Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 39.0s

Alternatives: 41

Speedup: 1.0×

• could not determine a ground truth

  1. branch4071 = -5.988598171033364e-51
  2. NdChar = -2.5405679666026776e-51
  3. Ec = 1.763346466401999e+99
  4. Vef = -2.371644136866769e+172
  5. EDonor = 6.984746136803155e-260
  6. mu = -2.000088648931254e-268
  7. KbT = 1.0288276364830914e-37
  8. NaChar = 2.531262827462028e+213
  9. Ev = -1.7800427491407299e+230
  10. EAccept = -5.167161106447286e-14

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

   1. *-un-lft-identity 100.0%

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

   2. exp-prod 100.0%

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

   3. +-commutative 100.0%

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

   4. associate-+l+ 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 61.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_4 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{if}\;Ev \leq -1.35 \cdot 10^{+174}:\\ \;\;\;\;t\_3 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.25 \cdot 10^{+133}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;Ev \leq -7 \cdot 10^{+108}:\\ \;\;\;\;t\_3 + t\_0\\ \mathbf{elif}\;Ev \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Ev \leq -8.2 \cdot 10^{-125}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 + Ec \cdot \left(\frac{\frac{Vef}{Ec}}{KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;Ev \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;Ev \leq -2.7 \cdot 10^{-182}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 + mu \cdot \left(\frac{\left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;Ev \leq -1.15 \cdot 10^{-281}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;Ev \leq -5.8 \cdot 10^{-298}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_3 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
        (t_4
         (+
          (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
          (/ NaChar (+ (/ Vef KbT) 2.0)))))
   (if (<= Ev -1.35e+174)
     (+ t_3 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
     (if (<= Ev -1.25e+133)
       t_4
       (if (<= Ev -7e+108)
         (+ t_3 t_0)
         (if (<= Ev -1.5e-27)
           t_1
           (if (<= Ev -8.2e-125)
             (+
              t_2
              (/ NdChar (+ 1.0 (* Ec (+ (/ (/ Vef Ec) KbT) (/ -1.0 KbT))))))
             (if (<= Ev -9.5e-166)
               t_4
               (if (<= Ev -2.7e-182)
                 (+
                  t_2
                  (/
                   NdChar
                   (+
                    1.0
                    (*
                     mu
                     (+
                      (/
                       (- (+ 1.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT))
                       mu)
                      (/ 1.0 KbT))))))
                 (if (<= Ev -1.15e-281)
                   (+ t_0 (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))
                   (if (<= Ev -5.8e-298)
                     (+ t_2 (/ NdChar (+ 1.0 (/ 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 = NdChar / (1.0 + exp((mu / KbT)));
	double t_1 = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	double t_2 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_3 = NaChar / (1.0 + exp((Ev / KbT)));
	double t_4 = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	double tmp;
	if (Ev <= -1.35e+174) {
		tmp = t_3 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (Ev <= -1.25e+133) {
		tmp = t_4;
	} else if (Ev <= -7e+108) {
		tmp = t_3 + t_0;
	} else if (Ev <= -1.5e-27) {
		tmp = t_1;
	} else if (Ev <= -8.2e-125) {
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((Vef / Ec) / KbT) + (-1.0 / KbT)))));
	} else if (Ev <= -9.5e-166) {
		tmp = t_4;
	} else if (Ev <= -2.7e-182) {
		tmp = t_2 + (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT)))));
	} else if (Ev <= -1.15e-281) {
		tmp = t_0 + (NaChar / (1.0 + exp((mu / -KbT))));
	} else if (Ev <= -5.8e-298) {
		tmp = t_2 + (NdChar / (1.0 + (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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((mu / kbt)))
    t_1 = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    t_2 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_3 = nachar / (1.0d0 + exp((ev / kbt)))
    t_4 = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    if (ev <= (-1.35d+174)) then
        tmp = t_3 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (ev <= (-1.25d+133)) then
        tmp = t_4
    else if (ev <= (-7d+108)) then
        tmp = t_3 + t_0
    else if (ev <= (-1.5d-27)) then
        tmp = t_1
    else if (ev <= (-8.2d-125)) then
        tmp = t_2 + (ndchar / (1.0d0 + (ec * (((vef / ec) / kbt) + ((-1.0d0) / kbt)))))
    else if (ev <= (-9.5d-166)) then
        tmp = t_4
    else if (ev <= (-2.7d-182)) then
        tmp = t_2 + (ndchar / (1.0d0 + (mu * ((((1.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu) + (1.0d0 / kbt)))))
    else if (ev <= (-1.15d-281)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((mu / -kbt))))
    else if (ev <= (-5.8d-298)) then
        tmp = t_2 + (ndchar / (1.0d0 + (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 = NdChar / (1.0 + Math.exp((mu / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	double t_2 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_3 = NaChar / (1.0 + Math.exp((Ev / KbT)));
	double t_4 = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	double tmp;
	if (Ev <= -1.35e+174) {
		tmp = t_3 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (Ev <= -1.25e+133) {
		tmp = t_4;
	} else if (Ev <= -7e+108) {
		tmp = t_3 + t_0;
	} else if (Ev <= -1.5e-27) {
		tmp = t_1;
	} else if (Ev <= -8.2e-125) {
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((Vef / Ec) / KbT) + (-1.0 / KbT)))));
	} else if (Ev <= -9.5e-166) {
		tmp = t_4;
	} else if (Ev <= -2.7e-182) {
		tmp = t_2 + (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT)))));
	} else if (Ev <= -1.15e-281) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	} else if (Ev <= -5.8e-298) {
		tmp = t_2 + (NdChar / (1.0 + (EDonor / KbT)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((mu / KbT)))
	t_1 = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	t_2 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_3 = NaChar / (1.0 + math.exp((Ev / KbT)))
	t_4 = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	tmp = 0
	if Ev <= -1.35e+174:
		tmp = t_3 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif Ev <= -1.25e+133:
		tmp = t_4
	elif Ev <= -7e+108:
		tmp = t_3 + t_0
	elif Ev <= -1.5e-27:
		tmp = t_1
	elif Ev <= -8.2e-125:
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((Vef / Ec) / KbT) + (-1.0 / KbT)))))
	elif Ev <= -9.5e-166:
		tmp = t_4
	elif Ev <= -2.7e-182:
		tmp = t_2 + (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT)))))
	elif Ev <= -1.15e-281:
		tmp = t_0 + (NaChar / (1.0 + math.exp((mu / -KbT))))
	elif Ev <= -5.8e-298:
		tmp = t_2 + (NdChar / (1.0 + (EDonor / KbT)))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_3 = Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT))))
	t_4 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)))
	tmp = 0.0
	if (Ev <= -1.35e+174)
		tmp = Float64(t_3 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (Ev <= -1.25e+133)
		tmp = t_4;
	elseif (Ev <= -7e+108)
		tmp = Float64(t_3 + t_0);
	elseif (Ev <= -1.5e-27)
		tmp = t_1;
	elseif (Ev <= -8.2e-125)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(Vef / Ec) / KbT) + Float64(-1.0 / KbT))))));
	elseif (Ev <= -9.5e-166)
		tmp = t_4;
	elseif (Ev <= -2.7e-182)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + Float64(mu * Float64(Float64(Float64(Float64(1.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu) + Float64(1.0 / KbT))))));
	elseif (Ev <= -1.15e-281)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))));
	elseif (Ev <= -5.8e-298)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + 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 = NdChar / (1.0 + exp((mu / KbT)));
	t_1 = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	t_2 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_3 = NaChar / (1.0 + exp((Ev / KbT)));
	t_4 = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	tmp = 0.0;
	if (Ev <= -1.35e+174)
		tmp = t_3 + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (Ev <= -1.25e+133)
		tmp = t_4;
	elseif (Ev <= -7e+108)
		tmp = t_3 + t_0;
	elseif (Ev <= -1.5e-27)
		tmp = t_1;
	elseif (Ev <= -8.2e-125)
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((Vef / Ec) / KbT) + (-1.0 / KbT)))));
	elseif (Ev <= -9.5e-166)
		tmp = t_4;
	elseif (Ev <= -2.7e-182)
		tmp = t_2 + (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT)))));
	elseif (Ev <= -1.15e-281)
		tmp = t_0 + (NaChar / (1.0 + exp((mu / -KbT))));
	elseif (Ev <= -5.8e-298)
		tmp = t_2 + (NdChar / (1.0 + (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[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -1.35e+174], N[(t$95$3 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.25e+133], t$95$4, If[LessEqual[Ev, -7e+108], N[(t$95$3 + t$95$0), $MachinePrecision], If[LessEqual[Ev, -1.5e-27], t$95$1, If[LessEqual[Ev, -8.2e-125], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(Vef / Ec), $MachinePrecision] / KbT), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -9.5e-166], t$95$4, If[LessEqual[Ev, -2.7e-182], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(mu * N[(N[(N[(N[(1.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.15e-281], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -5.8e-298], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if Ev < -1.35e174

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 90.9%

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

   6. Taylor expanded in EDonor around inf 74.4%

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

   if -1.35e174 < Ev < -1.2499999999999999e133 or -8.1999999999999995e-125 < Ev < -9.50000000000000046e-166

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 77.0%

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

   6. Taylor expanded in Vef around 0 77.3%

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

      1. +-commutative 67.8%

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

   8. Simplified 77.3%

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

   if -1.2499999999999999e133 < Ev < -7.0000000000000005e108

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 100.0%

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

   6. Taylor expanded in Ev around inf 100.0%

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

   if -7.0000000000000005e108 < Ev < -1.5000000000000001e-27 or -5.8000000000000003e-298 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 73.1%

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

   6. Taylor expanded in EDonor around 0 69.3%

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

      1. +-commutative 67.5%

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

   8. Simplified 69.3%

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

   if -1.5000000000000001e-27 < Ev < -8.1999999999999995e-125

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 44.3%

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

   6. Taylor expanded in Ec around -inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. *-commutative 58.2%

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

      3. distribute-rgt-neg-in 58.2%

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

      4. +-commutative 58.2%

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

      5. mul-1-neg 58.2%

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

      6. unsub-neg 58.2%

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

   8. Simplified 58.2%

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

   9. Taylor expanded in Vef around inf 65.6%

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

       1. associate-/r* 72.2%

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

   11. Simplified 72.2%

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

   if -9.50000000000000046e-166 < Ev < -2.69999999999999999e-182

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 100.0%

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

   6. Taylor expanded in mu around -inf 100.0%

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

   if -2.69999999999999999e-182 < Ev < -1.14999999999999994e-281

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 69.1%

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

   6. Taylor expanded in mu around inf 65.1%

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

      1. associate-*r/ 65.1%

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

      2. mul-1-neg 65.1%

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

   8. Simplified 65.1%

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

   if -1.14999999999999994e-281 < Ev < -5.8000000000000003e-298

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 78.0%

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

   6. Taylor expanded in Ec around -inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. *-commutative 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

      4. +-commutative 78.2%

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

      5. mul-1-neg 78.2%

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

      6. unsub-neg 78.2%

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

   8. Simplified 78.2%

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

   9. Taylor expanded in EDonor around inf 69.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.35 \cdot 10^{+174}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.25 \cdot 10^{+133}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;Ev \leq -7 \cdot 10^{+108}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Ev \leq -8.2 \cdot 10^{-125}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{\frac{Vef}{Ec}}{KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;Ev \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;Ev \leq -2.7 \cdot 10^{-182}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + mu \cdot \left(\frac{\left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;Ev \leq -1.15 \cdot 10^{-281}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;Ev \leq -5.8 \cdot 10^{-298}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;EAccept \leq -9.2 \cdot 10^{-156}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq -9 \cdot 10^{-209}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 2.7 \cdot 10^{-253}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq 8.9 \cdot 10^{-147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 6.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 6 \cdot 10^{-91}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;EAccept \leq 75000000000:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 8 \cdot 10^{+61}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;EAccept \leq 4.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.3 \cdot 10^{+137}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_2
         (+
          t_1
          (/
           NdChar
           (+
            1.0
            (*
             Ec
             (+
              (/ (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) Ec)
              (/ -1.0 KbT)))))))
        (t_3
         (+
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= EAccept -9.2e-156)
     t_3
     (if (<= EAccept -9e-209)
       (+
        t_0
        (/
         NaChar
         (+
          1.0
          (-
           (+ 1.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))))
           (/ mu KbT)))))
       (if (<= EAccept 2.7e-253)
         t_3
         (if (<= EAccept 8.9e-147)
           t_2
           (if (<= EAccept 6.5e-146)
             (/ NdChar (+ 1.0 (exp (/ mu KbT))))
             (if (<= EAccept 6e-91)
               (+ t_1 (/ NdChar (+ 1.0 (/ Vef KbT))))
               (if (<= EAccept 75000000000.0)
                 (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0)))
                 (if (<= EAccept 8e+61)
                   (+ t_1 (/ NdChar (+ 1.0 (/ mu KbT))))
                   (if (<= EAccept 4.6e+69)
                     (+
                      (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
                      (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))))
                     (if (<= EAccept 3.3e+137)
                       (+
                        t_1
                        (/
                         NdChar
                         (+
                          1.0
                          (* Ec (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT))))))
                       t_2))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	double t_3 = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (EAccept <= -9.2e-156) {
		tmp = t_3;
	} else if (EAccept <= -9e-209) {
		tmp = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	} else if (EAccept <= 2.7e-253) {
		tmp = t_3;
	} else if (EAccept <= 8.9e-147) {
		tmp = t_2;
	} else if (EAccept <= 6.5e-146) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else if (EAccept <= 6e-91) {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	} else if (EAccept <= 75000000000.0) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 8e+61) {
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	} else if (EAccept <= 4.6e+69) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((Ec / -KbT))));
	} else if (EAccept <= 3.3e+137) {
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_2 = t_1 + (ndchar / (1.0d0 + (ec * (((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) / ec) + ((-1.0d0) / kbt)))))
    t_3 = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (eaccept <= (-9.2d-156)) then
        tmp = t_3
    else if (eaccept <= (-9d-209)) then
        tmp = t_0 + (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (mu / kbt))))
    else if (eaccept <= 2.7d-253) then
        tmp = t_3
    else if (eaccept <= 8.9d-147) then
        tmp = t_2
    else if (eaccept <= 6.5d-146) then
        tmp = ndchar / (1.0d0 + exp((mu / kbt)))
    else if (eaccept <= 6d-91) then
        tmp = t_1 + (ndchar / (1.0d0 + (vef / kbt)))
    else if (eaccept <= 75000000000.0d0) then
        tmp = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    else if (eaccept <= 8d+61) then
        tmp = t_1 + (ndchar / (1.0d0 + (mu / kbt)))
    else if (eaccept <= 4.6d+69) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / (1.0d0 + exp((ec / -kbt))))
    else if (eaccept <= 3.3d+137) then
        tmp = t_1 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	double t_3 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (EAccept <= -9.2e-156) {
		tmp = t_3;
	} else if (EAccept <= -9e-209) {
		tmp = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	} else if (EAccept <= 2.7e-253) {
		tmp = t_3;
	} else if (EAccept <= 8.9e-147) {
		tmp = t_2;
	} else if (EAccept <= 6.5e-146) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else if (EAccept <= 6e-91) {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	} else if (EAccept <= 75000000000.0) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 8e+61) {
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	} else if (EAccept <= 4.6e+69) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (1.0 + Math.exp((Ec / -KbT))));
	} else if (EAccept <= 3.3e+137) {
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_2 = t_1 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))))
	t_3 = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if EAccept <= -9.2e-156:
		tmp = t_3
	elif EAccept <= -9e-209:
		tmp = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))))
	elif EAccept <= 2.7e-253:
		tmp = t_3
	elif EAccept <= 8.9e-147:
		tmp = t_2
	elif EAccept <= 6.5e-146:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	elif EAccept <= 6e-91:
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)))
	elif EAccept <= 75000000000.0:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	elif EAccept <= 8e+61:
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)))
	elif EAccept <= 4.6e+69:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (1.0 + math.exp((Ec / -KbT))))
	elif EAccept <= 3.3e+137:
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / KbT))))))
	t_3 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (EAccept <= -9.2e-156)
		tmp = t_3;
	elseif (EAccept <= -9e-209)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT)))));
	elseif (EAccept <= 2.7e-253)
		tmp = t_3;
	elseif (EAccept <= 8.9e-147)
		tmp = t_2;
	elseif (EAccept <= 6.5e-146)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	elseif (EAccept <= 6e-91)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	elseif (EAccept <= 75000000000.0)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (EAccept <= 8e+61)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(mu / KbT))));
	elseif (EAccept <= 4.6e+69)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))));
	elseif (EAccept <= 3.3e+137)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_2 = t_1 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	t_3 = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (EAccept <= -9.2e-156)
		tmp = t_3;
	elseif (EAccept <= -9e-209)
		tmp = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	elseif (EAccept <= 2.7e-253)
		tmp = t_3;
	elseif (EAccept <= 8.9e-147)
		tmp = t_2;
	elseif (EAccept <= 6.5e-146)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	elseif (EAccept <= 6e-91)
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	elseif (EAccept <= 75000000000.0)
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	elseif (EAccept <= 8e+61)
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	elseif (EAccept <= 4.6e+69)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((Ec / -KbT))));
	elseif (EAccept <= 3.3e+137)
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -9.2e-156], t$95$3, If[LessEqual[EAccept, -9e-209], N[(t$95$0 + N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 2.7e-253], t$95$3, If[LessEqual[EAccept, 8.9e-147], t$95$2, If[LessEqual[EAccept, 6.5e-146], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 6e-91], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 75000000000.0], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 8e+61], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 4.6e+69], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.3e+137], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if EAccept < -9.1999999999999998e-156 or -8.9999999999999996e-209 < EAccept < 2.69999999999999999e-253

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 70.8%

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

   6. Taylor expanded in EDonor around inf 55.4%

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

   if -9.1999999999999998e-156 < EAccept < -8.9999999999999996e-209

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.3%

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

      1. +-commutative 56.3%

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

   7. Simplified 56.3%

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

   if 2.69999999999999999e-253 < EAccept < 8.9000000000000005e-147 or 3.30000000000000003e137 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 53.4%

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

   6. Taylor expanded in Ec around -inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. *-commutative 61.6%

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

      3. distribute-rgt-neg-in 61.6%

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

      4. +-commutative 61.6%

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

      5. mul-1-neg 61.6%

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

      6. unsub-neg 61.6%

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

   8. Simplified 61.6%

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

   if 8.9000000000000005e-147 < EAccept < 6.4999999999999999e-146

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 67.8%

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

   6. Taylor expanded in KbT around inf 33.6%

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

      1. associate-+r+ 33.6%

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

      2. +-commutative 33.6%

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

   8. Simplified 33.6%

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

   9. Taylor expanded in mu around inf 20.1%

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

       1. associate-*r/ 20.1%

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

       2. associate-*r* 20.1%

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

       3. neg-mul-1 20.1%

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

   11. Simplified 20.1%

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

   12. Taylor expanded in NdChar around inf 28.8%

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

   if 6.4999999999999999e-146 < EAccept < 6.0000000000000004e-91

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.7%

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

   6. Taylor expanded in Ec around -inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. *-commutative 56.7%

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

      3. distribute-rgt-neg-in 56.7%

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

      4. +-commutative 56.7%

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

      5. mul-1-neg 56.7%

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

      6. unsub-neg 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in Vef around inf 78.2%

