= 3.2e+145)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(2.0 - Float64(Ec / 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 = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -3.3e+54)
		tmp = t_0;
	elseif (NdChar <= -2.6e-58)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= -6e-99)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	elseif (NdChar <= 3.2e+145)
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / (2.0 - (Ec / 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[(NdChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.3e+54], t$95$0, If[LessEqual[NdChar, -2.6e-58], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -6e-99], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.2e+145], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -3.3e54 or 3.20000000000000008e145 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

      3. add-exp-log 99.9%

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

      4. rec-exp 99.9%

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

      5. log1p-expm1-u 99.9%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.9%

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

      2. log1p-undefine 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. pow-exp 99.9%

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

      5. add-exp-log 99.9%

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

      6. pow-exp 99.9%

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

      7. *-un-lft-identity 99.9%

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

      8. associate--l+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in KbT around inf 74.9%

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

   if -3.3e54 < NdChar < -2.60000000000000007e-58

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-neg-frac2 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in EAccept around inf 63.3%

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

   9. Taylor expanded in EAccept around 0 52.3%

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

   if -2.60000000000000007e-58 < NdChar < -6.00000000000000012e-99

   1. Initial program 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in EDonor around inf 62.9%

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

   6. Taylor expanded in KbT around inf 62.7%

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

   if -6.00000000000000012e-99 < NdChar < 3.20000000000000008e145

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. distribute-neg-frac2 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in Ec around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   10. Simplified 63.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.3 \cdot 10^{+54}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -2.6 \cdot 10^{-58}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -6 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 57.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -3.5 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -5.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -6.1 \cdot 10^{-99} \lor \neg \left(NdChar \leq 1.5 \cdot 10^{+144}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
          (/ NaChar 2.0))))
   (if (<= NdChar -3.5e+54)
     t_0
     (if (<= NdChar -5.2e-67)
       (+
        (/ NdChar (+ 1.0 (exp (/ Ec (- KbT)))))
        (/ NaChar (+ (/ EAccept KbT) 2.0)))
       (if (or (<= NdChar -6.1e-99) (not (<= NdChar 1.5e+144)))
         t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))
          (/ NdChar (+ (/ mu KbT) 2.0))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.5e+54) {
		tmp = t_0;
	} else if (NdChar <= -5.2e-67) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if ((NdChar <= -6.1e-99) || !(NdChar <= 1.5e+144)) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))) + (nachar / 2.0d0)
    if (ndchar <= (-3.5d+54)) then
        tmp = t_0
    else if (ndchar <= (-5.2d-67)) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else if ((ndchar <= (-6.1d-99)) .or. (.not. (ndchar <= 1.5d+144))) then
        tmp = t_0
    else
        tmp = (nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.5e+54) {
		tmp = t_0;
	} else if (NdChar <= -5.2e-67) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if ((NdChar <= -6.1e-99) || !(NdChar <= 1.5e+144)) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -3.5e+54:
		tmp = t_0
	elif NdChar <= -5.2e-67:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	elif (NdChar <= -6.1e-99) or not (NdChar <= 1.5e+144):
		tmp = t_0
	else:
		tmp = (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -3.5e+54)
		tmp = t_0;
	elseif (NdChar <= -5.2e-67)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif ((NdChar <= -6.1e-99) || !(NdChar <= 1.5e+144))
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -3.5e+54)
		tmp = t_0;
	elseif (NdChar <= -5.2e-67)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	elseif ((NdChar <= -6.1e-99) || ~((NdChar <= 1.5e+144)))
		tmp = t_0;
	else
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.5e+54], t$95$0, If[LessEqual[NdChar, -5.2e-67], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NdChar, -6.1e-99], N[Not[LessEqual[NdChar, 1.5e+144]], $MachinePrecision]], t$95$0, N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -3.5000000000000001e54 or -5.1999999999999998e-67 < NdChar < -6.1000000000000003e-99 or 1.49999999999999995e144 < NdChar

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

      3. add-exp-log 99.8%

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

      4. rec-exp 99.8%

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

      5. log1p-expm1-u 99.8%

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

      6. log1p-define 99.8%

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

      7. expm1-log1p-u 99.8%

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

      8. div-inv 99.8%

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

      9. div-inv 99.8%

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

      10. associate-+r- 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. exp-neg 99.8%

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

      2. log1p-undefine 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. pow-exp 99.8%

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

      5. add-exp-log 99.8%

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

      6. pow-exp 99.8%

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

      7. *-un-lft-identity 99.8%

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

      8. associate--l+ 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in KbT around inf 73.1%