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

   if 6.0000000000000004e-91 < EAccept < 7.5e10

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 62.8%

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

   6. Taylor expanded in Vef around 0 59.8%

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

      1. +-commutative 55.3%

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

   8. Simplified 59.8%

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

   if 7.5e10 < EAccept < 7.9999999999999996e61

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 59.3%

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

   6. Taylor expanded in Ec around -inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

      4. +-commutative 67.6%

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

      5. mul-1-neg 67.6%

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

      6. unsub-neg 67.6%

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

   8. Simplified 67.6%

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

   9. Taylor expanded in mu around inf 91.9%

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

   if 7.9999999999999996e61 < EAccept < 4.60000000000000033e69

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 79.7%

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

   6. Taylor expanded in Ec around inf 75.9%

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

      1. associate-*r/ 75.9%

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

      2. mul-1-neg 75.9%

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

   8. Simplified 75.9%

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

   if 4.60000000000000033e69 < EAccept < 3.30000000000000003e137

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.5%

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

   6. Taylor expanded in Ec around -inf 73.7%

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

      1. mul-1-neg 73.7%

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

      2. *-commutative 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. +-commutative 73.7%

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

      5. mul-1-neg 73.7%

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

      6. unsub-neg 73.7%

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

   8. Simplified 73.7%

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

   9. Taylor expanded in EDonor around inf 82.1%

      \[\leadsto \frac{NdChar}{1 + \left(\frac{1}{KbT} - \color{blue}{\frac{EDonor}{Ec \cdot KbT}}\right) \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -9.2 \cdot 10^{-156}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EAccept \leq -9 \cdot 10^{-209}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 2.7 \cdot 10^{-253}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 8.9 \cdot 10^{-147}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 6.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 6 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;EAccept \leq 75000000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 8 \cdot 10^{+61}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;EAccept \leq 4.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.3 \cdot 10^{+137}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Ev \leq -1.95 \cdot 10^{+33}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -7.8 \cdot 10^{-165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Ev \leq -9.5 \cdot 10^{-183}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + mu \cdot \left(\frac{\left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;Ev \leq -7.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;Ev \leq -2.1 \cdot 10^{-262}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ev \leq 1.16 \cdot 10^{-178}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
        (t_2 (+ t_1 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Ev -1.95e+33)
     (+ t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= Ev -7.8e-165)
       t_2
       (if (<= Ev -9.5e-183)
         (+
          t_0
          (/
           NdChar
           (+
            1.0
            (*
             mu
             (+
              (/ (- (+ 1.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)) mu)
              (/ 1.0 KbT))))))
         (if (<= Ev -7.8e-193)
           (+
            (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
            (/ NaChar (+ (/ Vef KbT) 2.0)))
           (if (<= Ev -2.1e-262)
             (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
             (if (<= Ev 1.16e-178)
               t_2
               (+ t_1 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Ev <= -1.95e+33) {
		tmp = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Ev <= -7.8e-165) {
		tmp = t_2;
	} else if (Ev <= -9.5e-183) {
		tmp = t_0 + (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT)))));
	} else if (Ev <= -7.8e-193) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (Ev <= -2.1e-262) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Ev <= 1.16e-178) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))
    t_2 = t_1 + (nachar / (1.0d0 + exp((vef / kbt))))
    if (ev <= (-1.95d+33)) then
        tmp = t_1 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (ev <= (-7.8d-165)) then
        tmp = t_2
    else if (ev <= (-9.5d-183)) then
        tmp = t_0 + (ndchar / (1.0d0 + (mu * ((((1.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu) + (1.0d0 / kbt)))))
    else if (ev <= (-7.8d-193)) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else if (ev <= (-2.1d-262)) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (ev <= 1.16d-178) then
        tmp = t_2
    else
        tmp = t_1 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Ev <= -1.95e+33) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Ev <= -7.8e-165) {
		tmp = t_2;
	} else if (Ev <= -9.5e-183) {
		tmp = t_0 + (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT)))));
	} else if (Ev <= -7.8e-193) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (Ev <= -2.1e-262) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Ev <= 1.16e-178) {
		tmp = t_2;
	} else {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	t_2 = t_1 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Ev <= -1.95e+33:
		tmp = t_1 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Ev <= -7.8e-165:
		tmp = t_2
	elif Ev <= -9.5e-183:
		tmp = t_0 + (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT)))))
	elif Ev <= -7.8e-193:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	elif Ev <= -2.1e-262:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Ev <= 1.16e-178:
		tmp = t_2
	else:
		tmp = t_1 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Ev <= -1.95e+33)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Ev <= -7.8e-165)
		tmp = t_2;
	elseif (Ev <= -9.5e-183)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(mu * Float64(Float64(Float64(Float64(1.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu) + Float64(1.0 / KbT))))));
	elseif (Ev <= -7.8e-193)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (Ev <= -2.1e-262)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Ev <= 1.16e-178)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	t_2 = t_1 + (NaChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Ev <= -1.95e+33)
		tmp = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Ev <= -7.8e-165)
		tmp = t_2;
	elseif (Ev <= -9.5e-183)
		tmp = t_0 + (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT)))));
	elseif (Ev <= -7.8e-193)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	elseif (Ev <= -2.1e-262)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Ev <= 1.16e-178)
		tmp = t_2;
	else
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -1.95e+33], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -7.8e-165], t$95$2, If[LessEqual[Ev, -9.5e-183], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(mu * N[(N[(N[(N[(1.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -7.8e-193], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -2.1e-262], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 1.16e-178], t$95$2, N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if Ev < -1.9500000000000001e33

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 82.8%

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

   if -1.9500000000000001e33 < Ev < -7.7999999999999997e-165 or -2.1e-262 < Ev < 1.16e-178

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 77.6%

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

   if -7.7999999999999997e-165 < Ev < -9.5000000000000008e-183

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 100.0%

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

   6. Taylor expanded in mu around -inf 100.0%

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

   if -9.5000000000000008e-183 < Ev < -7.7999999999999997e-193

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 76.2%

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

   6. Taylor expanded in EDonor around 0 76.2%

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

      1. +-commutative 76.2%

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

   8. Simplified 76.2%

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

   9. Taylor expanded in Vef around 0 76.2%

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

       1. +-commutative 76.2%

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

   11. Simplified 76.2%

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

   if -7.7999999999999997e-193 < Ev < -2.1e-262

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 76.7%

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

   if 1.16e-178 < Ev

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 72.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.95 \cdot 10^{+33}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -7.8 \cdot 10^{-165}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ev \leq -9.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + mu \cdot \left(\frac{\left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu} + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;Ev \leq -7.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;Ev \leq -2.1 \cdot 10^{-262}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ev \leq 1.16 \cdot 10^{-178}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_2 := t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;mu \leq -2.35 \cdot 10^{+115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq -7 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -1.22 \cdot 10^{-119}:\\ \;\;\;\;t\_3 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.05 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq 5.5 \cdot 10^{-193}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t\_3\\ \mathbf{elif}\;mu \leq 1920000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_2 (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT))))))
        (t_3 (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))))
   (if (<= mu -2.35e+115)
     t_2
     (if (<= mu -7e-56)
       t_1
       (if (<= mu -1.22e-119)
         (+ t_3 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
         (if (<= mu -1.05e-294)
           t_1
           (if (<= mu 5.5e-193)
             (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_3)
             (if (<= mu 1920000000000.0) t_1 t_2))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	double t_3 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (mu <= -2.35e+115) {
		tmp = t_2;
	} else if (mu <= -7e-56) {
		tmp = t_1;
	} else if (mu <= -1.22e-119) {
		tmp = t_3 + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (mu <= -1.05e-294) {
		tmp = t_1;
	} else if (mu <= 5.5e-193) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_3;
	} else if (mu <= 1920000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_2 = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    t_3 = ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))
    if (mu <= (-2.35d+115)) then
        tmp = t_2
    else if (mu <= (-7d-56)) then
        tmp = t_1
    else if (mu <= (-1.22d-119)) then
        tmp = t_3 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (mu <= (-1.05d-294)) then
        tmp = t_1
    else if (mu <= 5.5d-193) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + t_3
    else if (mu <= 1920000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_2 = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double t_3 = NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (mu <= -2.35e+115) {
		tmp = t_2;
	} else if (mu <= -7e-56) {
		tmp = t_1;
	} else if (mu <= -1.22e-119) {
		tmp = t_3 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (mu <= -1.05e-294) {
		tmp = t_1;
	} else if (mu <= 5.5e-193) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + t_3;
	} else if (mu <= 1920000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_2 = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	t_3 = NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))
	tmp = 0
	if mu <= -2.35e+115:
		tmp = t_2
	elif mu <= -7e-56:
		tmp = t_1
	elif mu <= -1.22e-119:
		tmp = t_3 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif mu <= -1.05e-294:
		tmp = t_1
	elif mu <= 5.5e-193:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + t_3
	elif mu <= 1920000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_2 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	t_3 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))))
	tmp = 0.0
	if (mu <= -2.35e+115)
		tmp = t_2;
	elseif (mu <= -7e-56)
		tmp = t_1;
	elseif (mu <= -1.22e-119)
		tmp = Float64(t_3 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (mu <= -1.05e-294)
		tmp = t_1;
	elseif (mu <= 5.5e-193)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + t_3);
	elseif (mu <= 1920000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_2 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	t_3 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	tmp = 0.0;
	if (mu <= -2.35e+115)
		tmp = t_2;
	elseif (mu <= -7e-56)
		tmp = t_1;
	elseif (mu <= -1.22e-119)
		tmp = t_3 + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (mu <= -1.05e-294)
		tmp = t_1;
	elseif (mu <= 5.5e-193)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_3;
	elseif (mu <= 1920000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -2.35e+115], t$95$2, If[LessEqual[mu, -7e-56], t$95$1, If[LessEqual[mu, -1.22e-119], N[(t$95$3 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -1.05e-294], t$95$1, If[LessEqual[mu, 5.5e-193], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[mu, 1920000000000.0], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if mu < -2.3499999999999998e115 or 1.92e12 < 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%

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

   5. Taylor expanded in mu around inf 83.7%

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

   if -2.3499999999999998e115 < mu < -6.9999999999999996e-56 or -1.22e-119 < mu < -1.04999999999999992e-294 or 5.50000000000000014e-193 < mu < 1.92e12

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 81.2%

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

   if -6.9999999999999996e-56 < mu < -1.22e-119

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 100.0%

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

   6. Taylor expanded in EDonor around 0 100.0%

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

      1. +-commutative 62.7%

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

   8. Simplified 100.0%

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

   if -1.04999999999999992e-294 < mu < 5.50000000000000014e-193

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 77.1%

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

   6. Taylor expanded in EDonor around 0 67.7%

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

      1. +-commutative 67.8%

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

   8. Simplified 67.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -2.35 \cdot 10^{+115}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -7 \cdot 10^{-56}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.22 \cdot 10^{-119}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.05 \cdot 10^{-294}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 5.5 \cdot 10^{-193}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;mu \leq 1920000000000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -7.5 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -4.1 \cdot 10^{-53}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq -4.2 \cdot 10^{-121}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))))
   (if (<= mu -7.5e+114)
     t_1
     (if (<= mu -4.1e-53)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
       (if (<= mu -1.3e-119)
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
         (if (<= mu -4.2e-121)
           (+
            t_0
            (/ NdChar (+ 1.0 (* Ec (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT))))))
           (if (<= mu 1.35e-12)
             (+
              (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
              (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
             t_1)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	double tmp;
	if (mu <= -7.5e+114) {
		tmp = t_1;
	} else if (mu <= -4.1e-53) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (mu <= -1.3e-119) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (mu <= -4.2e-121) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else if (mu <= 1.35e-12) {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    if (mu <= (-7.5d+114)) then
        tmp = t_1
    else if (mu <= (-4.1d-53)) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (mu <= (-1.3d-119)) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (mu <= (-4.2d-121)) then
        tmp = t_0 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    else if (mu <= 1.35d-12) then
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double tmp;
	if (mu <= -7.5e+114) {
		tmp = t_1;
	} else if (mu <= -4.1e-53) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (mu <= -1.3e-119) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (mu <= -4.2e-121) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else if (mu <= 1.35e-12) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	tmp = 0
	if mu <= -7.5e+114:
		tmp = t_1
	elif mu <= -4.1e-53:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif mu <= -1.3e-119:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif mu <= -4.2e-121:
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	elif mu <= 1.35e-12:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	tmp = 0.0
	if (mu <= -7.5e+114)
		tmp = t_1;
	elseif (mu <= -4.1e-53)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (mu <= -1.3e-119)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (mu <= -4.2e-121)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	elseif (mu <= 1.35e-12)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	tmp = 0.0;
	if (mu <= -7.5e+114)
		tmp = t_1;
	elseif (mu <= -4.1e-53)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (mu <= -1.3e-119)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (mu <= -4.2e-121)
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	elseif (mu <= 1.35e-12)
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -7.5e+114], t$95$1, If[LessEqual[mu, -4.1e-53], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -1.3e-119], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -4.2e-121], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.35e-12], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if mu < -7.5000000000000001e114 or 1.3499999999999999e-12 < 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%

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

   5. Taylor expanded in mu around inf 83.5%

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

   if -7.5000000000000001e114 < mu < -4.1000000000000001e-53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 77.7%

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

   if -4.1000000000000001e-53 < mu < -1.30000000000000006e-119

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 100.0%

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

   6. Taylor expanded in EDonor around 0 100.0%

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

      1. +-commutative 62.7%

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

   8. Simplified 100.0%

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

   if -1.30000000000000006e-119 < mu < -4.1999999999999997e-121

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 52.6%

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

   6. Taylor expanded in Ec around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in EDonor around inf 100.0%

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

   if -4.1999999999999997e-121 < mu < 1.3499999999999999e-12

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 76.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -7.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -4.1 \cdot 10^{-53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq -4.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;NdChar \leq -9 \cdot 10^{+80}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t\_2\\ \mathbf{elif}\;NdChar \leq -11000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NdChar \leq -5.8 \cdot 10^{-15}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))))
   (if (<= NdChar -9e+80)
     (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) t_2)
     (if (<= NdChar -11000.0)
       t_1
       (if (<= NdChar -5.8e-15)
         (+
          t_0
          (/ NdChar (+ 1.0 (* Ec (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT))))))
         (if (<= NdChar 2.4e+52)
           t_1
           (+ t_2 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_2 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (NdChar <= -9e+80) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + t_2;
	} else if (NdChar <= -11000.0) {
		tmp = t_1;
	} else if (NdChar <= -5.8e-15) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else if (NdChar <= 2.4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_2 = ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))
    if (ndchar <= (-9d+80)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + t_2
    else if (ndchar <= (-11000.0d0)) then
        tmp = t_1
    else if (ndchar <= (-5.8d-15)) then
        tmp = t_0 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    else if (ndchar <= 2.4d+52) then
        tmp = t_1
    else
        tmp = t_2 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_2 = NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (NdChar <= -9e+80) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + t_2;
	} else if (NdChar <= -11000.0) {
		tmp = t_1;
	} else if (NdChar <= -5.8e-15) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else if (NdChar <= 2.4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_2 = NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))
	tmp = 0
	if NdChar <= -9e+80:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + t_2
	elif NdChar <= -11000.0:
		tmp = t_1
	elif NdChar <= -5.8e-15:
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	elif NdChar <= 2.4e+52:
		tmp = t_1
	else:
		tmp = t_2 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))))
	tmp = 0.0
	if (NdChar <= -9e+80)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + t_2);
	elseif (NdChar <= -11000.0)
		tmp = t_1;
	elseif (NdChar <= -5.8e-15)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	elseif (NdChar <= 2.4e+52)
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_2 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	tmp = 0.0;
	if (NdChar <= -9e+80)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + t_2;
	elseif (NdChar <= -11000.0)
		tmp = t_1;
	elseif (NdChar <= -5.8e-15)
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	elseif (NdChar <= 2.4e+52)
		tmp = t_1;
	else
		tmp = t_2 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -9e+80], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[NdChar, -11000.0], t$95$1, If[LessEqual[NdChar, -5.8e-15], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2.4e+52], t$95$1, N[(t$95$2 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -9.00000000000000013e80

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 76.0%

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

   6. Taylor expanded in EDonor around 0 67.4%

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

      1. +-commutative 67.4%

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

   8. Simplified 67.4%

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

   if -9.00000000000000013e80 < NdChar < -11000 or -5.80000000000000037e-15 < NdChar < 2.4e52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 80.2%

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

   if -11000 < NdChar < -5.80000000000000037e-15

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 50.7%

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

   6. Taylor expanded in Ec around -inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. *-commutative 50.8%

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

      3. distribute-rgt-neg-in 50.8%

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

      4. +-commutative 50.8%

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

      5. mul-1-neg 50.8%

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

      6. unsub-neg 50.8%

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

   8. Simplified 50.8%

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

   9. Taylor expanded in EDonor around inf 100.0%

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

   if 2.4e52 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 76.3%

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

   6. Taylor expanded in EDonor around 0 71.7%

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

      1. +-commutative 65.6%

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

   8. Simplified 71.7%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -9 \cdot 10^{+80}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -11000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -5.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+52}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t\_1\\ \mathbf{if}\;EAccept \leq 10^{-166}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 7 \cdot 10^{-92}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;EAccept \leq 6 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 4.4 \cdot 10^{+141}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
        (t_2 (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_1)))
   (if (<= EAccept 1e-166)
     t_2
     (if (<= EAccept 7e-92)
       (+ t_0 (/ NdChar (+ 1.0 (/ Vef KbT))))
       (if (<= EAccept 6e+42)
         t_2
         (if (<= EAccept 4.4e+141)
           (+
            t_0
            (/ NdChar (+ 1.0 (* Ec (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT))))))
           (+ t_1 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	double t_2 = (NaChar / (1.0 + exp((Ev / KbT)))) + t_1;
	double tmp;
	if (EAccept <= 1e-166) {
		tmp = t_2;
	} else if (EAccept <= 7e-92) {
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	} else if (EAccept <= 6e+42) {
		tmp = t_2;
	} else if (EAccept <= 4.4e+141) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else {
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))
    t_2 = (nachar / (1.0d0 + exp((ev / kbt)))) + t_1
    if (eaccept <= 1d-166) then
        tmp = t_2
    else if (eaccept <= 7d-92) then
        tmp = t_0 + (ndchar / (1.0d0 + (vef / kbt)))
    else if (eaccept <= 6d+42) then
        tmp = t_2
    else if (eaccept <= 4.4d+141) then
        tmp = t_0 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    else
        tmp = t_1 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)));
	double t_2 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + t_1;
	double tmp;
	if (EAccept <= 1e-166) {
		tmp = t_2;
	} else if (EAccept <= 7e-92) {
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	} else if (EAccept <= 6e+42) {
		tmp = t_2;
	} else if (EAccept <= 4.4e+141) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))
	t_2 = (NaChar / (1.0 + math.exp((Ev / KbT)))) + t_1
	tmp = 0
	if EAccept <= 1e-166:
		tmp = t_2
	elif EAccept <= 7e-92:
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)))
	elif EAccept <= 6e+42:
		tmp = t_2
	elif EAccept <= 4.4e+141:
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	else:
		tmp = t_1 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + t_1)
	tmp = 0.0
	if (EAccept <= 1e-166)
		tmp = t_2;
	elseif (EAccept <= 7e-92)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	elseif (EAccept <= 6e+42)
		tmp = t_2;
	elseif (EAccept <= 4.4e+141)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	t_2 = (NaChar / (1.0 + exp((Ev / KbT)))) + t_1;
	tmp = 0.0;
	if (EAccept <= 1e-166)
		tmp = t_2;
	elseif (EAccept <= 7e-92)
		tmp = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	elseif (EAccept <= 6e+42)
		tmp = t_2;
	elseif (EAccept <= 4.4e+141)
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	else
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[EAccept, 1e-166], t$95$2, If[LessEqual[EAccept, 7e-92], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 6e+42], t$95$2, If[LessEqual[EAccept, 4.4e+141], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if EAccept < 1.00000000000000004e-166 or 7e-92 < EAccept < 6.00000000000000058e42

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 71.2%

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

   6. Taylor expanded in EDonor around 0 64.8%

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

      1. +-commutative 63.6%

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

   8. Simplified 64.8%

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

   if 1.00000000000000004e-166 < EAccept < 7e-92

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.1%

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

   6. Taylor expanded in Ec around -inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. *-commutative 65.1%

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

      3. distribute-rgt-neg-in 65.1%

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

      4. +-commutative 65.1%

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

      5. mul-1-neg 65.1%

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

      6. unsub-neg 65.1%

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

   8. Simplified 65.1%

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

   9. Taylor expanded in Vef around inf 73.5%

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

   if 6.00000000000000058e42 < EAccept < 4.4e141

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 61.3%

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

   6. Taylor expanded in Ec around -inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. *-commutative 66.2%

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

      3. distribute-rgt-neg-in 66.2%

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

      4. +-commutative 66.2%

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

      5. mul-1-neg 66.2%

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

      6. unsub-neg 66.2%

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

   8. Simplified 66.2%

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

   9. Taylor expanded in EDonor around inf 70.4%

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

   if 4.4e141 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 85.7%

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

   6. Taylor expanded in EDonor around 0 76.9%

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

      1. +-commutative 46.7%

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

   8. Simplified 76.9%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 10^{-166}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 7 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;EAccept \leq 6 \cdot 10^{+42}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 4.4 \cdot 10^{+141}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;EAccept \leq -6.7 \cdot 10^{-280}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t\_0\\ \mathbf{elif}\;EAccept \leq 5.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t\_0\\ \mathbf{elif}\;EAccept \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))))
   (if (<= EAccept -6.7e-280)
     (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_0)
     (if (<= EAccept 5.4e+42)
       (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) t_0)
       (if (<= EAccept 4.8e+141)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
          (/ NdChar (+ 1.0 (* Ec (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT))))))
         (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (EAccept <= -6.7e-280) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	} else if (EAccept <= 5.4e+42) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + t_0;
	} else if (EAccept <= 4.8e+141) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))
    if (eaccept <= (-6.7d-280)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + t_0
    else if (eaccept <= 5.4d+42) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + t_0
    else if (eaccept <= 4.8d+141) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (EAccept <= -6.7e-280) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + t_0;
	} else if (EAccept <= 5.4e+42) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + t_0;
	} else if (EAccept <= 4.8e+141) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))
	tmp = 0
	if EAccept <= -6.7e-280:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + t_0
	elif EAccept <= 5.4e+42:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + t_0
	elif EAccept <= 4.8e+141:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))))
	tmp = 0.0
	if (EAccept <= -6.7e-280)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + t_0);
	elseif (EAccept <= 5.4e+42)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + t_0);
	elseif (EAccept <= 4.8e+141)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	tmp = 0.0;
	if (EAccept <= -6.7e-280)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	elseif (EAccept <= 5.4e+42)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + t_0;
	elseif (EAccept <= 4.8e+141)
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -6.7e-280], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[EAccept, 5.4e+42], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[EAccept, 4.8e+141], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if EAccept < -6.70000000000000015e-280

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 70.2%

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

   6. Taylor expanded in EDonor around 0 63.8%

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

      1. +-commutative 62.9%

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

   8. Simplified 63.8%

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

   if -6.70000000000000015e-280 < EAccept < 5.4000000000000001e42

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 70.5%

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

   6. Taylor expanded in EDonor around 0 66.4%

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

      1. +-commutative 66.4%

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

   8. Simplified 66.4%

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

   if 5.4000000000000001e42 < EAccept < 4.79999999999999995e141

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 61.3%

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

   6. Taylor expanded in Ec around -inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. *-commutative 66.2%

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

      3. distribute-rgt-neg-in 66.2%

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

      4. +-commutative 66.2%

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

      5. mul-1-neg 66.2%

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

      6. unsub-neg 66.2%

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

   8. Simplified 66.2%

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

   9. Taylor expanded in EDonor around inf 70.4%

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

   if 4.79999999999999995e141 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 85.7%

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

   6. Taylor expanded in EDonor around 0 76.9%

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

      1. +-commutative 46.7%

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

   8. Simplified 76.9%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -6.7 \cdot 10^{-280}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 5.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;EAccept \leq -7.5 \cdot 10^{-148}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq -3 \cdot 10^{-209}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 2.8 \cdot 10^{-254}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq 4 \cdot 10^{-146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 4.1 \cdot 10^{-146}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 2.6 \cdot 10^{-92}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;EAccept \leq 400000000:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 7.8 \cdot 10^{+61}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;EAccept \leq 1.15 \cdot 10^{+83}:\\ \;\;\;\;t\_0 + \frac{NaChar}{2}\\ \mathbf{elif}\;EAccept \leq 4 \cdot 10^{+131}:\\ \;\;\;\;t\_1 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_2
         (+
          t_1
          (/
           NdChar
           (+
            1.0
            (*
             Ec
             (+
              (/ (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) Ec)
              (/ -1.0 KbT)))))))
        (t_3
         (+
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= EAccept -7.5e-148)
     t_3
     (if (<= EAccept -3e-209)
       (+
        t_0
        (/
         NaChar
         (+
          1.0
          (-
           (+ 1.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))))
           (/ mu KbT)))))
       (if (<= EAccept 2.8e-254)
         t_3
         (if (<= EAccept 4e-146)
           t_2
           (if (<= EAccept 4.1e-146)
             (/ NdChar (+ 1.0 (exp (/ mu KbT))))
             (if (<= EAccept 2.6e-92)
               (+ t_1 (/ NdChar (+ 1.0 (/ Vef KbT))))
               (if (<= EAccept 400000000.0)
                 (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0)))
                 (if (<= EAccept 7.8e+61)
                   (+ t_1 (/ NdChar (+ 1.0 (/ mu KbT))))
                   (if (<= EAccept 1.15e+83)
                     (+ t_0 (/ NaChar 2.0))
                     (if (<= EAccept 4e+131)
                       (+
                        t_1
                        (/
                         NdChar
                         (+
                          1.0
                          (* Ec (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT))))))
                       t_2))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	double t_3 = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (EAccept <= -7.5e-148) {
		tmp = t_3;
	} else if (EAccept <= -3e-209) {
		tmp = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	} else if (EAccept <= 2.8e-254) {
		tmp = t_3;
	} else if (EAccept <= 4e-146) {
		tmp = t_2;
	} else if (EAccept <= 4.1e-146) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else if (EAccept <= 2.6e-92) {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	} else if (EAccept <= 400000000.0) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 7.8e+61) {
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	} else if (EAccept <= 1.15e+83) {
		tmp = t_0 + (NaChar / 2.0);
	} else if (EAccept <= 4e+131) {
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_2 = t_1 + (ndchar / (1.0d0 + (ec * (((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) / ec) + ((-1.0d0) / kbt)))))
    t_3 = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (eaccept <= (-7.5d-148)) then
        tmp = t_3
    else if (eaccept <= (-3d-209)) then
        tmp = t_0 + (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (mu / kbt))))
    else if (eaccept <= 2.8d-254) then
        tmp = t_3
    else if (eaccept <= 4d-146) then
        tmp = t_2
    else if (eaccept <= 4.1d-146) then
        tmp = ndchar / (1.0d0 + exp((mu / kbt)))
    else if (eaccept <= 2.6d-92) then
        tmp = t_1 + (ndchar / (1.0d0 + (vef / kbt)))
    else if (eaccept <= 400000000.0d0) then
        tmp = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    else if (eaccept <= 7.8d+61) then
        tmp = t_1 + (ndchar / (1.0d0 + (mu / kbt)))
    else if (eaccept <= 1.15d+83) then
        tmp = t_0 + (nachar / 2.0d0)
    else if (eaccept <= 4d+131) then
        tmp = t_1 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	double t_3 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (EAccept <= -7.5e-148) {
		tmp = t_3;
	} else if (EAccept <= -3e-209) {
		tmp = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	} else if (EAccept <= 2.8e-254) {
		tmp = t_3;
	} else if (EAccept <= 4e-146) {
		tmp = t_2;
	} else if (EAccept <= 4.1e-146) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else if (EAccept <= 2.6e-92) {
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	} else if (EAccept <= 400000000.0) {
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	} else if (EAccept <= 7.8e+61) {
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	} else if (EAccept <= 1.15e+83) {
		tmp = t_0 + (NaChar / 2.0);
	} else if (EAccept <= 4e+131) {
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_1 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_2 = t_1 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))))
	t_3 = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if EAccept <= -7.5e-148:
		tmp = t_3
	elif EAccept <= -3e-209:
		tmp = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))))
	elif EAccept <= 2.8e-254:
		tmp = t_3
	elif EAccept <= 4e-146:
		tmp = t_2
	elif EAccept <= 4.1e-146:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	elif EAccept <= 2.6e-92:
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)))
	elif EAccept <= 400000000.0:
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	elif EAccept <= 7.8e+61:
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)))
	elif EAccept <= 1.15e+83:
		tmp = t_0 + (NaChar / 2.0)
	elif EAccept <= 4e+131:
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / KbT))))))
	t_3 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (EAccept <= -7.5e-148)
		tmp = t_3;
	elseif (EAccept <= -3e-209)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT)))));
	elseif (EAccept <= 2.8e-254)
		tmp = t_3;
	elseif (EAccept <= 4e-146)
		tmp = t_2;
	elseif (EAccept <= 4.1e-146)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	elseif (EAccept <= 2.6e-92)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))));
	elseif (EAccept <= 400000000.0)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (EAccept <= 7.8e+61)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(mu / KbT))));
	elseif (EAccept <= 1.15e+83)
		tmp = Float64(t_0 + Float64(NaChar / 2.0));
	elseif (EAccept <= 4e+131)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_1 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_2 = t_1 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	t_3 = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (EAccept <= -7.5e-148)
		tmp = t_3;
	elseif (EAccept <= -3e-209)
		tmp = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	elseif (EAccept <= 2.8e-254)
		tmp = t_3;
	elseif (EAccept <= 4e-146)
		tmp = t_2;
	elseif (EAccept <= 4.1e-146)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	elseif (EAccept <= 2.6e-92)
		tmp = t_1 + (NdChar / (1.0 + (Vef / KbT)));
	elseif (EAccept <= 400000000.0)
		tmp = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	elseif (EAccept <= 7.8e+61)
		tmp = t_1 + (NdChar / (1.0 + (mu / KbT)));
	elseif (EAccept <= 1.15e+83)
		tmp = t_0 + (NaChar / 2.0);
	elseif (EAccept <= 4e+131)
		tmp = t_1 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -7.5e-148], t$95$3, If[LessEqual[EAccept, -3e-209], N[(t$95$0 + N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 2.8e-254], t$95$3, If[LessEqual[EAccept, 4e-146], t$95$2, If[LessEqual[EAccept, 4.1e-146], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 2.6e-92], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 400000000.0], N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 7.8e+61], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.15e+83], N[(t$95$0 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 4e+131], N[(t$95$1 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if EAccept < -7.5000000000000005e-148 or -2.9999999999999999e-209 < EAccept < 2.79999999999999983e-254

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 70.8%

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

   6. Taylor expanded in EDonor around inf 55.4%

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

   if -7.5000000000000005e-148 < EAccept < -2.9999999999999999e-209

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.3%

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

      1. +-commutative 56.3%

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

   7. Simplified 56.3%

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

   if 2.79999999999999983e-254 < EAccept < 4.0000000000000001e-146 or 3.9999999999999996e131 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 53.4%

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

   6. Taylor expanded in Ec around -inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. *-commutative 61.6%

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

      3. distribute-rgt-neg-in 61.6%

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

      4. +-commutative 61.6%

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

      5. mul-1-neg 61.6%

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

      6. unsub-neg 61.6%

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

   8. Simplified 61.6%

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

   if 4.0000000000000001e-146 < EAccept < 4.0999999999999997e-146

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 67.8%

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

   6. Taylor expanded in KbT around inf 33.6%

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

      1. associate-+r+ 33.6%

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

      2. +-commutative 33.6%

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

   8. Simplified 33.6%

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

   9. Taylor expanded in mu around inf 20.1%

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

       1. associate-*r/ 20.1%

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

       2. associate-*r* 20.1%

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

       3. neg-mul-1 20.1%

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

   11. Simplified 20.1%

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

   12. Taylor expanded in NdChar around inf 28.8%

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

   if 4.0999999999999997e-146 < EAccept < 2.6e-92

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.7%

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

   6. Taylor expanded in Ec around -inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. *-commutative 56.7%

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

      3. distribute-rgt-neg-in 56.7%

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

      4. +-commutative 56.7%

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

      5. mul-1-neg 56.7%

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

      6. unsub-neg 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in Vef around inf 78.2%

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

   if 2.6e-92 < EAccept < 4e8

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 62.8%

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

   6. Taylor expanded in Vef around 0 59.8%

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

      1. +-commutative 55.3%

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

   8. Simplified 59.8%

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

   if 4e8 < EAccept < 7.79999999999999975e61

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 59.3%

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

   6. Taylor expanded in Ec around -inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

      4. +-commutative 67.6%

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

      5. mul-1-neg 67.6%

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

      6. unsub-neg 67.6%

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

   8. Simplified 67.6%

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

   9. Taylor expanded in mu around inf 91.9%

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

   if 7.79999999999999975e61 < EAccept < 1.14999999999999997e83

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 51.2%

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

   if 1.14999999999999997e83 < EAccept < 3.9999999999999996e131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.7%

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

   6. Taylor expanded in Ec around -inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

      4. +-commutative 76.7%

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

      5. mul-1-neg 76.7%

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

      6. unsub-neg 76.7%

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

   8. Simplified 76.7%

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

   9. Taylor expanded in EDonor around inf 74.5%

      \[\leadsto \frac{NdChar}{1 + \left(\frac{1}{KbT} - \color{blue}{\frac{EDonor}{Ec \cdot KbT}}\right) \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -7.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EAccept \leq -3 \cdot 10^{-209}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 2.8 \cdot 10^{-254}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 4 \cdot 10^{-146}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 4.1 \cdot 10^{-146}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 2.6 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;EAccept \leq 400000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 7.8 \cdot 10^{+61}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;EAccept \leq 1.15 \cdot 10^{+83}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;EAccept \leq 4 \cdot 10^{+131}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 12: 56.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := t\_0 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ t_3 := \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ t_4 := t\_1 + t\_3\\ \mathbf{if}\;EAccept \leq -0.00018:\\ \;\;\;\;t\_1 + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;EAccept \leq -2.5 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq -5.5 \cdot 10^{-254}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;EAccept \leq -6.1 \cdot 10^{-281}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{mu \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 1.7 \cdot 10^{-138}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 1.95 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 10000000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;EAccept \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;EAccept \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 3.4 \cdot 10^{+117}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + t\_3\\ \mathbf{elif}\;EAccept \leq 2.5 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)))))
        (t_2 (+ t_0 (/ NdChar (+ 1.0 (/ EDonor KbT)))))
        (t_3 (/ NaChar (+ (/ Vef KbT) 2.0)))
        (t_4 (+ t_1 t_3)))
   (if (<= EAccept -0.00018)
     (+ t_1 (/ NaChar (+ 2.0 (/ EAccept KbT))))
     (if (<= EAccept -2.5e-49)
       t_2
       (if (<= EAccept -5.5e-254)
         t_4
         (if (<= EAccept -6.1e-281)
           (+
            t_0
            (/
             NdChar
             (+
              1.0
              (-
               (+
                1.0
                (+ (/ EDonor KbT) (* mu (+ (/ 1.0 KbT) (/ Vef (* mu KbT))))))
               (/ Ec KbT)))))
           (if (<= EAccept 1.7e-138)
             (+
              t_1
              (/
               NaChar
               (+
                1.0
                (-
                 (+ 1.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))))
                 (/ mu KbT)))))
             (if (<= EAccept 1.95e-59)
               t_2
               (if (<= EAccept 10000000.0)
                 t_4
                 (if (<= EAccept 2.2e+50)
                   (+ t_0 (/ NdChar (+ 1.0 (/ mu KbT))))
                   (if (<= EAccept 3.1e+102)
                     (+
                      t_0
                      (/
                       NdChar
                       (+ 1.0 (* Ec (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT))))))
                     (if (<= EAccept 3.4e+117)
                       (+
                        (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
                        t_3)
                       (if (<= EAccept 2.5e+127)
                         t_2
                         (+
                          t_0
                          (/
                           NdChar
                           (+
                            1.0
                            (*
                             Ec
                             (+
                              (/
                               (+
                                1.0
                                (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
                               Ec)
                              (/ -1.0 KbT)))))))))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	double t_3 = NaChar / ((Vef / KbT) + 2.0);
	double t_4 = t_1 + t_3;
	double tmp;
	if (EAccept <= -0.00018) {
		tmp = t_1 + (NaChar / (2.0 + (EAccept / KbT)));
	} else if (EAccept <= -2.5e-49) {
		tmp = t_2;
	} else if (EAccept <= -5.5e-254) {
		tmp = t_4;
	} else if (EAccept <= -6.1e-281) {
		tmp = t_0 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))));
	} else if (EAccept <= 1.7e-138) {
		tmp = t_1 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	} else if (EAccept <= 1.95e-59) {
		tmp = t_2;
	} else if (EAccept <= 10000000.0) {
		tmp = t_4;
	} else if (EAccept <= 2.2e+50) {
		tmp = t_0 + (NdChar / (1.0 + (mu / KbT)));
	} else if (EAccept <= 3.1e+102) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else if (EAccept <= 3.4e+117) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + t_3;
	} else if (EAccept <= 2.5e+127) {
		tmp = t_2;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = ndchar / (1.0d0 + exp(((edonor + (mu + (vef - ec))) / kbt)))
    t_2 = t_0 + (ndchar / (1.0d0 + (edonor / kbt)))
    t_3 = nachar / ((vef / kbt) + 2.0d0)
    t_4 = t_1 + t_3
    if (eaccept <= (-0.00018d0)) then
        tmp = t_1 + (nachar / (2.0d0 + (eaccept / kbt)))
    else if (eaccept <= (-2.5d-49)) then
        tmp = t_2
    else if (eaccept <= (-5.5d-254)) then
        tmp = t_4
    else if (eaccept <= (-6.1d-281)) then
        tmp = t_0 + (ndchar / (1.0d0 + ((1.0d0 + ((edonor / kbt) + (mu * ((1.0d0 / kbt) + (vef / (mu * kbt)))))) - (ec / kbt))))
    else if (eaccept <= 1.7d-138) then
        tmp = t_1 + (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (mu / kbt))))
    else if (eaccept <= 1.95d-59) then
        tmp = t_2
    else if (eaccept <= 10000000.0d0) then
        tmp = t_4
    else if (eaccept <= 2.2d+50) then
        tmp = t_0 + (ndchar / (1.0d0 + (mu / kbt)))
    else if (eaccept <= 3.1d+102) then
        tmp = t_0 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    else if (eaccept <= 3.4d+117) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + t_3
    else if (eaccept <= 2.5d+127) then
        tmp = t_2
    else
        tmp = t_0 + (ndchar / (1.0d0 + (ec * (((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) / ec) + ((-1.0d0) / kbt)))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	double t_2 = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	double t_3 = NaChar / ((Vef / KbT) + 2.0);
	double t_4 = t_1 + t_3;
	double tmp;
	if (EAccept <= -0.00018) {
		tmp = t_1 + (NaChar / (2.0 + (EAccept / KbT)));
	} else if (EAccept <= -2.5e-49) {
		tmp = t_2;
	} else if (EAccept <= -5.5e-254) {
		tmp = t_4;
	} else if (EAccept <= -6.1e-281) {
		tmp = t_0 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))));
	} else if (EAccept <= 1.7e-138) {
		tmp = t_1 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	} else if (EAccept <= 1.95e-59) {
		tmp = t_2;
	} else if (EAccept <= 10000000.0) {
		tmp = t_4;
	} else if (EAccept <= 2.2e+50) {
		tmp = t_0 + (NdChar / (1.0 + (mu / KbT)));
	} else if (EAccept <= 3.1e+102) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else if (EAccept <= 3.4e+117) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + t_3;
	} else if (EAccept <= 2.5e+127) {
		tmp = t_2;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = NdChar / (1.0 + math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)))
	t_2 = t_0 + (NdChar / (1.0 + (EDonor / KbT)))
	t_3 = NaChar / ((Vef / KbT) + 2.0)
	t_4 = t_1 + t_3
	tmp = 0
	if EAccept <= -0.00018:
		tmp = t_1 + (NaChar / (2.0 + (EAccept / KbT)))
	elif EAccept <= -2.5e-49:
		tmp = t_2
	elif EAccept <= -5.5e-254:
		tmp = t_4
	elif EAccept <= -6.1e-281:
		tmp = t_0 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))))
	elif EAccept <= 1.7e-138:
		tmp = t_1 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))))
	elif EAccept <= 1.95e-59:
		tmp = t_2
	elif EAccept <= 10000000.0:
		tmp = t_4
	elif EAccept <= 2.2e+50:
		tmp = t_0 + (NdChar / (1.0 + (mu / KbT)))
	elif EAccept <= 3.1e+102:
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	elif EAccept <= 3.4e+117:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + t_3
	elif EAccept <= 2.5e+127:
		tmp = t_2
	else:
		tmp = t_0 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))))
	t_3 = Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0))
	t_4 = Float64(t_1 + t_3)
	tmp = 0.0
	if (EAccept <= -0.00018)
		tmp = Float64(t_1 + Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))));
	elseif (EAccept <= -2.5e-49)
		tmp = t_2;
	elseif (EAccept <= -5.5e-254)
		tmp = t_4;
	elseif (EAccept <= -6.1e-281)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(mu * Float64(Float64(1.0 / KbT) + Float64(Vef / Float64(mu * KbT)))))) - Float64(Ec / KbT)))));
	elseif (EAccept <= 1.7e-138)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT)))));
	elseif (EAccept <= 1.95e-59)
		tmp = t_2;
	elseif (EAccept <= 10000000.0)
		tmp = t_4;
	elseif (EAccept <= 2.2e+50)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(mu / KbT))));
	elseif (EAccept <= 3.1e+102)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	elseif (EAccept <= 3.4e+117)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + t_3);
	elseif (EAccept <= 2.5e+127)
		tmp = t_2;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / KbT))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = NdChar / (1.0 + exp(((EDonor + (mu + (Vef - Ec))) / KbT)));
	t_2 = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	t_3 = NaChar / ((Vef / KbT) + 2.0);
	t_4 = t_1 + t_3;
	tmp = 0.0;
	if (EAccept <= -0.00018)
		tmp = t_1 + (NaChar / (2.0 + (EAccept / KbT)));
	elseif (EAccept <= -2.5e-49)
		tmp = t_2;
	elseif (EAccept <= -5.5e-254)
		tmp = t_4;
	elseif (EAccept <= -6.1e-281)
		tmp = t_0 + (NdChar / (1.0 + ((1.0 + ((EDonor / KbT) + (mu * ((1.0 / KbT) + (Vef / (mu * KbT)))))) - (Ec / KbT))));
	elseif (EAccept <= 1.7e-138)
		tmp = t_1 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	elseif (EAccept <= 1.95e-59)
		tmp = t_2;
	elseif (EAccept <= 10000000.0)
		tmp = t_4;
	elseif (EAccept <= 2.2e+50)
		tmp = t_0 + (NdChar / (1.0 + (mu / KbT)));
	elseif (EAccept <= 3.1e+102)
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	elseif (EAccept <= 3.4e+117)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + t_3;
	elseif (EAccept <= 2.5e+127)
		tmp = t_2;
	else
		tmp = t_0 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 + t$95$3), $MachinePrecision]}, If[LessEqual[EAccept, -0.00018], N[(t$95$1 + N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, -2.5e-49], t$95$2, If[LessEqual[EAccept, -5.5e-254], t$95$4, If[LessEqual[EAccept, -6.1e-281], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(mu * N[(N[(1.0 / KbT), $MachinePrecision] + N[(Vef / N[(mu * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.7e-138], N[(t$95$1 + N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.95e-59], t$95$2, If[LessEqual[EAccept, 10000000.0], t$95$4, If[LessEqual[EAccept, 2.2e+50], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.1e+102], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.4e+117], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[EAccept, 2.5e+127], t$95$2, N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if EAccept < -1.80000000000000011e-4