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

   if -3.5000000000000001e54 < NdChar < -5.1999999999999998e-67

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ec around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-neg-frac2 68.3%

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

   7. Simplified 68.3%

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

   8. Taylor expanded in EAccept around inf 61.0%

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

   9. Taylor expanded in EAccept around 0 50.4%

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

   if -6.1000000000000003e-99 < NdChar < 1.49999999999999995e144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 76.9%

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

   6. Taylor expanded in mu around 0 62.1%

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

      1. +-commutative 62.1%

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

   8. Simplified 62.1%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.5 \cdot 10^{+54}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -5.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -6.1 \cdot 10^{-99} \lor \neg \left(NdChar \leq 1.5 \cdot 10^{+144}\right):\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 56.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -94 \lor \neg \left(NaChar \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -94.0) (not (<= NaChar 7.8e-16)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))
    (/ NdChar 2.0))
   (+
    (* NdChar (/ 1.0 (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
    (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -94.0) || !(NaChar <= 7.8e-16)) {
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-94.0d0)) .or. (.not. (nachar <= 7.8d-16))) then
        tmp = (nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar * (1.0d0 / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt))))) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -94.0) || !(NaChar <= 7.8e-16)) {
		tmp = (NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar * (1.0 / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -94.0) or not (NaChar <= 7.8e-16):
		tmp = (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar * (1.0 / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -94.0) || !(NaChar <= 7.8e-16))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -94.0) || ~((NaChar <= 7.8e-16)))
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar * (1.0 / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT))))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -94.0], N[Not[LessEqual[NaChar, 7.8e-16]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -94 or 7.79999999999999954e-16 < 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%

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

   5. Taylor expanded in KbT around inf 59.2%

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

   if -94 < NaChar < 7.79999999999999954e-16

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

      3. add-exp-log 99.9%

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

      4. rec-exp 99.9%

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

      5. log1p-expm1-u 99.9%

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

      6. log1p-define 99.9%

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

      7. expm1-log1p-u 99.9%

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

      8. div-inv 99.9%

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

      9. div-inv 99.9%

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

      10. associate-+r- 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. exp-neg 99.9%

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

      2. log1p-undefine 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. pow-exp 99.9%

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

      5. add-exp-log 99.9%

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

      6. pow-exp 99.9%

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

      7. *-un-lft-identity 99.9%

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

      8. associate--l+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in KbT around inf 58.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -94 \lor \neg \left(NaChar \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot \frac{1}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -2.7 \cdot 10^{-127}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.26 \cdot 10^{+147}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar -2.7e-127)
   (+
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
    (/ NaChar (+ (/ EAccept KbT) 2.0)))
   (if (<= NdChar 1.26e+147)
     (+
      (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))
      (/ NdChar 2.0))
     (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (/ NaChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -2.7e-127) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 1.26e+147) {
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ndchar <= (-2.7d-127)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= 1.26d+147) then
        tmp = (nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -2.7e-127) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 1.26e+147) {
		tmp = (NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= -2.7e-127:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= 1.26e+147:
		tmp = (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= -2.7e-127)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= 1.26e+147)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= -2.7e-127)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= 1.26e+147)
		tmp = (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, -2.7e-127], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.26e+147], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 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 / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -2.7e-127

   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%

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

   5. Taylor expanded in EDonor around inf 69.4%

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

   6. Taylor expanded in EAccept around inf 54.5%

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

   7. Taylor expanded in EAccept around 0 52.2%

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

   if -2.7e-127 < NdChar < 1.26e147

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.2%

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

   if 1.26e147 < NdChar

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in Ec around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. distribute-neg-frac2 66.4%

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

   7. Simplified 66.4%

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

   8. Taylor expanded in KbT around inf 60.5%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.7 \cdot 10^{-127}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.26 \cdot 10^{+147}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 41.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -1.2e+26)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (if (<= NaChar 3.1e-10)
     (+
      (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
      (/ NaChar (+ (/ EAccept KbT) 2.0)))
     (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.2e+26) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 3.1e-10) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-1.2d+26)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (nachar <= 3.1d-10) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.2e+26) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 3.1e-10) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -1.2e+26:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif NaChar <= 3.1e-10:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -1.2e+26)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (NaChar <= 3.1e-10)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -1.2e+26)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (NaChar <= 3.1e-10)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -1.2e+26], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.1e-10], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.20000000000000002e26