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 83.8%

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

   6. Taylor expanded in EAccept around 0 58.2%

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

      1. +-commutative 58.2%

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

   8. Simplified 58.2%

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

   if -1.80000000000000011e-4 < EAccept < -2.4999999999999999e-49 or 1.7000000000000001e-138 < EAccept < 1.95000000000000009e-59 or 3.4000000000000001e117 < EAccept < 2.5000000000000002e127

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 49.8%

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

   6. Taylor expanded in Ec around -inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. *-commutative 53.6%

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

      3. distribute-rgt-neg-in 53.6%

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

      4. +-commutative 53.6%

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

      5. mul-1-neg 53.6%

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

      6. unsub-neg 53.6%

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

   8. Simplified 53.6%

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

   9. Taylor expanded in EDonor around inf 67.4%

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

   if -2.4999999999999999e-49 < EAccept < -5.4999999999999999e-254 or 1.95000000000000009e-59 < EAccept < 1e7

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 68.5%

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

   6. Taylor expanded in Vef around 0 63.2%

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

      1. +-commutative 57.8%

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

   8. Simplified 63.2%

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

   if -5.4999999999999999e-254 < EAccept < -6.1000000000000006e-281

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 61.4%

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

   6. Taylor expanded in mu around inf 61.4%

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

   if -6.1000000000000006e-281 < EAccept < 1.7000000000000001e-138

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 62.9%

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

      1. +-commutative 62.9%

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

   7. Simplified 62.9%

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

   if 1e7 < EAccept < 2.20000000000000017e50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.6%

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

   6. Taylor expanded in Ec around -inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

      4. +-commutative 64.7%

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

      5. mul-1-neg 64.7%

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

      6. unsub-neg 64.7%

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

   8. Simplified 64.7%

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

   9. Taylor expanded in mu around inf 91.2%

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

   if 2.20000000000000017e50 < EAccept < 3.09999999999999987e102

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.5%

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

   6. Taylor expanded in Ec around -inf 62.1%

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

      1. mul-1-neg 62.1%

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

      2. *-commutative 62.1%

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

      3. distribute-rgt-neg-in 62.1%

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

      4. +-commutative 62.1%

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

      5. mul-1-neg 62.1%

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

      6. unsub-neg 62.1%

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

   8. Simplified 62.1%

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

   9. Taylor expanded in EDonor around inf 68.9%

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

   if 3.09999999999999987e102 < EAccept < 3.4000000000000001e117

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 100.0%

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

   6. Taylor expanded in EDonor around 0 100.0%

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

      1. +-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in Vef around 0 100.0%

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

       1. +-commutative 100.0%

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

   11. Simplified 100.0%

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

   if 2.5000000000000002e127 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 47.3%

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

   6. Taylor expanded in Ec around -inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. *-commutative 55.7%

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

      3. distribute-rgt-neg-in 55.7%

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

      4. +-commutative 55.7%

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

      5. mul-1-neg 55.7%

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

      6. unsub-neg 55.7%

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

   8. Simplified 55.7%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} - \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right) \cdot \left(-Ec\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -0.00018:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;EAccept \leq -2.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;EAccept \leq -5.5 \cdot 10^{-254}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq -6.1 \cdot 10^{-281}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{mu \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 1.7 \cdot 10^{-138}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 1.95 \cdot 10^{-59}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;EAccept \leq 10000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;EAccept \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 3.4 \cdot 10^{+117}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 2.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ t_2 := t\_0 + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_4 := t\_3 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{if}\;NaChar \leq -2.9 \cdot 10^{+59}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;NaChar \leq -1.02 \cdot 10^{-101}:\\ \;\;\;\;t\_0 + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NaChar \leq -2.75 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{-207}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 3.85 \cdot 10^{-31}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;NaChar \leq 5.6 \cdot 10^{+100}:\\ \;\;\;\;t\_3 + \frac{NdChar}{1 + \frac{Ec \cdot \left(-1 + \left(\frac{EDonor}{Ec} + \left(\frac{Vef}{Ec} + \frac{mu}{Ec}\right)\right)\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.6 \cdot 10^{+289}:\\ \;\;\;\;t\_3 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.15 \cdot 10^{+294}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_3 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0))))
        (t_2
         (+
          t_0
          (/
           NaChar
           (+
            1.0
            (-
             (+ 1.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))))
             (/ mu KbT))))))
        (t_3 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_4 (+ t_3 (/ NdChar (+ 1.0 (/ Vef KbT))))))
   (if (<= NaChar -2.9e+59)
     t_4
     (if (<= NaChar -1.02e-101)
       (+ t_0 (/ NaChar (+ 2.0 (/ EAccept KbT))))
       (if (<= NaChar -1e-101)
         (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* KbT (/ NdChar Vef)))
         (if (<= NaChar -2.75e-170)
           t_2
           (if (<= NaChar -2.3e-231)
             t_1
             (if (<= NaChar 1.3e-207)
               t_2
               (if (<= NaChar 1.45e-93)
                 t_1
                 (if (<= NaChar 3.85e-31)
                   t_4
                   (if (<= NaChar 5.6e+100)
                     (+
                      t_3
                      (/
                       NdChar
                       (+
                        1.0
                        (/
                         (*
                          Ec
                          (+ -1.0 (+ (/ EDonor Ec) (+ (/ Vef Ec) (/ mu Ec)))))
                         KbT))))
                     (if (<= NaChar 1.6e+289)
                       (+ t_3 (/ NdChar (+ 1.0 (/ EDonor KbT))))
                       (if (<= NaChar 2.15e+294)
                         (+
                          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
                          (/
                           NdChar
                           (-
                            (+
                             2.0
                             (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
                            (/ Ec KbT))))
                         (+
                          t_3
                          (/
                           NdChar
                           (+
                            1.0
                            (*
                             Ec
                             (+
                              (/ EDonor (* Ec KbT))
                              (/ -1.0 KbT)))))))))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	double t_3 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_4 = t_3 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -2.9e+59) {
		tmp = t_4;
	} else if (NaChar <= -1.02e-101) {
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)));
	} else if (NaChar <= -1e-101) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (KbT * (NdChar / Vef));
	} else if (NaChar <= -2.75e-170) {
		tmp = t_2;
	} else if (NaChar <= -2.3e-231) {
		tmp = t_1;
	} else if (NaChar <= 1.3e-207) {
		tmp = t_2;
	} else if (NaChar <= 1.45e-93) {
		tmp = t_1;
	} else if (NaChar <= 3.85e-31) {
		tmp = t_4;
	} else if (NaChar <= 5.6e+100) {
		tmp = t_3 + (NdChar / (1.0 + ((Ec * (-1.0 + ((EDonor / Ec) + ((Vef / Ec) + (mu / Ec))))) / KbT)));
	} else if (NaChar <= 1.6e+289) {
		tmp = t_3 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NaChar <= 2.15e+294) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else {
		tmp = t_3 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))
    t_1 = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    t_2 = t_0 + (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (mu / kbt))))
    t_3 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_4 = t_3 + (ndchar / (1.0d0 + (vef / kbt)))
    if (nachar <= (-2.9d+59)) then
        tmp = t_4
    else if (nachar <= (-1.02d-101)) then
        tmp = t_0 + (nachar / (2.0d0 + (eaccept / kbt)))
    else if (nachar <= (-1d-101)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (kbt * (ndchar / vef))
    else if (nachar <= (-2.75d-170)) then
        tmp = t_2
    else if (nachar <= (-2.3d-231)) then
        tmp = t_1
    else if (nachar <= 1.3d-207) then
        tmp = t_2
    else if (nachar <= 1.45d-93) then
        tmp = t_1
    else if (nachar <= 3.85d-31) then
        tmp = t_4
    else if (nachar <= 5.6d+100) then
        tmp = t_3 + (ndchar / (1.0d0 + ((ec * ((-1.0d0) + ((edonor / ec) + ((vef / ec) + (mu / ec))))) / kbt)))
    else if (nachar <= 1.6d+289) then
        tmp = t_3 + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (nachar <= 2.15d+294) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)))
    else
        tmp = t_3 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	double t_3 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_4 = t_3 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -2.9e+59) {
		tmp = t_4;
	} else if (NaChar <= -1.02e-101) {
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)));
	} else if (NaChar <= -1e-101) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (KbT * (NdChar / Vef));
	} else if (NaChar <= -2.75e-170) {
		tmp = t_2;
	} else if (NaChar <= -2.3e-231) {
		tmp = t_1;
	} else if (NaChar <= 1.3e-207) {
		tmp = t_2;
	} else if (NaChar <= 1.45e-93) {
		tmp = t_1;
	} else if (NaChar <= 3.85e-31) {
		tmp = t_4;
	} else if (NaChar <= 5.6e+100) {
		tmp = t_3 + (NdChar / (1.0 + ((Ec * (-1.0 + ((EDonor / Ec) + ((Vef / Ec) + (mu / Ec))))) / KbT)));
	} else if (NaChar <= 1.6e+289) {
		tmp = t_3 + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NaChar <= 2.15e+294) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	} else {
		tmp = t_3 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	t_2 = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))))
	t_3 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_4 = t_3 + (NdChar / (1.0 + (Vef / KbT)))
	tmp = 0
	if NaChar <= -2.9e+59:
		tmp = t_4
	elif NaChar <= -1.02e-101:
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)))
	elif NaChar <= -1e-101:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (KbT * (NdChar / Vef))
	elif NaChar <= -2.75e-170:
		tmp = t_2
	elif NaChar <= -2.3e-231:
		tmp = t_1
	elif NaChar <= 1.3e-207:
		tmp = t_2
	elif NaChar <= 1.45e-93:
		tmp = t_1
	elif NaChar <= 3.85e-31:
		tmp = t_4
	elif NaChar <= 5.6e+100:
		tmp = t_3 + (NdChar / (1.0 + ((Ec * (-1.0 + ((EDonor / Ec) + ((Vef / Ec) + (mu / Ec))))) / KbT)))
	elif NaChar <= 1.6e+289:
		tmp = t_3 + (NdChar / (1.0 + (EDonor / KbT)))
	elif NaChar <= 2.15e+294:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)))
	else:
		tmp = t_3 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)))
	t_2 = Float64(t_0 + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT)))))
	t_3 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_4 = Float64(t_3 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))))
	tmp = 0.0
	if (NaChar <= -2.9e+59)
		tmp = t_4;
	elseif (NaChar <= -1.02e-101)
		tmp = Float64(t_0 + Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))));
	elseif (NaChar <= -1e-101)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(KbT * Float64(NdChar / Vef)));
	elseif (NaChar <= -2.75e-170)
		tmp = t_2;
	elseif (NaChar <= -2.3e-231)
		tmp = t_1;
	elseif (NaChar <= 1.3e-207)
		tmp = t_2;
	elseif (NaChar <= 1.45e-93)
		tmp = t_1;
	elseif (NaChar <= 3.85e-31)
		tmp = t_4;
	elseif (NaChar <= 5.6e+100)
		tmp = Float64(t_3 + Float64(NdChar / Float64(1.0 + Float64(Float64(Ec * Float64(-1.0 + Float64(Float64(EDonor / Ec) + Float64(Float64(Vef / Ec) + Float64(mu / Ec))))) / KbT))));
	elseif (NaChar <= 1.6e+289)
		tmp = Float64(t_3 + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (NaChar <= 2.15e+294)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))));
	else
		tmp = Float64(t_3 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	t_2 = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	t_3 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_4 = t_3 + (NdChar / (1.0 + (Vef / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.9e+59)
		tmp = t_4;
	elseif (NaChar <= -1.02e-101)
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)));
	elseif (NaChar <= -1e-101)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (KbT * (NdChar / Vef));
	elseif (NaChar <= -2.75e-170)
		tmp = t_2;
	elseif (NaChar <= -2.3e-231)
		tmp = t_1;
	elseif (NaChar <= 1.3e-207)
		tmp = t_2;
	elseif (NaChar <= 1.45e-93)
		tmp = t_1;
	elseif (NaChar <= 3.85e-31)
		tmp = t_4;
	elseif (NaChar <= 5.6e+100)
		tmp = t_3 + (NdChar / (1.0 + ((Ec * (-1.0 + ((EDonor / Ec) + ((Vef / Ec) + (mu / Ec))))) / KbT)));
	elseif (NaChar <= 1.6e+289)
		tmp = t_3 + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (NaChar <= 2.15e+294)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)));
	else
		tmp = t_3 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.9e+59], t$95$4, If[LessEqual[NaChar, -1.02e-101], N[(t$95$0 + N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1e-101], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NdChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2.75e-170], t$95$2, If[LessEqual[NaChar, -2.3e-231], t$95$1, If[LessEqual[NaChar, 1.3e-207], t$95$2, If[LessEqual[NaChar, 1.45e-93], t$95$1, If[LessEqual[NaChar, 3.85e-31], t$95$4, If[LessEqual[NaChar, 5.6e+100], N[(t$95$3 + N[(NdChar / N[(1.0 + N[(N[(Ec * N[(-1.0 + N[(N[(EDonor / Ec), $MachinePrecision] + N[(N[(Vef / Ec), $MachinePrecision] + N[(mu / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.6e+289], N[(t$95$3 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.15e+294], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / 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], N[(t$95$3 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if NaChar < -2.89999999999999991e59 or 1.4499999999999999e-93 < NaChar < 3.85000000000000006e-31

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.6%

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

   6. Taylor expanded in Ec around -inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

      4. +-commutative 64.7%

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

      5. mul-1-neg 64.7%

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

      6. unsub-neg 64.7%

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

   8. Simplified 64.7%

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

   9. Taylor expanded in Vef around inf 72.8%

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

   if -2.89999999999999991e59 < NaChar < -1.02e-101

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.0%

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

   6. Taylor expanded in EAccept around 0 72.5%

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

      1. +-commutative 72.5%

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

   8. Simplified 72.5%

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

   if -1.02e-101 < NaChar < -1.00000000000000005e-101

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 100.0%

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

   6. Taylor expanded in Vef around inf 100.0%

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

      1. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in EAccept around inf 100.0%

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

   if -1.00000000000000005e-101 < NaChar < -2.75000000000000009e-170 or -2.3e-231 < NaChar < 1.3e-207

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 74.3%

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

      1. +-commutative 74.3%

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

   7. Simplified 74.3%

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

   if -2.75000000000000009e-170 < NaChar < -2.3e-231 or 1.3e-207 < NaChar < 1.4499999999999999e-93

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 74.2%

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

   6. Taylor expanded in Vef around 0 67.8%

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

      1. +-commutative 62.4%

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

   8. Simplified 67.8%

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

   if 3.85000000000000006e-31 < NaChar < 5.5999999999999996e100

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 62.4%

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

   6. Taylor expanded in Ec around -inf 74.4%

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

      1. mul-1-neg 74.4%

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

      2. *-commutative 74.4%

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

      3. distribute-rgt-neg-in 74.4%

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

      4. +-commutative 74.4%

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

      5. mul-1-neg 74.4%

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

      6. unsub-neg 74.4%

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

   8. Simplified 74.4%

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

   9. Taylor expanded in KbT around 0 68.0%

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

       1. associate-*r/ 68.0%

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

       2. mul-1-neg 68.0%

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

   11. Simplified 68.0%

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

   if 5.5999999999999996e100 < NaChar < 1.6e289

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.2%

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

   6. Taylor expanded in Ec around -inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. *-commutative 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

      4. +-commutative 70.3%

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

      5. mul-1-neg 70.3%

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

      6. unsub-neg 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in EDonor around inf 79.5%

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

   if 1.6e289 < NaChar < 2.1500000000000001e294

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 52.6%

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

   6. Taylor expanded in KbT around inf 52.6%

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

   if 2.1500000000000001e294 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 5.1%

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

   6. Taylor expanded in Ec around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in EDonor around inf 100.0%

      \[\leadsto \frac{NdChar}{1 + \left(\frac{1}{KbT} - \color{blue}{\frac{EDonor}{Ec \cdot KbT}}\right) \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.9 \cdot 10^{+59}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.02 \cdot 10^{-101}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NaChar \leq -2.75 \cdot 10^{-170}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-231}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{-207}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-93}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 3.85 \cdot 10^{-31}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 5.6 \cdot 10^{+100}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Ec \cdot \left(-1 + \left(\frac{EDonor}{Ec} + \left(\frac{Vef}{Ec} + \frac{mu}{Ec}\right)\right)\right)}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.6 \cdot 10^{+289}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.15 \cdot 10^{+294}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ t_2 := t\_0 + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_4 := t\_3 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{if}\;NaChar \leq -4.4 \cdot 10^{+55}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;NaChar \leq -1.02 \cdot 10^{-101}:\\ \;\;\;\;t\_0 + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NaChar \leq -1.62 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -2.25 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 1.4 \cdot 10^{-207}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 6.8 \cdot 10^{-25}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0))))
        (t_2
         (+
          t_0
          (/
           NaChar
           (+
            1.0
            (-
             (+ 1.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))))
             (/ mu KbT))))))
        (t_3 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_4 (+ t_3 (/ NdChar (+ 1.0 (/ Vef KbT))))))
   (if (<= NaChar -4.4e+55)
     t_4
     (if (<= NaChar -1.02e-101)
       (+ t_0 (/ NaChar (+ 2.0 (/ EAccept KbT))))
       (if (<= NaChar -1e-101)
         (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* KbT (/ NdChar Vef)))
         (if (<= NaChar -1.62e-170)
           t_2
           (if (<= NaChar -2.25e-231)
             t_1
             (if (<= NaChar 1.4e-207)
               t_2
               (if (<= NaChar 1.9e-93)
                 t_1
                 (if (<= NaChar 6.8e-25)
                   t_4
                   (+
                    t_3
                    (/
                     NdChar
                     (+
                      1.0
                      (*
                       Ec
                       (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT))))))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	double t_3 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_4 = t_3 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -4.4e+55) {
		tmp = t_4;
	} else if (NaChar <= -1.02e-101) {
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)));
	} else if (NaChar <= -1e-101) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (KbT * (NdChar / Vef));
	} else if (NaChar <= -1.62e-170) {
		tmp = t_2;
	} else if (NaChar <= -2.25e-231) {
		tmp = t_1;
	} else if (NaChar <= 1.4e-207) {
		tmp = t_2;
	} else if (NaChar <= 1.9e-93) {
		tmp = t_1;
	} else if (NaChar <= 6.8e-25) {
		tmp = t_4;
	} else {
		tmp = t_3 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))
    t_1 = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    t_2 = t_0 + (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (mu / kbt))))
    t_3 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_4 = t_3 + (ndchar / (1.0d0 + (vef / kbt)))
    if (nachar <= (-4.4d+55)) then
        tmp = t_4
    else if (nachar <= (-1.02d-101)) then
        tmp = t_0 + (nachar / (2.0d0 + (eaccept / kbt)))
    else if (nachar <= (-1d-101)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (kbt * (ndchar / vef))
    else if (nachar <= (-1.62d-170)) then
        tmp = t_2
    else if (nachar <= (-2.25d-231)) then
        tmp = t_1
    else if (nachar <= 1.4d-207) then
        tmp = t_2
    else if (nachar <= 1.9d-93) then
        tmp = t_1
    else if (nachar <= 6.8d-25) then
        tmp = t_4
    else
        tmp = t_3 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	double t_3 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_4 = t_3 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -4.4e+55) {
		tmp = t_4;
	} else if (NaChar <= -1.02e-101) {
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)));
	} else if (NaChar <= -1e-101) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (KbT * (NdChar / Vef));
	} else if (NaChar <= -1.62e-170) {
		tmp = t_2;
	} else if (NaChar <= -2.25e-231) {
		tmp = t_1;
	} else if (NaChar <= 1.4e-207) {
		tmp = t_2;
	} else if (NaChar <= 1.9e-93) {
		tmp = t_1;
	} else if (NaChar <= 6.8e-25) {
		tmp = t_4;
	} else {
		tmp = t_3 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	t_2 = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))))
	t_3 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_4 = t_3 + (NdChar / (1.0 + (Vef / KbT)))
	tmp = 0
	if NaChar <= -4.4e+55:
		tmp = t_4
	elif NaChar <= -1.02e-101:
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)))
	elif NaChar <= -1e-101:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (KbT * (NdChar / Vef))
	elif NaChar <= -1.62e-170:
		tmp = t_2
	elif NaChar <= -2.25e-231:
		tmp = t_1
	elif NaChar <= 1.4e-207:
		tmp = t_2
	elif NaChar <= 1.9e-93:
		tmp = t_1
	elif NaChar <= 6.8e-25:
		tmp = t_4
	else:
		tmp = t_3 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)))
	t_2 = Float64(t_0 + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT)))))
	t_3 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_4 = Float64(t_3 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))))
	tmp = 0.0
	if (NaChar <= -4.4e+55)
		tmp = t_4;
	elseif (NaChar <= -1.02e-101)
		tmp = Float64(t_0 + Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))));
	elseif (NaChar <= -1e-101)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(KbT * Float64(NdChar / Vef)));
	elseif (NaChar <= -1.62e-170)
		tmp = t_2;
	elseif (NaChar <= -2.25e-231)
		tmp = t_1;
	elseif (NaChar <= 1.4e-207)
		tmp = t_2;
	elseif (NaChar <= 1.9e-93)
		tmp = t_1;
	elseif (NaChar <= 6.8e-25)
		tmp = t_4;
	else
		tmp = Float64(t_3 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	t_2 = t_0 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT))));
	t_3 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_4 = t_3 + (NdChar / (1.0 + (Vef / KbT)));
	tmp = 0.0;
	if (NaChar <= -4.4e+55)
		tmp = t_4;
	elseif (NaChar <= -1.02e-101)
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)));
	elseif (NaChar <= -1e-101)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (KbT * (NdChar / Vef));
	elseif (NaChar <= -1.62e-170)
		tmp = t_2;
	elseif (NaChar <= -2.25e-231)
		tmp = t_1;
	elseif (NaChar <= 1.4e-207)
		tmp = t_2;
	elseif (NaChar <= 1.9e-93)
		tmp = t_1;
	elseif (NaChar <= 6.8e-25)
		tmp = t_4;
	else
		tmp = t_3 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.4e+55], t$95$4, If[LessEqual[NaChar, -1.02e-101], N[(t$95$0 + N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1e-101], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NdChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.62e-170], t$95$2, If[LessEqual[NaChar, -2.25e-231], t$95$1, If[LessEqual[NaChar, 1.4e-207], t$95$2, If[LessEqual[NaChar, 1.9e-93], t$95$1, If[LessEqual[NaChar, 6.8e-25], t$95$4, N[(t$95$3 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if NaChar < -4.40000000000000021e55 or 1.8999999999999999e-93 < NaChar < 6.80000000000000003e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.6%

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

   6. Taylor expanded in Ec around -inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

      4. +-commutative 64.7%

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

      5. mul-1-neg 64.7%

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

      6. unsub-neg 64.7%

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

   8. Simplified 64.7%

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

   9. Taylor expanded in Vef around inf 72.8%

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

   if -4.40000000000000021e55 < NaChar < -1.02e-101

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.0%

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

   6. Taylor expanded in EAccept around 0 72.5%

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

      1. +-commutative 72.5%

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

   8. Simplified 72.5%

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

   if -1.02e-101 < NaChar < -1.00000000000000005e-101

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 100.0%

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

   6. Taylor expanded in Vef around inf 100.0%

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

      1. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in EAccept around inf 100.0%

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

   if -1.00000000000000005e-101 < NaChar < -1.62e-170 or -2.2499999999999999e-231 < NaChar < 1.39999999999999996e-207

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 74.3%

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

      1. +-commutative 74.3%

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

   7. Simplified 74.3%

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

   if -1.62e-170 < NaChar < -2.2499999999999999e-231 or 1.39999999999999996e-207 < NaChar < 1.8999999999999999e-93

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 74.2%

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

   6. Taylor expanded in Vef around 0 67.8%

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

      1. +-commutative 62.4%

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

   8. Simplified 67.8%

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

   if 6.80000000000000003e-25 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.9%

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

   6. Taylor expanded in Ec around -inf 74.6%

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

      1. mul-1-neg 74.6%

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

      2. *-commutative 74.6%

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

      3. distribute-rgt-neg-in 74.6%

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

      4. +-commutative 74.6%

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

      5. mul-1-neg 74.6%

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

      6. unsub-neg 74.6%

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

   8. Simplified 74.6%

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

   9. Taylor expanded in EDonor around inf 70.2%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.4 \cdot 10^{+55}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.02 \cdot 10^{-101}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NaChar \leq -1.62 \cdot 10^{-170}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.25 \cdot 10^{-231}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.4 \cdot 10^{-207}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{-93}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 6.8 \cdot 10^{-25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{if}\;NaChar \leq -9.5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 9.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.6 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + Ec \cdot \left(\frac{\frac{Vef}{Ec}}{KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.4 \cdot 10^{+123}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{+189}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (/ Vef KbT))))))
   (if (<= NaChar -9.5e+133)
     t_1
     (if (<= NaChar 9.6e-99)
       (+
        (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
        (/ NaChar (+ (/ Vef KbT) 2.0)))
       (if (<= NaChar 4.6e-23)
         t_1
         (if (<= NaChar 4.8e-23)
           (+ (/ NaChar 2.0) (* NdChar 0.5))
           (if (<= NaChar 2e+74)
             (+
              t_0
              (/ NdChar (+ 1.0 (* Ec (+ (/ (/ Vef Ec) KbT) (/ -1.0 KbT))))))
             (if (<= NaChar 1.4e+123)
               (+
                t_0
                (/
                 NdChar
                 (+ 1.0 (* Ec (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT))))))
               (if (<= NaChar 1.45e+189)
                 t_1
                 (+ t_0 (/ NdChar (+ 1.0 (/ EDonor KbT)))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -9.5e+133) {
		tmp = t_1;
	} else if (NaChar <= 9.6e-99) {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 4.6e-23) {
		tmp = t_1;
	} else if (NaChar <= 4.8e-23) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else if (NaChar <= 2e+74) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * (((Vef / Ec) / KbT) + (-1.0 / KbT)))));
	} else if (NaChar <= 1.4e+123) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else if (NaChar <= 1.45e+189) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (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) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + (vef / kbt)))
    if (nachar <= (-9.5d+133)) then
        tmp = t_1
    else if (nachar <= 9.6d-99) then
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else if (nachar <= 4.6d-23) then
        tmp = t_1
    else if (nachar <= 4.8d-23) then
        tmp = (nachar / 2.0d0) + (ndchar * 0.5d0)
    else if (nachar <= 2d+74) then
        tmp = t_0 + (ndchar / (1.0d0 + (ec * (((vef / ec) / kbt) + ((-1.0d0) / kbt)))))
    else if (nachar <= 1.4d+123) then
        tmp = t_0 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    else if (nachar <= 1.45d+189) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (1.0d0 + (edonor / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -9.5e+133) {
		tmp = t_1;
	} else if (NaChar <= 9.6e-99) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 4.6e-23) {
		tmp = t_1;
	} else if (NaChar <= 4.8e-23) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else if (NaChar <= 2e+74) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * (((Vef / Ec) / KbT) + (-1.0 / KbT)))));
	} else if (NaChar <= 1.4e+123) {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	} else if (NaChar <= 1.45e+189) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)))
	tmp = 0
	if NaChar <= -9.5e+133:
		tmp = t_1
	elif NaChar <= 9.6e-99:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	elif NaChar <= 4.6e-23:
		tmp = t_1
	elif NaChar <= 4.8e-23:
		tmp = (NaChar / 2.0) + (NdChar * 0.5)
	elif NaChar <= 2e+74:
		tmp = t_0 + (NdChar / (1.0 + (Ec * (((Vef / Ec) / KbT) + (-1.0 / KbT)))))
	elif NaChar <= 1.4e+123:
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	elif NaChar <= 1.45e+189:
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))))
	tmp = 0.0
	if (NaChar <= -9.5e+133)
		tmp = t_1;
	elseif (NaChar <= 9.6e-99)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NaChar <= 4.6e-23)
		tmp = t_1;
	elseif (NaChar <= 4.8e-23)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar * 0.5));
	elseif (NaChar <= 2e+74)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(Vef / Ec) / KbT) + Float64(-1.0 / KbT))))));
	elseif (NaChar <= 1.4e+123)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	elseif (NaChar <= 1.45e+189)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + 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(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	tmp = 0.0;
	if (NaChar <= -9.5e+133)
		tmp = t_1;
	elseif (NaChar <= 9.6e-99)
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	elseif (NaChar <= 4.6e-23)
		tmp = t_1;
	elseif (NaChar <= 4.8e-23)
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	elseif (NaChar <= 2e+74)
		tmp = t_0 + (NdChar / (1.0 + (Ec * (((Vef / Ec) / KbT) + (-1.0 / KbT)))));
	elseif (NaChar <= 1.4e+123)
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	elseif (NaChar <= 1.45e+189)
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -9.5e+133], t$95$1, If[LessEqual[NaChar, 9.6e-99], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.6e-23], t$95$1, If[LessEqual[NaChar, 4.8e-23], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2e+74], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(Vef / Ec), $MachinePrecision] / KbT), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.4e+123], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.45e+189], t$95$1, N[(t$95$0 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if NaChar < -9.49999999999999996e133 or 9.6000000000000002e-99 < NaChar < 4.6000000000000002e-23 or 1.40000000000000006e123 < NaChar < 1.4500000000000001e189

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.6%

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

   6. Taylor expanded in Ec around -inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. *-commutative 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

      4. +-commutative 68.9%

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

      5. mul-1-neg 68.9%

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

      6. unsub-neg 68.9%

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

   8. Simplified 68.9%

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

   9. Taylor expanded in Vef around inf 76.8%

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

   if -9.49999999999999996e133 < NaChar < 9.6000000000000002e-99

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 74.1%

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

   6. Taylor expanded in Vef around 0 67.1%

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

      1. +-commutative 61.6%

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

   8. Simplified 67.1%

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

   if 4.6000000000000002e-23 < NaChar < 4.79999999999999993e-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%

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

   5. Taylor expanded in KbT around inf 100.0%

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

   6. Taylor expanded in KbT around inf 100.0%

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

   7. Taylor expanded in KbT around inf 100.0%

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

   if 4.79999999999999993e-23 < NaChar < 1.9999999999999999e74

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.8%

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

   6. Taylor expanded in Ec around -inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. *-commutative 76.3%

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

      3. distribute-rgt-neg-in 76.3%

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

      4. +-commutative 76.3%

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

      5. mul-1-neg 76.3%

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

      6. unsub-neg 76.3%

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

   8. Simplified 76.3%

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

   9. Taylor expanded in Vef around inf 72.5%

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

       1. associate-/r* 76.9%

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

   11. Simplified 76.9%

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

   if 1.9999999999999999e74 < NaChar < 1.40000000000000006e123

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.2%

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

   6. Taylor expanded in Ec around -inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. *-commutative 59.3%

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

      3. distribute-rgt-neg-in 59.3%

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

      4. +-commutative 59.3%

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

      5. mul-1-neg 59.3%

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

      6. unsub-neg 59.3%

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

   8. Simplified 59.3%

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

   9. Taylor expanded in EDonor around inf 72.7%

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

   if 1.4500000000000001e189 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.0%

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

   6. Taylor expanded in Ec around -inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

      4. +-commutative 76.7%

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

      5. mul-1-neg 76.7%

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

      6. unsub-neg 76.7%

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

   8. Simplified 76.7%

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

   9. Taylor expanded in EDonor around inf 75.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -9.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 9.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{\frac{Vef}{Ec}}{KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.4 \cdot 10^{+123}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{+189}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{if}\;NaChar \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 7 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 9 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (/ Vef KbT))))))
   (if (<= NaChar -4.3e+133)
     t_1
     (if (<= NaChar 7e-99)
       (+
        (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
        (/ NaChar (+ (/ Vef KbT) 2.0)))
       (if (<= NaChar 9e-25)
         t_1
         (+
          t_0
          (/
           NdChar
           (+ 1.0 (* Ec (+ (/ EDonor (* Ec KbT)) (/ -1.0 KbT)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -4.3e+133) {
		tmp = t_1;
	} else if (NaChar <= 7e-99) {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 9e-25) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + (vef / kbt)))
    if (nachar <= (-4.3d+133)) then
        tmp = t_1
    else if (nachar <= 7d-99) then
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else if (nachar <= 9d-25) then
        tmp = t_1
    else
        tmp = t_0 + (ndchar / (1.0d0 + (ec * ((edonor / (ec * kbt)) + ((-1.0d0) / kbt)))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -4.3e+133) {
		tmp = t_1;
	} else if (NaChar <= 7e-99) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 9e-25) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)))
	tmp = 0
	if NaChar <= -4.3e+133:
		tmp = t_1
	elif NaChar <= 7e-99:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	elif NaChar <= 9e-25:
		tmp = t_1
	else:
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))))
	tmp = 0.0
	if (NaChar <= -4.3e+133)
		tmp = t_1;
	elseif (NaChar <= 7e-99)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NaChar <= 9e-25)
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(EDonor / Float64(Ec * KbT)) + Float64(-1.0 / KbT))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	tmp = 0.0;
	if (NaChar <= -4.3e+133)
		tmp = t_1;
	elseif (NaChar <= 7e-99)
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	elseif (NaChar <= 9e-25)
		tmp = t_1;
	else
		tmp = t_0 + (NdChar / (1.0 + (Ec * ((EDonor / (Ec * KbT)) + (-1.0 / KbT)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.3e+133], t$95$1, If[LessEqual[NaChar, 7e-99], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 9e-25], t$95$1, N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(EDonor / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -4.29999999999999994e133 or 6.9999999999999997e-99 < NaChar < 9.0000000000000002e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.6%

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

   6. Taylor expanded in Ec around -inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. *-commutative 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

      4. +-commutative 68.0%

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

      5. mul-1-neg 68.0%

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

      6. unsub-neg 68.0%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in Vef around inf 75.8%

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

   if -4.29999999999999994e133 < NaChar < 6.9999999999999997e-99

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 74.1%

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

   6. Taylor expanded in Vef around 0 67.1%

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

      1. +-commutative 61.6%

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

   8. Simplified 67.1%

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

   if 9.0000000000000002e-25 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.9%