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 59.0%

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

   6. Taylor expanded in EAccept around inf 48.6%

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

   if -1.20000000000000002e26 < NaChar < 3.10000000000000015e-10

   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%

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

   5. Taylor expanded in EDonor around inf 64.7%

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

   6. Taylor expanded in EAccept around inf 50.3%

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

   7. Taylor expanded in EAccept around 0 47.6%

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

   if 3.10000000000000015e-10 < 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%

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

   5. Taylor expanded in KbT around inf 64.1%

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

   6. Taylor expanded in Ev around inf 54.1%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 39.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 3.1 \cdot 10^{-12}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -5.8e-23)
   (+ (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))) (/ NdChar 2.0))
   (if (<= NaChar 3.1e-12)
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
     (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -5.8e-23) {
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 3.1e-12) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-5.8d-23)) then
        tmp = (nachar / (1.0d0 + exp((mu / -kbt)))) + (ndchar / 2.0d0)
    else if (nachar <= 3.1d-12) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -5.8e-23) {
		tmp = (NaChar / (1.0 + Math.exp((mu / -KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 3.1e-12) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -5.8e-23:
		tmp = (NaChar / (1.0 + math.exp((mu / -KbT)))) + (NdChar / 2.0)
	elif NaChar <= 3.1e-12:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -5.8e-23)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))) + Float64(NdChar / 2.0));
	elseif (NaChar <= 3.1e-12)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -5.8e-23)
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) + (NdChar / 2.0);
	elseif (NaChar <= 3.1e-12)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -5.8e-23], N[(N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.1e-12], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -5.8000000000000003e-23

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.4%

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

   6. Taylor expanded in mu around inf 42.6%

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

      1. associate-*r/ 62.6%

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

      2. mul-1-neg 62.6%

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

   8. Simplified 42.6%

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

   if -5.8000000000000003e-23 < NaChar < 3.1000000000000001e-12

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EDonor around inf 64.8%

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

   6. Taylor expanded in KbT around inf 45.2%

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

   if 3.1000000000000001e-12 < 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%

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

   5. Taylor expanded in KbT around inf 63.4%

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

   6. Taylor expanded in Ev around inf 53.6%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 3.1 \cdot 10^{-12}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 39.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.45 \cdot 10^{+14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -1.45e+14)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (if (<= NaChar 2.9e-12)
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
     (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.45e+14) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 2.9e-12) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-1.45d+14)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (nachar <= 2.9d-12) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.45e+14) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 2.9e-12) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -1.45e+14:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif NaChar <= 2.9e-12:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -1.45e+14)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (NaChar <= 2.9e-12)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -1.45e+14)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (NaChar <= 2.9e-12)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -1.45e+14], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.9e-12], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.45e14

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.9%

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

   6. Taylor expanded in EAccept around inf 46.6%

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

   if -1.45e14 < NaChar < 2.9000000000000002e-12

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EDonor around inf 63.7%

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

   6. Taylor expanded in KbT around inf 43.5%

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

   if 2.9000000000000002e-12 < 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%

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

   5. Taylor expanded in KbT around inf 63.4%

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

   6. Taylor expanded in Ev around inf 53.6%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.45 \cdot 10^{+14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 36.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 7.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 7.8e+117)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ 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 <= 7.8e+117) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} 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 <= 7.8d+117) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    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 <= 7.8e+117) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} 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 <= 7.8e+117:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	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 <= 7.8e+117)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(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 <= 7.8e+117)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	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, 7.8e+117], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 7.79999999999999981e117

   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%

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

   5. Taylor expanded in KbT around inf 46.2%

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

   6. Taylor expanded in Ev around inf 39.0%

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

   if 7.79999999999999981e117 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 51.3%

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

   6. Taylor expanded in EAccept around inf 49.5%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 7.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 35.1% 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 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%

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

5. Taylor expanded in KbT around inf 47.1%

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

6. Taylor expanded in EAccept around inf 38.2%

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

7. Final simplification 38.2%

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

Alternative 27: 27.4% accurate, 32.7× speedup

Math

\[\begin{array}{l} \\ \frac{NaChar}{2} + \frac{NdChar}{2} \end{array} \]

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / 2.0) + (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 / 2.0d0) + (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 / 2.0) + (NdChar / 2.0);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in KbT around inf 47.1%

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

6. Taylor expanded in KbT around inf 30.1%

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

7. Final simplification 30.1%

   \[\leadsto \frac{NaChar}{2} + \frac{NdChar}{2} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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))))))