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

   6. Taylor expanded in Ec around -inf 74.6%

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

      1. mul-1-neg 74.6%

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

      2. *-commutative 74.6%

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

      3. distribute-rgt-neg-in 74.6%

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

      4. +-commutative 74.6%

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

      5. mul-1-neg 74.6%

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

      6. unsub-neg 74.6%

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

   8. Simplified 74.6%

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

   9. Taylor expanded in EDonor around inf 70.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 7 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 9 \cdot 10^{-25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{EDonor}{Ec \cdot KbT} + \frac{-1}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -4.6 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -2 \cdot 10^{+93}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 5.1 \cdot 10^{-42}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + t\_0\\ \mathbf{elif}\;NaChar \leq 9.8 \cdot 10^{+201} \lor \neg \left(NaChar \leq 5 \cdot 10^{+206}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (/ Ev KbT) 2.0)))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
          (* NdChar 0.5))))
   (if (<= NaChar -4.6e+133)
     t_1
     (if (<= NaChar -2e+93)
       (+
        (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
        (/ NaChar (+ (/ Vef KbT) 2.0)))
       (if (<= NaChar 5.1e-42)
         (+ (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))) t_0)
         (if (or (<= NaChar 9.8e+201) (not (<= NaChar 5e+206)))
           t_1
           (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / ((Ev / KbT) + 2.0);
	double t_1 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -4.6e+133) {
		tmp = t_1;
	} else if (NaChar <= -2e+93) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 5.1e-42) {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + t_0;
	} else if ((NaChar <= 9.8e+201) || !(NaChar <= 5e+206)) {
		tmp = t_1;
	} else {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / ((ev / kbt) + 2.0d0)
    t_1 = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar * 0.5d0)
    if (nachar <= (-4.6d+133)) then
        tmp = t_1
    else if (nachar <= (-2d+93)) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else if (nachar <= 5.1d-42) then
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + t_0
    else if ((nachar <= 9.8d+201) .or. (.not. (nachar <= 5d+206))) then
        tmp = t_1
    else
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / ((Ev / KbT) + 2.0);
	double t_1 = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -4.6e+133) {
		tmp = t_1;
	} else if (NaChar <= -2e+93) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 5.1e-42) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + t_0;
	} else if ((NaChar <= 9.8e+201) || !(NaChar <= 5e+206)) {
		tmp = t_1;
	} else {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / ((Ev / KbT) + 2.0)
	t_1 = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5)
	tmp = 0
	if NaChar <= -4.6e+133:
		tmp = t_1
	elif NaChar <= -2e+93:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	elif NaChar <= 5.1e-42:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + t_0
	elif (NaChar <= 9.8e+201) or not (NaChar <= 5e+206):
		tmp = t_1
	else:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar * 0.5))
	tmp = 0.0
	if (NaChar <= -4.6e+133)
		tmp = t_1;
	elseif (NaChar <= -2e+93)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NaChar <= 5.1e-42)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + t_0);
	elseif ((NaChar <= 9.8e+201) || !(NaChar <= 5e+206))
		tmp = t_1;
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / ((Ev / KbT) + 2.0);
	t_1 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	tmp = 0.0;
	if (NaChar <= -4.6e+133)
		tmp = t_1;
	elseif (NaChar <= -2e+93)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	elseif (NaChar <= 5.1e-42)
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + t_0;
	elseif ((NaChar <= 9.8e+201) || ~((NaChar <= 5e+206)))
		tmp = t_1;
	else
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.6e+133], t$95$1, If[LessEqual[NaChar, -2e+93], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 5.1e-42], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[Or[LessEqual[NaChar, 9.8e+201], N[Not[LessEqual[NaChar, 5e+206]], $MachinePrecision]], t$95$1, N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -4.5999999999999998e133 or 5.1e-42 < NaChar < 9.79999999999999991e201 or 5.0000000000000002e206 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.9%

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

   6. Taylor expanded in KbT around inf 63.8%

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

   if -4.5999999999999998e133 < NaChar < -2.00000000000000009e93

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 75.4%

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

   6. Taylor expanded in EDonor around 0 75.4%

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

      1. +-commutative 75.4%

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

   8. Simplified 75.4%

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

   9. Taylor expanded in Vef around 0 75.7%

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

       1. +-commutative 75.7%

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

   11. Simplified 75.7%

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

   if -2.00000000000000009e93 < NaChar < 5.1e-42

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 74.1%

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

   6. Taylor expanded in Ev around 0 61.7%

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

   if 9.79999999999999991e201 < NaChar < 5.0000000000000002e206

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 100.0%

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

   6. Taylor expanded in EDonor around inf 100.0%

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

   7. Taylor expanded in Ev around 0 53.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.6 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -2 \cdot 10^{+93}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 5.1 \cdot 10^{-42}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 9.8 \cdot 10^{+201} \lor \neg \left(NaChar \leq 5 \cdot 10^{+206}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 60.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.02 \cdot 10^{+139} \lor \neg \left(NaChar \leq 8.8 \cdot 10^{+51} \lor \neg \left(NaChar \leq 5.4 \cdot 10^{+103}\right) \land NaChar \leq 1.25 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.02e+139)
         (not
          (or (<= NaChar 8.8e+51)
              (and (not (<= NaChar 5.4e+103)) (<= NaChar 1.25e+144)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
    (* NdChar 0.5))
   (+
    (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
    (/ NaChar (+ (/ Vef KbT) 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.02e+139) || !((NaChar <= 8.8e+51) || (!(NaChar <= 5.4e+103) && (NaChar <= 1.25e+144)))) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-1.02d+139)) .or. (.not. (nachar <= 8.8d+51) .or. (.not. (nachar <= 5.4d+103)) .and. (nachar <= 1.25d+144))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.02e+139) || !((NaChar <= 8.8e+51) || (!(NaChar <= 5.4e+103) && (NaChar <= 1.25e+144)))) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.02e+139) or not ((NaChar <= 8.8e+51) or (not (NaChar <= 5.4e+103) and (NaChar <= 1.25e+144))):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.02e+139) || !((NaChar <= 8.8e+51) || (!(NaChar <= 5.4e+103) && (NaChar <= 1.25e+144))))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1.02e+139) || ~(((NaChar <= 8.8e+51) || (~((NaChar <= 5.4e+103)) && (NaChar <= 1.25e+144)))))
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.02e+139], N[Not[Or[LessEqual[NaChar, 8.8e+51], And[N[Not[LessEqual[NaChar, 5.4e+103]], $MachinePrecision], LessEqual[NaChar, 1.25e+144]]]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.02e139 or 8.79999999999999967e51 < NaChar < 5.39999999999999985e103 or 1.25e144 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.2%

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

   6. Taylor expanded in KbT around inf 66.8%

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

   if -1.02e139 < NaChar < 8.79999999999999967e51 or 5.39999999999999985e103 < NaChar < 1.25e144

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 74.1%

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

   6. Taylor expanded in Vef around 0 65.3%

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

      1. +-commutative 60.4%

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

   8. Simplified 65.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.02 \cdot 10^{+139} \lor \neg \left(NaChar \leq 8.8 \cdot 10^{+51} \lor \neg \left(NaChar \leq 5.4 \cdot 10^{+103}\right) \land NaChar \leq 1.25 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 62.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{if}\;NaChar \leq -4.4 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 9.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.6 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (/ Vef KbT))))))
   (if (<= NaChar -4.4e+133)
     t_1
     (if (<= NaChar 9.6e-99)
       (+
        (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
        (/ NaChar (+ (/ Vef KbT) 2.0)))
       (if (<= NaChar 4.6e-23)
         t_1
         (if (<= NaChar 4.8e-23)
           (+ (/ NaChar 2.0) (* NdChar 0.5))
           (+ t_0 (/ NdChar (+ 1.0 (/ EDonor KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -4.4e+133) {
		tmp = t_1;
	} else if (NaChar <= 9.6e-99) {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 4.6e-23) {
		tmp = t_1;
	} else if (NaChar <= 4.8e-23) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else {
		tmp = t_0 + (NdChar / (1.0 + (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) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + (vef / kbt)))
    if (nachar <= (-4.4d+133)) then
        tmp = t_1
    else if (nachar <= 9.6d-99) then
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else if (nachar <= 4.6d-23) then
        tmp = t_1
    else if (nachar <= 4.8d-23) then
        tmp = (nachar / 2.0d0) + (ndchar * 0.5d0)
    else
        tmp = t_0 + (ndchar / (1.0d0 + (edonor / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -4.4e+133) {
		tmp = t_1;
	} else if (NaChar <= 9.6e-99) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else if (NaChar <= 4.6e-23) {
		tmp = t_1;
	} else if (NaChar <= 4.8e-23) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else {
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)))
	tmp = 0
	if NaChar <= -4.4e+133:
		tmp = t_1
	elif NaChar <= 9.6e-99:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	elif NaChar <= 4.6e-23:
		tmp = t_1
	elif NaChar <= 4.8e-23:
		tmp = (NaChar / 2.0) + (NdChar * 0.5)
	else:
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))))
	tmp = 0.0
	if (NaChar <= -4.4e+133)
		tmp = t_1;
	elseif (NaChar <= 9.6e-99)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NaChar <= 4.6e-23)
		tmp = t_1;
	elseif (NaChar <= 4.8e-23)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar * 0.5));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + 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(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + (Vef / KbT)));
	tmp = 0.0;
	if (NaChar <= -4.4e+133)
		tmp = t_1;
	elseif (NaChar <= 9.6e-99)
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	elseif (NaChar <= 4.6e-23)
		tmp = t_1;
	elseif (NaChar <= 4.8e-23)
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	else
		tmp = t_0 + (NdChar / (1.0 + (EDonor / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.4e+133], t$95$1, If[LessEqual[NaChar, 9.6e-99], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.6e-23], t$95$1, If[LessEqual[NaChar, 4.8e-23], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -4.4e133 or 9.6000000000000002e-99 < NaChar < 4.6000000000000002e-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%

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

   5. Taylor expanded in KbT around inf 64.6%

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

   6. Taylor expanded in Ec around -inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. *-commutative 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

      4. +-commutative 68.0%

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

      5. mul-1-neg 68.0%

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

      6. unsub-neg 68.0%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in Vef around inf 75.8%

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

   if -4.4e133 < NaChar < 9.6000000000000002e-99

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 74.1%

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

   6. Taylor expanded in Vef around 0 67.1%

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

      1. +-commutative 61.6%

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

   8. Simplified 67.1%

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

   if 4.6000000000000002e-23 < NaChar < 4.79999999999999993e-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%

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

   5. Taylor expanded in KbT around inf 100.0%

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

   6. Taylor expanded in KbT around inf 100.0%

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

   7. Taylor expanded in KbT around inf 100.0%

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

   if 4.79999999999999993e-23 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.4%

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

   6. Taylor expanded in Ec around -inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. *-commutative 74.2%

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

      3. distribute-rgt-neg-in 74.2%

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

      4. +-commutative 74.2%

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

      5. mul-1-neg 74.2%

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

      6. unsub-neg 74.2%

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

   8. Simplified 74.2%

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

   9. Taylor expanded in EDonor around inf 69.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.4 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 9.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 62.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{if}\;NaChar \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -1.32 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -7.2 \cdot 10^{-51}:\\ \;\;\;\;t\_0 + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.4 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ (/ Vef KbT) 2.0))))
        (t_2
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
          (/ NdChar (+ 1.0 (/ EDonor KbT))))))
   (if (<= NaChar -4.3e+133)
     t_2
     (if (<= NaChar -1.32e+53)
       t_1
       (if (<= NaChar -7.2e-51)
         (+ t_0 (/ NaChar (+ 2.0 (/ EAccept KbT))))
         (if (<= NaChar 3.4e-99) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)));
	double tmp;
	if (NaChar <= -4.3e+133) {
		tmp = t_2;
	} else if (NaChar <= -1.32e+53) {
		tmp = t_1;
	} else if (NaChar <= -7.2e-51) {
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)));
	} else if (NaChar <= 3.4e-99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))
    t_1 = t_0 + (nachar / ((vef / kbt) + 2.0d0))
    t_2 = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar / (1.0d0 + (edonor / kbt)))
    if (nachar <= (-4.3d+133)) then
        tmp = t_2
    else if (nachar <= (-1.32d+53)) then
        tmp = t_1
    else if (nachar <= (-7.2d-51)) then
        tmp = t_0 + (nachar / (2.0d0 + (eaccept / kbt)))
    else if (nachar <= 3.4d-99) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	double t_2 = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)));
	double tmp;
	if (NaChar <= -4.3e+133) {
		tmp = t_2;
	} else if (NaChar <= -1.32e+53) {
		tmp = t_1;
	} else if (NaChar <= -7.2e-51) {
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)));
	} else if (NaChar <= 3.4e-99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0))
	t_2 = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)))
	tmp = 0
	if NaChar <= -4.3e+133:
		tmp = t_2
	elif NaChar <= -1.32e+53:
		tmp = t_1
	elif NaChar <= -7.2e-51:
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)))
	elif NaChar <= 3.4e-99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))))
	tmp = 0.0
	if (NaChar <= -4.3e+133)
		tmp = t_2;
	elseif (NaChar <= -1.32e+53)
		tmp = t_1;
	elseif (NaChar <= -7.2e-51)
		tmp = Float64(t_0 + Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))));
	elseif (NaChar <= 3.4e-99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	t_1 = t_0 + (NaChar / ((Vef / KbT) + 2.0));
	t_2 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)));
	tmp = 0.0;
	if (NaChar <= -4.3e+133)
		tmp = t_2;
	elseif (NaChar <= -1.32e+53)
		tmp = t_1;
	elseif (NaChar <= -7.2e-51)
		tmp = t_0 + (NaChar / (2.0 + (EAccept / KbT)));
	elseif (NaChar <= 3.4e-99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.3e+133], t$95$2, If[LessEqual[NaChar, -1.32e+53], t$95$1, If[LessEqual[NaChar, -7.2e-51], N[(t$95$0 + N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.4e-99], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -4.29999999999999994e133 or 3.40000000000000007e-99 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.9%

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

   6. Taylor expanded in Ec around -inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. *-commutative 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

      4. +-commutative 71.5%

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

      5. mul-1-neg 71.5%

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

      6. unsub-neg 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in EDonor around inf 70.7%

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

   if -4.29999999999999994e133 < NaChar < -1.32e53 or -7.2000000000000001e-51 < NaChar < 3.40000000000000007e-99

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 75.4%

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

   6. Taylor expanded in Vef around 0 68.0%

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

      1. +-commutative 61.5%

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

   8. Simplified 68.0%

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

   if -1.32e53 < NaChar < -7.2000000000000001e-51

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 63.2%

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

   6. Taylor expanded in EAccept around 0 68.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{EAccept}{KbT}}} \]
   7. Step-by-step derivation

      1. +-commutative 68.8%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   8. Simplified 68.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.32 \cdot 10^{+53}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq -7.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.4 \cdot 10^{-99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 56.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -6.7 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -1.66 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -3.3 \cdot 10^{+72}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
          (/ NaChar (+ (/ Vef KbT) 2.0))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
          (* NdChar 0.5))))
   (if (<= NaChar -6.7e+133)
     t_1
     (if (<= NaChar -1.66e+93)
       t_0
       (if (<= NaChar -3.3e+72)
         (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
         (if (<= NaChar 1.7e+50) t_0 t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	double t_1 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -6.7e+133) {
		tmp = t_1;
	} else if (NaChar <= -1.66e+93) {
		tmp = t_0;
	} else if (NaChar <= -3.3e+72) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 1.7e+50) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    t_1 = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar * 0.5d0)
    if (nachar <= (-6.7d+133)) then
        tmp = t_1
    else if (nachar <= (-1.66d+93)) then
        tmp = t_0
    else if (nachar <= (-3.3d+72)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (nachar <= 1.7d+50) then
        tmp = t_0
    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 = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	double t_1 = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -6.7e+133) {
		tmp = t_1;
	} else if (NaChar <= -1.66e+93) {
		tmp = t_0;
	} else if (NaChar <= -3.3e+72) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NaChar <= 1.7e+50) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	t_1 = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5)
	tmp = 0
	if NaChar <= -6.7e+133:
		tmp = t_1
	elif NaChar <= -1.66e+93:
		tmp = t_0
	elif NaChar <= -3.3e+72:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif NaChar <= 1.7e+50:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar * 0.5))
	tmp = 0.0
	if (NaChar <= -6.7e+133)
		tmp = t_1;
	elseif (NaChar <= -1.66e+93)
		tmp = t_0;
	elseif (NaChar <= -3.3e+72)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (NaChar <= 1.7e+50)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	t_1 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	tmp = 0.0;
	if (NaChar <= -6.7e+133)
		tmp = t_1;
	elseif (NaChar <= -1.66e+93)
		tmp = t_0;
	elseif (NaChar <= -3.3e+72)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (NaChar <= 1.7e+50)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.7e+133], t$95$1, If[LessEqual[NaChar, -1.66e+93], t$95$0, If[LessEqual[NaChar, -3.3e+72], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.7e+50], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -6.7000000000000003e133 or 1.6999999999999999e50 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 64.6%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 66.4%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   if -6.7000000000000003e133 < NaChar < -1.65999999999999999e93 or -3.3e72 < NaChar < 1.6999999999999999e50

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Vef around inf 75.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Vef}{KbT}}}} \]

   6. Taylor expanded in EDonor around 0 69.6%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]
   7. Step-by-step derivation

      1. +-commutative 69.6%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(mu + Vef\right)} - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]

   8. Simplified 69.6%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(mu + Vef\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]

   9. Taylor expanded in Vef around 0 61.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Vef}{KbT}}} \]
   10. Step-by-step derivation

       1. +-commutative 61.8%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\color{blue}{\frac{Vef}{KbT} + 2}} \]

   11. Simplified 61.8%

       \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\color{blue}{\frac{Vef}{KbT} + 2}} \]

   if -1.65999999999999999e93 < NaChar < -3.3e72

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in EAccept around inf 100.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in EDonor around 0 83.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   7. Step-by-step derivation

      1. +-commutative 37.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(mu + Vef\right)} - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]

   8. Simplified 83.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(mu + Vef\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   9. Taylor expanded in KbT around inf 72.9%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{1}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.7 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -1.66 \cdot 10^{+93}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq -3.3 \cdot 10^{+72}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -3.7 \cdot 10^{+124}:\\ \;\;\;\;\frac{NdChar}{1 + {e}^{\left(\frac{mu}{KbT}\right)}}\\ \mathbf{elif}\;NdChar \leq -7.6 \cdot 10^{+21}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NdChar \leq 5600000000000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 4.1 \cdot 10^{+139}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))))
   (if (<= NdChar -3.7e+124)
     (/ NdChar (+ 1.0 (pow E (/ mu KbT))))
     (if (<= NdChar -7.6e+21)
       t_0
       (if (<= NdChar -1.12e-13)
         (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (* KbT (/ NdChar Vef)))
         (if (<= NdChar 5600000000000.0)
           (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
           (if (<= NdChar 4.1e+139)
             (/ NdChar (+ 1.0 (exp (/ mu KbT))))
             t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.7e+124) {
		tmp = NdChar / (1.0 + pow(((double) M_E), (mu / KbT)));
	} else if (NdChar <= -7.6e+21) {
		tmp = t_0;
	} else if (NdChar <= -1.12e-13) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (KbT * (NdChar / Vef));
	} else if (NdChar <= 5600000000000.0) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NdChar <= 4.1e+139) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -3.7e+124) {
		tmp = NdChar / (1.0 + Math.pow(Math.E, (mu / KbT)));
	} else if (NdChar <= -7.6e+21) {
		tmp = t_0;
	} else if (NdChar <= -1.12e-13) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (KbT * (NdChar / Vef));
	} else if (NdChar <= 5600000000000.0) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (NdChar <= 4.1e+139) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -3.7e+124:
		tmp = NdChar / (1.0 + math.pow(math.e, (mu / KbT)))
	elif NdChar <= -7.6e+21:
		tmp = t_0
	elif NdChar <= -1.12e-13:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (KbT * (NdChar / Vef))
	elif NdChar <= 5600000000000.0:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif NdChar <= 4.1e+139:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -3.7e+124)
		tmp = Float64(NdChar / Float64(1.0 + (exp(1) ^ Float64(mu / KbT))));
	elseif (NdChar <= -7.6e+21)
		tmp = t_0;
	elseif (NdChar <= -1.12e-13)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(KbT * Float64(NdChar / Vef)));
	elseif (NdChar <= 5600000000000.0)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (NdChar <= 4.1e+139)
		tmp = Float64(NdChar / Float64(1.0 + exp(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((EDonor / KbT)))) + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -3.7e+124)
		tmp = NdChar / (1.0 + (2.71828182845904523536 ^ (mu / KbT)));
	elseif (NdChar <= -7.6e+21)
		tmp = t_0;
	elseif (NdChar <= -1.12e-13)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (KbT * (NdChar / Vef));
	elseif (NdChar <= 5600000000000.0)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (NdChar <= 4.1e+139)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.7e+124], N[(NdChar / N[(1.0 + N[Power[E, N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -7.6e+21], t$95$0, If[LessEqual[NdChar, -1.12e-13], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NdChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 5600000000000.0], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 4.1e+139], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -3.70000000000000008e124

   1. Initial program 99.9%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in mu around inf 60.9%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 38.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-+r+ 38.2%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)} - \frac{mu}{KbT}} \]

      2. +-commutative 38.2%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \color{blue}{\left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)}\right) - \frac{mu}{KbT}} \]

   8. Simplified 38.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}} \]

   9. Taylor expanded in mu around inf 24.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{-1 \cdot \frac{KbT \cdot NaChar}{mu}} \]
   10. Step-by-step derivation

       1. associate-*r/ 24.3%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{-1 \cdot \left(KbT \cdot NaChar\right)}{mu}} \]

       2. associate-*r* 24.3%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-1 \cdot KbT\right) \cdot NaChar}}{mu} \]

       3. neg-mul-1 24.3%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-KbT\right)} \cdot NaChar}{mu} \]

   11. Simplified 24.3%

       \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{\left(-KbT\right) \cdot NaChar}{mu}} \]

   12. Taylor expanded in NdChar around inf 41.2%

       \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}} \]
   13. Step-by-step derivation

       1. *-un-lft-identity 41.2%

          \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{1 \cdot \frac{mu}{KbT}}}} \]

       2. exp-prod 41.3%

          \[\leadsto \frac{NdChar}{1 + \color{blue}{{\left(e^{1}\right)}^{\left(\frac{mu}{KbT}\right)}}} \]

   14. Applied egg-rr 41.3%

       \[\leadsto \frac{NdChar}{1 + \color{blue}{{\left(e^{1}\right)}^{\left(\frac{mu}{KbT}\right)}}} \]
   15. Step-by-step derivation

       1. exp-1-e 41.3%

          \[\leadsto \frac{NdChar}{1 + {\color{blue}{e}}^{\left(\frac{mu}{KbT}\right)}} \]

   16. Simplified 41.3%

       \[\leadsto \frac{NdChar}{1 + \color{blue}{{e}^{\left(\frac{mu}{KbT}\right)}}} \]

   if -3.70000000000000008e124 < NdChar < -7.6e21 or 4.1000000000000002e139 < NdChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in EDonor around inf 69.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 39.1%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\color{blue}{2}} \]

   if -7.6e21 < NdChar < -1.12e-13

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 38.6%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in Vef around inf 35.1%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 35.1%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   8. Simplified 35.1%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in Ev around inf 5.1%

      \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   if -1.12e-13 < NdChar < 5.6e12

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in EAccept around inf 67.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in EDonor around 0 64.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   7. Step-by-step derivation

      1. +-commutative 61.1%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(mu + Vef\right)} - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]

   8. Simplified 64.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(mu + Vef\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   9. Taylor expanded in KbT around inf 45.0%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{1}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   if 5.6e12 < NdChar < 4.1000000000000002e139

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in mu around inf 63.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 39.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-+r+ 39.2%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)} - \frac{mu}{KbT}} \]

      2. +-commutative 39.2%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \color{blue}{\left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)}\right) - \frac{mu}{KbT}} \]

   8. Simplified 39.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}} \]

   9. Taylor expanded in mu around inf 34.1%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{-1 \cdot \frac{KbT \cdot NaChar}{mu}} \]
   10. Step-by-step derivation

       1. associate-*r/ 34.1%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{-1 \cdot \left(KbT \cdot NaChar\right)}{mu}} \]

       2. associate-*r* 34.1%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-1 \cdot KbT\right) \cdot NaChar}}{mu} \]

       3. neg-mul-1 34.1%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-KbT\right)} \cdot NaChar}{mu} \]

   11. Simplified 34.1%

       \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{\left(-KbT\right) \cdot NaChar}{mu}} \]

   12. Taylor expanded in NdChar around inf 38.9%

       \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.7 \cdot 10^{+124}:\\ \;\;\;\;\frac{NdChar}{1 + {e}^{\left(\frac{mu}{KbT}\right)}}\\ \mathbf{elif}\;NdChar \leq -7.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NdChar \leq 5600000000000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 4.1 \cdot 10^{+139}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 34.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{if}\;NaChar \leq -8.2 \cdot 10^{+232}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -2.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{+48}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (* KbT (/ NdChar Vef)))))
   (if (<= NaChar -8.2e+232)
     t_0
     (if (<= NaChar -2.5e+150)
       (- (/ NaChar 2.0) (/ NdChar (- -1.0 (/ EDonor KbT))))
       (if (<= NaChar -1.6e+114)
         (/ NaChar (+ 2.0 (/ EAccept KbT)))
         (if (<= NaChar 1.45e+48)
           (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
           t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp((Ev / KbT)))) + (KbT * (NdChar / Vef));
	double tmp;
	if (NaChar <= -8.2e+232) {
		tmp = t_0;
	} else if (NaChar <= -2.5e+150) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else if (NaChar <= -1.6e+114) {
		tmp = NaChar / (2.0 + (EAccept / KbT));
	} else if (NaChar <= 1.45e+48) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp((ev / kbt)))) + (kbt * (ndchar / vef))
    if (nachar <= (-8.2d+232)) then
        tmp = t_0
    else if (nachar <= (-2.5d+150)) then
        tmp = (nachar / 2.0d0) - (ndchar / ((-1.0d0) - (edonor / kbt)))
    else if (nachar <= (-1.6d+114)) then
        tmp = nachar / (2.0d0 + (eaccept / kbt))
    else if (nachar <= 1.45d+48) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (KbT * (NdChar / Vef));
	double tmp;
	if (NaChar <= -8.2e+232) {
		tmp = t_0;
	} else if (NaChar <= -2.5e+150) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else if (NaChar <= -1.6e+114) {
		tmp = NaChar / (2.0 + (EAccept / KbT));
	} else if (NaChar <= 1.45e+48) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (KbT * (NdChar / Vef))
	tmp = 0
	if NaChar <= -8.2e+232:
		tmp = t_0
	elif NaChar <= -2.5e+150:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)))
	elif NaChar <= -1.6e+114:
		tmp = NaChar / (2.0 + (EAccept / KbT))
	elif NaChar <= 1.45e+48:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(KbT * Float64(NdChar / Vef)))
	tmp = 0.0
	if (NaChar <= -8.2e+232)
		tmp = t_0;
	elseif (NaChar <= -2.5e+150)
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 - Float64(EDonor / KbT))));
	elseif (NaChar <= -1.6e+114)
		tmp = Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT)));
	elseif (NaChar <= 1.45e+48)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp((Ev / KbT)))) + (KbT * (NdChar / Vef));
	tmp = 0.0;
	if (NaChar <= -8.2e+232)
		tmp = t_0;
	elseif (NaChar <= -2.5e+150)
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	elseif (NaChar <= -1.6e+114)
		tmp = NaChar / (2.0 + (EAccept / KbT));
	elseif (NaChar <= 1.45e+48)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NdChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -8.2e+232], t$95$0, If[LessEqual[NaChar, -2.5e+150], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.6e+114], N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.45e+48], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -8.20000000000000005e232 or 1.4499999999999999e48 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 65.9%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in Vef around inf 53.9%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 53.3%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   8. Simplified 53.3%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in Ev around inf 33.9%

      \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   if -8.20000000000000005e232 < NaChar < -2.50000000000000004e150

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 55.0%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 38.1%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in mu around inf 38.1%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \color{blue}{mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{KbT \cdot mu}\right)}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{2} \]

   8. Taylor expanded in EDonor around inf 48.9%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\frac{EDonor}{KbT}}} + \frac{NaChar}{2} \]

   if -2.50000000000000004e150 < NaChar < -1.6e114

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 66.8%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in Vef around inf 68.3%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 60.9%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   8. Simplified 60.9%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in EAccept around inf 45.9%

      \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
   10. Step-by-step derivation

       1. clear-num 45.9%

          \[\leadsto KbT \cdot \color{blue}{\frac{1}{\frac{Vef}{NdChar}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

       2. un-div-inv 45.9%

          \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   11. Applied egg-rr 45.9%

       \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   12. Step-by-step derivation

       1. associate-/r/ 45.9%

          \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   13. Simplified 45.9%

       \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   14. Taylor expanded in EAccept around 0 29.8%

       \[\leadsto \frac{KbT}{Vef} \cdot NdChar + \frac{NaChar}{\color{blue}{2 + \frac{EAccept}{KbT}}} \]
   15. Step-by-step derivation

       1. +-commutative 52.8%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   16. Simplified 29.8%

       \[\leadsto \frac{KbT}{Vef} \cdot NdChar + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   17. Taylor expanded in Vef around inf 52.8%

       \[\leadsto \color{blue}{\frac{NaChar}{2 + \frac{EAccept}{KbT}}} \]

   if -1.6e114 < NaChar < 1.4499999999999999e48

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in EDonor around inf 63.1%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 40.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\color{blue}{2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8.2 \cdot 10^{+232}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;NaChar \leq -2.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{+48}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 55.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -1.26 \cdot 10^{-51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
          (* NdChar 0.5))))
   (if (<= NaChar -4.3e+133)
     t_0
     (if (<= NaChar -1.26e-51)
       (+
        (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
        (/ NaChar (+ (/ Ev KbT) 2.0)))
       (if (<= NaChar 8.5e-108)
         (+
          (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
          (/ NaChar 2.0))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -4.3e+133) {
		tmp = t_0;
	} else if (NaChar <= -1.26e-51) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NaChar <= 8.5e-108) {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar * 0.5d0)
    if (nachar <= (-4.3d+133)) then
        tmp = t_0
    else if (nachar <= (-1.26d-51)) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / ((ev / kbt) + 2.0d0))
    else if (nachar <= 8.5d-108) then
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	double tmp;
	if (NaChar <= -4.3e+133) {
		tmp = t_0;
	} else if (NaChar <= -1.26e-51) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NaChar <= 8.5e-108) {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5)
	tmp = 0
	if NaChar <= -4.3e+133:
		tmp = t_0
	elif NaChar <= -1.26e-51:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0))
	elif NaChar <= 8.5e-108:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar * 0.5))
	tmp = 0.0
	if (NaChar <= -4.3e+133)
		tmp = t_0;
	elseif (NaChar <= -1.26e-51)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (NaChar <= 8.5e-108)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	tmp = 0.0;
	if (NaChar <= -4.3e+133)
		tmp = t_0;
	elseif (NaChar <= -1.26e-51)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	elseif (NaChar <= 8.5e-108)
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.3e+133], t$95$0, If[LessEqual[NaChar, -1.26e-51], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8.5e-108], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -4.29999999999999994e133 or 8.49999999999999986e-108 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 65.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 62.5%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   if -4.29999999999999994e133 < NaChar < -1.2600000000000001e-51

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Ev around inf 70.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   6. Taylor expanded in Ev around 0 56.1%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Ev}{KbT}}} \]

   7. Taylor expanded in EDonor around 0 52.8%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}} \]
   8. Step-by-step derivation

      1. +-commutative 66.2%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(mu + Vef\right)} - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]

   9. Simplified 52.8%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(mu + Vef\right) - Ec}{KbT}}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}} \]

   if -1.2600000000000001e-51 < NaChar < 8.49999999999999986e-108

   1. Initial program 99.9%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 59.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -1.26 \cdot 10^{-51}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 55.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -8 \cdot 10^{+145} \lor \neg \left(NaChar \leq 8.5 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -8e+145) (not (<= NaChar 8.5e-108)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
    (* NdChar 0.5))
   (+
    (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) 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 <= -8e+145) || !(NaChar <= 8.5e-108)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / 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 <= (-8d+145)) .or. (.not. (nachar <= 8.5d-108))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / 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 <= -8e+145) || !(NaChar <= 8.5e-108)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -8e+145) or not (NaChar <= 8.5e-108):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -8e+145) || !(NaChar <= 8.5e-108))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / 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 <= -8e+145) || ~((NaChar <= 8.5e-108)))
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -8e+145], N[Not[LessEqual[NaChar, 8.5e-108]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -7.9999999999999999e145 or 8.49999999999999986e-108 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 65.0%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 61.8%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   if -7.9999999999999999e145 < NaChar < 8.49999999999999986e-108

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 55.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8 \cdot 10^{+145} \lor \neg \left(NaChar \leq 8.5 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 52.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{+82} \lor \neg \left(NaChar \leq 2.25 \cdot 10^{-142}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -8.5e+82) (not (<= NaChar 2.25e-142)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
    (* NdChar 0.5))
   (+ (/ NdChar (+ 1.0 (exp (/ (- (+ 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 <= -8.5e+82) || !(NaChar <= 2.25e-142)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp((((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 <= (-8.5d+82)) .or. (.not. (nachar <= 2.25d-142))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp((((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 <= -8.5e+82) || !(NaChar <= 2.25e-142)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((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 <= -8.5e+82) or not (NaChar <= 2.25e-142):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp((((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 <= -8.5e+82) || !(NaChar <= 2.25e-142))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + 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 <= -8.5e+82) || ~((NaChar <= 2.25e-142)))
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp((((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, -8.5e+82], N[Not[LessEqual[NaChar, 2.25e-142]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -8.4999999999999995e82 or 2.25000000000000009e-142 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 61.8%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 59.5%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   if -8.4999999999999995e82 < NaChar < 2.25000000000000009e-142

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 56.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{1}} \]

   6. Taylor expanded in EDonor around 0 52.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + 1} \]
   7. Step-by-step derivation

      1. +-commutative 68.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(mu + Vef\right)} - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]

   8. Simplified 52.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(mu + Vef\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8.5 \cdot 10^{+82} \lor \neg \left(NaChar \leq 2.25 \cdot 10^{-142}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 37.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;KbT \leq 7.2 \cdot 10^{-291}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{-246}:\\ \;\;\;\;t\_0 + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;KbT \leq 7 \cdot 10^{-195}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT))))))
   (if (<= KbT 7.2e-291)
     (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (/ NaChar (+ (/ Ev KbT) 2.0)))
     (if (<= KbT 2.1e-246)
       (+ t_0 (* KbT (/ NdChar Vef)))
       (if (<= KbT 7e-195)
         (/ NdChar (+ 1.0 (exp (/ mu KbT))))
         (+ t_0 (/ NdChar 2.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((Ev / KbT)));
	double tmp;
	if (KbT <= 7.2e-291) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= 2.1e-246) {
		tmp = t_0 + (KbT * (NdChar / Vef));
	} else if (KbT <= 7e-195) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else {
		tmp = t_0 + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((ev / kbt)))
    if (kbt <= 7.2d-291) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / ((ev / kbt) + 2.0d0))
    else if (kbt <= 2.1d-246) then
        tmp = t_0 + (kbt * (ndchar / vef))
    else if (kbt <= 7d-195) then
        tmp = ndchar / (1.0d0 + exp((mu / kbt)))
    else
        tmp = t_0 + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((Ev / KbT)));
	double tmp;
	if (KbT <= 7.2e-291) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= 2.1e-246) {
		tmp = t_0 + (KbT * (NdChar / Vef));
	} else if (KbT <= 7e-195) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else {
		tmp = t_0 + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((Ev / KbT)))
	tmp = 0
	if KbT <= 7.2e-291:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / ((Ev / KbT) + 2.0))
	elif KbT <= 2.1e-246:
		tmp = t_0 + (KbT * (NdChar / Vef))
	elif KbT <= 7e-195:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	else:
		tmp = t_0 + (NdChar / 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(Ev / KbT))))
	tmp = 0.0
	if (KbT <= 7.2e-291)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (KbT <= 2.1e-246)
		tmp = Float64(t_0 + Float64(KbT * Float64(NdChar / Vef)));
	elseif (KbT <= 7e-195)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	else
		tmp = Float64(t_0 + Float64(NdChar / 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 / KbT)));
	tmp = 0.0;
	if (KbT <= 7.2e-291)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	elseif (KbT <= 2.1e-246)
		tmp = t_0 + (KbT * (NdChar / Vef));
	elseif (KbT <= 7e-195)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	else
		tmp = t_0 + (NdChar / 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[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, 7.2e-291], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.1e-246], N[(t$95$0 + N[(KbT * N[(NdChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 7e-195], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < 7.1999999999999993e-291

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Ev around inf 73.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   6. Taylor expanded in Ev around 0 49.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Ev}{KbT}}} \]

   7. Taylor expanded in Ec around inf 38.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-1 \cdot \frac{Ec}{KbT}}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}} \]
   8. Step-by-step derivation

      1. associate-*r/ 50.5%

         \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-1 \cdot Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      2. mul-1-neg 50.5%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{-Ec}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   9. Simplified 38.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}} \]

   if 7.1999999999999993e-291 < KbT < 2.09999999999999995e-246

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 33.3%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in Vef around inf 100.0%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in Ev around inf 67.5%

      \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   if 2.09999999999999995e-246 < KbT < 7.00000000000000028e-195

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in mu around inf 80.5%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 46.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-+r+ 46.8%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)} - \frac{mu}{KbT}} \]

      2. +-commutative 46.8%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \color{blue}{\left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)}\right) - \frac{mu}{KbT}} \]

   8. Simplified 46.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}} \]

   9. Taylor expanded in mu around inf 49.1%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{-1 \cdot \frac{KbT \cdot NaChar}{mu}} \]
   10. Step-by-step derivation

       1. associate-*r/ 49.1%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{-1 \cdot \left(KbT \cdot NaChar\right)}{mu}} \]

       2. associate-*r* 49.1%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-1 \cdot KbT\right) \cdot NaChar}}{mu} \]

       3. neg-mul-1 49.1%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-KbT\right)} \cdot NaChar}{mu} \]

   11. Simplified 49.1%

       \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{\left(-KbT\right) \cdot NaChar}{mu}} \]

   12. Taylor expanded in NdChar around inf 64.5%

       \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}} \]

   if 7.00000000000000028e-195 < KbT

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Ev around inf 64.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   6. Taylor expanded in EDonor around inf 50.2%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   7. Taylor expanded in EDonor around 0 36.8%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{1}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 7.2 \cdot 10^{-291}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{-246}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{elif}\;KbT \leq 7 \cdot 10^{-195}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 37.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;KbT \leq 1.95 \cdot 10^{-286}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{-184}:\\ \;\;\;\;t\_0 + \frac{NdChar \cdot KbT}{EDonor}\\ \mathbf{elif}\;KbT \leq 4 \cdot 10^{-160}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT))))))
   (if (<= KbT 1.95e-286)
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar (+ (/ Ev KbT) 2.0)))
     (if (<= KbT 2.1e-184)
       (+ t_0 (/ (* NdChar KbT) EDonor))
       (if (<= KbT 4e-160)
         (/ NdChar (+ 1.0 (exp (/ mu KbT))))
         (+ t_0 (/ NdChar 2.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((Ev / KbT)));
	double tmp;
	if (KbT <= 1.95e-286) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= 2.1e-184) {
		tmp = t_0 + ((NdChar * KbT) / EDonor);
	} else if (KbT <= 4e-160) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else {
		tmp = t_0 + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((ev / kbt)))
    if (kbt <= 1.95d-286) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / ((ev / kbt) + 2.0d0))
    else if (kbt <= 2.1d-184) then
        tmp = t_0 + ((ndchar * kbt) / edonor)
    else if (kbt <= 4d-160) then
        tmp = ndchar / (1.0d0 + exp((mu / kbt)))
    else
        tmp = t_0 + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((Ev / KbT)));
	double tmp;
	if (KbT <= 1.95e-286) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= 2.1e-184) {
		tmp = t_0 + ((NdChar * KbT) / EDonor);
	} else if (KbT <= 4e-160) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else {
		tmp = t_0 + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((Ev / KbT)))
	tmp = 0
	if KbT <= 1.95e-286:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / ((Ev / KbT) + 2.0))
	elif KbT <= 2.1e-184:
		tmp = t_0 + ((NdChar * KbT) / EDonor)
	elif KbT <= 4e-160:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	else:
		tmp = t_0 + (NdChar / 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(Ev / KbT))))
	tmp = 0.0
	if (KbT <= 1.95e-286)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (KbT <= 2.1e-184)
		tmp = Float64(t_0 + Float64(Float64(NdChar * KbT) / EDonor));
	elseif (KbT <= 4e-160)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	else
		tmp = Float64(t_0 + Float64(NdChar / 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 / KbT)));
	tmp = 0.0;
	if (KbT <= 1.95e-286)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	elseif (KbT <= 2.1e-184)
		tmp = t_0 + ((NdChar * KbT) / EDonor);
	elseif (KbT <= 4e-160)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	else
		tmp = t_0 + (NdChar / 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[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, 1.95e-286], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.1e-184], N[(t$95$0 + N[(N[(NdChar * KbT), $MachinePrecision] / EDonor), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4e-160], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < 1.94999999999999998e-286

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Ev around inf 73.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   6. Taylor expanded in EDonor around inf 55.3%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   7. Taylor expanded in Ev around 0 37.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Ev}{KbT}}} \]

   if 1.94999999999999998e-286 < KbT < 2.0999999999999999e-184

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 40.6%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in EDonor around inf 51.8%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{EDonor}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in Ev around inf 37.9%

      \[\leadsto \frac{KbT \cdot NdChar}{EDonor} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   if 2.0999999999999999e-184 < KbT < 4e-160

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in mu around inf 67.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 33.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-+r+ 33.3%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)} - \frac{mu}{KbT}} \]

      2. +-commutative 33.3%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \color{blue}{\left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)}\right) - \frac{mu}{KbT}} \]

   8. Simplified 33.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}} \]

   9. Taylor expanded in mu around inf 67.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{-1 \cdot \frac{KbT \cdot NaChar}{mu}} \]
   10. Step-by-step derivation

       1. associate-*r/ 67.4%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{-1 \cdot \left(KbT \cdot NaChar\right)}{mu}} \]

       2. associate-*r* 67.4%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-1 \cdot KbT\right) \cdot NaChar}}{mu} \]

       3. neg-mul-1 67.4%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-KbT\right)} \cdot NaChar}{mu} \]

   11. Simplified 67.4%

       \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{\left(-KbT\right) \cdot NaChar}{mu}} \]

   12. Taylor expanded in NdChar around inf 67.4%

       \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}} \]

   if 4e-160 < KbT

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Ev around inf 65.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   6. Taylor expanded in EDonor around inf 49.6%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   7. Taylor expanded in EDonor around 0 37.3%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{1}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 1.95 \cdot 10^{-286}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{-184}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar \cdot KbT}{EDonor}\\ \mathbf{elif}\;KbT \leq 4 \cdot 10^{-160}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 37.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -3 \cdot 10^{+33}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Ev \leq -4.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -3e+33)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (if (<= Ev -4.5e-164)
     (+ (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))) (/ NaChar 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 (Ev <= -3e+33) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (Ev <= -4.5e-164) {
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / 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 (ev <= (-3d+33)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else if (ev <= (-4.5d-164)) then
        tmp = (ndchar / (1.0d0 + exp((ec / -kbt)))) + (nachar / 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 (Ev <= -3e+33) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (Ev <= -4.5e-164) {
		tmp = (NdChar / (1.0 + Math.exp((Ec / -KbT)))) + (NaChar / 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 Ev <= -3e+33:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	elif Ev <= -4.5e-164:
		tmp = (NdChar / (1.0 + math.exp((Ec / -KbT)))) + (NaChar / 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 (Ev <= -3e+33)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	elseif (Ev <= -4.5e-164)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))) + Float64(NaChar / 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 (Ev <= -3e+33)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	elseif (Ev <= -4.5e-164)
		tmp = (NdChar / (1.0 + exp((Ec / -KbT)))) + (NaChar / 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[Ev, -3e+33], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -4.5e-164], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 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 3 regimes

2. if Ev < -2.99999999999999984e33

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Ev around inf 82.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   6. Taylor expanded in EDonor around inf 68.1%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   7. Taylor expanded in EDonor around 0 40.2%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{1}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -2.99999999999999984e33 < Ev < -4.4999999999999997e-164

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 52.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{1}} \]

   6. Taylor expanded in Ec around inf 37.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-1 \cdot \frac{Ec}{KbT}}}} + \frac{NaChar}{1 + 1} \]
   7. Step-by-step derivation

      1. associate-*r/ 62.5%

         \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-1 \cdot Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      2. mul-1-neg 62.5%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{-Ec}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   8. Simplified 37.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{1 + 1} \]

   if -4.4999999999999997e-164 < Ev

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in EAccept around inf 74.5%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in EDonor around 0 69.5%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   7. Step-by-step derivation

      1. +-commutative 65.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(mu + Vef\right)} - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]

   8. Simplified 69.5%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(mu + Vef\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   9. Taylor expanded in KbT around inf 39.0%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{1}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -3 \cdot 10^{+33}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Ev \leq -4.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 46.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq -1.65 \cdot 10^{+282}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ec -1.65e+282)
   (/ NaChar (+ 2.0 (/ EAccept KbT)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))
    (* NdChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -1.65e+282) {
		tmp = NaChar / (2.0 + (EAccept / KbT));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ec <= (-1.65d+282)) then
        tmp = nachar / (2.0d0 + (eaccept / kbt))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (ev + (eaccept - mu))) / kbt)))) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= -1.65e+282) {
		tmp = NaChar / (2.0 + (EAccept / KbT));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ec <= -1.65e+282:
		tmp = NaChar / (2.0 + (EAccept / KbT))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ec <= -1.65e+282)
		tmp = Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT)));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ec <= -1.65e+282)
		tmp = NaChar / (2.0 + (EAccept / KbT));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (Ev + (EAccept - mu))) / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ec, -1.65e+282], N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < -1.65e282

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 34.5%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in Vef around inf 17.2%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 25.2%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   8. Simplified 25.2%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in EAccept around inf 16.6%

      \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
   10. Step-by-step derivation

       1. clear-num 16.6%

          \[\leadsto KbT \cdot \color{blue}{\frac{1}{\frac{Vef}{NdChar}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

       2. un-div-inv 16.6%

          \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   11. Applied egg-rr 16.6%

       \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   12. Step-by-step derivation

       1. associate-/r/ 24.1%

          \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   13. Simplified 24.1%

       \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   14. Taylor expanded in EAccept around 0 3.1%

       \[\leadsto \frac{KbT}{Vef} \cdot NdChar + \frac{NaChar}{\color{blue}{2 + \frac{EAccept}{KbT}}} \]
   15. Step-by-step derivation

       1. +-commutative 43.7%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   16. Simplified 3.1%

       \[\leadsto \frac{KbT}{Vef} \cdot NdChar + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   17. Taylor expanded in Vef around inf 27.3%

       \[\leadsto \color{blue}{\frac{NaChar}{2 + \frac{EAccept}{KbT}}} \]

   if -1.65e282 < Ec

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 53.8%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 48.5%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -1.65 \cdot 10^{+282}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 37.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -4.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Ev \leq -2.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -4.2e+110)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (if (<= Ev -2.7e-205)
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 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 (Ev <= -4.2e+110) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (Ev <= -2.7e-205) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 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 (ev <= (-4.2d+110)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else if (ev <= (-2.7d-205)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 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 (Ev <= -4.2e+110) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (Ev <= -2.7e-205) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 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 Ev <= -4.2e+110:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	elif Ev <= -2.7e-205:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 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 (Ev <= -4.2e+110)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	elseif (Ev <= -2.7e-205)
		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(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 (Ev <= -4.2e+110)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	elseif (Ev <= -2.7e-205)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 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[Ev, -4.2e+110], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -2.7e-205], 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[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -4.2000000000000003e110

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Ev around inf 84.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   6. Taylor expanded in EDonor around inf 70.1%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   7. Taylor expanded in EDonor around 0 39.8%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{1}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -4.2000000000000003e110 < Ev < -2.7000000000000001e-205

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in EDonor around inf 72.8%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 39.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\color{blue}{2}} \]

   if -2.7000000000000001e-205 < Ev

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in EAccept around inf 75.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   6. Taylor expanded in EDonor around 0 70.2%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   7. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(mu + Vef\right)} - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]

   8. Simplified 70.2%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(mu + Vef\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

   9. Taylor expanded in KbT around inf 40.2%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{1}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -4.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Ev \leq -2.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 32.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -9.8 \cdot 10^{+128}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 + \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.2 \cdot 10^{-192}:\\ \;\;\;\;\frac{NdChar}{1 + {e}^{\left(\frac{mu}{KbT}\right)}}\\ \mathbf{elif}\;NaChar \leq 4.05 \cdot 10^{-35}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -9.8e+128)
   (- (/ NaChar 2.0) (/ NdChar (+ -1.0 (/ Ec KbT))))
   (if (<= NaChar 1.2e-192)
     (/ NdChar (+ 1.0 (pow E (/ mu KbT))))
     (if (<= NaChar 4.05e-35)
       (- (/ NaChar 2.0) (/ NdChar (- -1.0 (/ EDonor KbT))))
       (+
        (/
         NdChar
         (+
          1.0
          (*
           Ec
           (+
            (/ (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) Ec)
            (/ -1.0 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 <= -9.8e+128) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 + (Ec / KbT)));
	} else if (NaChar <= 1.2e-192) {
		tmp = NdChar / (1.0 + pow(((double) M_E), (mu / KbT)));
	} else if (NaChar <= 4.05e-35) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else {
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0);
	}
	return tmp;
}

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 <= -9.8e+128) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 + (Ec / KbT)));
	} else if (NaChar <= 1.2e-192) {
		tmp = NdChar / (1.0 + Math.pow(Math.E, (mu / KbT)));
	} else if (NaChar <= 4.05e-35) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else {
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -9.8e+128:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 + (Ec / KbT)))
	elif NaChar <= 1.2e-192:
		tmp = NdChar / (1.0 + math.pow(math.e, (mu / KbT)))
	elif NaChar <= 4.05e-35:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)))
	else:
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -9.8e+128)
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 + Float64(Ec / KbT))));
	elseif (NaChar <= 1.2e-192)
		tmp = Float64(NdChar / Float64(1.0 + (exp(1) ^ Float64(mu / KbT))));
	elseif (NaChar <= 4.05e-35)
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 - Float64(EDonor / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / 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 <= -9.8e+128)
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 + (Ec / KbT)));
	elseif (NaChar <= 1.2e-192)
		tmp = NdChar / (1.0 + (2.71828182845904523536 ^ (mu / KbT)));
	elseif (NaChar <= 4.05e-35)
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	else
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -9.8e+128], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 + N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.2e-192], N[(NdChar / N[(1.0 + N[Power[E, N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.05e-35], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -9.80000000000000035e128

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 64.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 27.0%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in mu around inf 27.4%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \color{blue}{mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{KbT \cdot mu}\right)}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{2} \]

   8. Taylor expanded in Ec around inf 31.1%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{-1 \cdot \frac{Ec}{KbT}}} + \frac{NaChar}{2} \]
   9. Step-by-step derivation

      1. neg-mul-1 31.1%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(-\frac{Ec}{KbT}\right)}} + \frac{NaChar}{2} \]

      2. distribute-neg-frac2 31.1%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\frac{Ec}{-KbT}}} + \frac{NaChar}{2} \]

   10. Simplified 31.1%

       \[\leadsto \frac{NdChar}{1 + \color{blue}{\frac{Ec}{-KbT}}} + \frac{NaChar}{2} \]

   if -9.80000000000000035e128 < NaChar < 1.2e-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%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in mu around inf 59.9%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 37.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-+r+ 37.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)} - \frac{mu}{KbT}} \]

      2. +-commutative 37.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \color{blue}{\left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)}\right) - \frac{mu}{KbT}} \]

   8. Simplified 37.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}} \]

   9. Taylor expanded in mu around inf 28.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{-1 \cdot \frac{KbT \cdot NaChar}{mu}} \]
   10. Step-by-step derivation

       1. associate-*r/ 28.4%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{-1 \cdot \left(KbT \cdot NaChar\right)}{mu}} \]

       2. associate-*r* 28.4%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-1 \cdot KbT\right) \cdot NaChar}}{mu} \]

       3. neg-mul-1 28.4%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-KbT\right)} \cdot NaChar}{mu} \]

   11. Simplified 28.4%

       \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{\left(-KbT\right) \cdot NaChar}{mu}} \]

   12. Taylor expanded in NdChar around inf 37.0%

       \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}} \]
   13. Step-by-step derivation

       1. *-un-lft-identity 37.0%

          \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{1 \cdot \frac{mu}{KbT}}}} \]

       2. exp-prod 37.0%

          \[\leadsto \frac{NdChar}{1 + \color{blue}{{\left(e^{1}\right)}^{\left(\frac{mu}{KbT}\right)}}} \]

   14. Applied egg-rr 37.0%

       \[\leadsto \frac{NdChar}{1 + \color{blue}{{\left(e^{1}\right)}^{\left(\frac{mu}{KbT}\right)}}} \]
   15. Step-by-step derivation

       1. exp-1-e 37.0%

          \[\leadsto \frac{NdChar}{1 + {\color{blue}{e}}^{\left(\frac{mu}{KbT}\right)}} \]

   16. Simplified 37.0%

       \[\leadsto \frac{NdChar}{1 + \color{blue}{{e}^{\left(\frac{mu}{KbT}\right)}}} \]

   if 1.2e-192 < NaChar < 4.05000000000000015e-35

   1. Initial program 99.9%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 47.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 23.5%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in mu around inf 23.5%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \color{blue}{mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{KbT \cdot mu}\right)}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{2} \]

   8. Taylor expanded in EDonor around inf 36.3%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\frac{EDonor}{KbT}}} + \frac{NaChar}{2} \]

   if 4.05000000000000015e-35 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 67.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 29.4%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in Ec around -inf 30.0%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{-1 \cdot \left(Ec \cdot \left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right)\right)}} + \frac{NaChar}{2} \]
   8. Step-by-step derivation

      1. mul-1-neg 74.9%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(-Ec \cdot \left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right)\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      2. *-commutative 74.9%

         \[\leadsto \frac{NdChar}{1 + \left(-\color{blue}{\left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right) \cdot Ec}\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      3. distribute-rgt-neg-in 74.9%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right) \cdot \left(-Ec\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      4. +-commutative 74.9%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} + -1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right)} \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      5. mul-1-neg 74.9%

         \[\leadsto \frac{NdChar}{1 + \left(\frac{1}{KbT} + \color{blue}{\left(-\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right)}\right) \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      6. unsub-neg 74.9%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} - \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right)} \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Simplified 30.0%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} - \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right) \cdot \left(-Ec\right)}} + \frac{NaChar}{2} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -9.8 \cdot 10^{+128}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 + \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.2 \cdot 10^{-192}:\\ \;\;\;\;\frac{NdChar}{1 + {e}^{\left(\frac{mu}{KbT}\right)}}\\ \mathbf{elif}\;NaChar \leq 4.05 \cdot 10^{-35}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 35.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+227}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -6.8e+227)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* KbT (/ NdChar Vef)))
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -6.8e+227) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (KbT * (NdChar / Vef));
	} else {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-6.8d+227)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (kbt * (ndchar / vef))
    else
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -6.8e+227) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (KbT * (NdChar / Vef));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -6.8e+227:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (KbT * (NdChar / Vef))
	else:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -6.8e+227)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(KbT * Float64(NdChar / Vef)));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -6.8e+227)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (KbT * (NdChar / Vef));
	else
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -6.8e+227], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NdChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -6.79999999999999979e227

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 66.9%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in Vef around inf 68.0%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 66.4%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   8. Simplified 66.4%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in EAccept around inf 24.5%

      \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   if -6.79999999999999979e227 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in EDonor around inf 68.8%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 37.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\color{blue}{2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+227}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + KbT \cdot \frac{NdChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 32.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2 \cdot 10^{+129}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 + \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.25 \cdot 10^{-192}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 2.35 \cdot 10^{-35}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -2e+129)
   (- (/ NaChar 2.0) (/ NdChar (+ -1.0 (/ Ec KbT))))
   (if (<= NaChar 1.25e-192)
     (/ NdChar (+ 1.0 (exp (/ mu KbT))))
     (if (<= NaChar 2.35e-35)
       (- (/ NaChar 2.0) (/ NdChar (- -1.0 (/ EDonor KbT))))
       (+
        (/
         NdChar
         (+
          1.0
          (*
           Ec
           (+
            (/ (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) Ec)
            (/ -1.0 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 <= -2e+129) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 + (Ec / KbT)));
	} else if (NaChar <= 1.25e-192) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else if (NaChar <= 2.35e-35) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else {
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / 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 <= (-2d+129)) then
        tmp = (nachar / 2.0d0) - (ndchar / ((-1.0d0) + (ec / kbt)))
    else if (nachar <= 1.25d-192) then
        tmp = ndchar / (1.0d0 + exp((mu / kbt)))
    else if (nachar <= 2.35d-35) then
        tmp = (nachar / 2.0d0) - (ndchar / ((-1.0d0) - (edonor / kbt)))
    else
        tmp = (ndchar / (1.0d0 + (ec * (((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) / ec) + ((-1.0d0) / 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 <= -2e+129) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 + (Ec / KbT)));
	} else if (NaChar <= 1.25e-192) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else if (NaChar <= 2.35e-35) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else {
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -2e+129:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 + (Ec / KbT)))
	elif NaChar <= 1.25e-192:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	elif NaChar <= 2.35e-35:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)))
	else:
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -2e+129)
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 + Float64(Ec / KbT))));
	elseif (NaChar <= 1.25e-192)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	elseif (NaChar <= 2.35e-35)
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 - Float64(EDonor / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / 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 <= -2e+129)
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 + (Ec / KbT)));
	elseif (NaChar <= 1.25e-192)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	elseif (NaChar <= 2.35e-35)
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	else
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -2e+129], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 + N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.25e-192], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.35e-35], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2e129

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 64.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 27.0%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in mu around inf 27.4%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \color{blue}{mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{KbT \cdot mu}\right)}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{2} \]

   8. Taylor expanded in Ec around inf 31.1%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{-1 \cdot \frac{Ec}{KbT}}} + \frac{NaChar}{2} \]
   9. Step-by-step derivation

      1. neg-mul-1 31.1%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(-\frac{Ec}{KbT}\right)}} + \frac{NaChar}{2} \]

      2. distribute-neg-frac2 31.1%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\frac{Ec}{-KbT}}} + \frac{NaChar}{2} \]

   10. Simplified 31.1%

       \[\leadsto \frac{NdChar}{1 + \color{blue}{\frac{Ec}{-KbT}}} + \frac{NaChar}{2} \]

   if -2e129 < NaChar < 1.25e-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%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in mu around inf 59.9%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 37.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-+r+ 37.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)} - \frac{mu}{KbT}} \]

      2. +-commutative 37.0%

         \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \color{blue}{\left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)}\right) - \frac{mu}{KbT}} \]

   8. Simplified 37.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{\left(\left(2 + \frac{EAccept}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}} \]

   9. Taylor expanded in mu around inf 28.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{-1 \cdot \frac{KbT \cdot NaChar}{mu}} \]
   10. Step-by-step derivation

       1. associate-*r/ 28.4%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{-1 \cdot \left(KbT \cdot NaChar\right)}{mu}} \]

       2. associate-*r* 28.4%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-1 \cdot KbT\right) \cdot NaChar}}{mu} \]

       3. neg-mul-1 28.4%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{\color{blue}{\left(-KbT\right)} \cdot NaChar}{mu} \]

   11. Simplified 28.4%

       \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \color{blue}{\frac{\left(-KbT\right) \cdot NaChar}{mu}} \]

   12. Taylor expanded in NdChar around inf 37.0%

       \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}} \]

   if 1.25e-192 < NaChar < 2.35e-35

   1. Initial program 99.9%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 47.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 23.5%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in mu around inf 23.5%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \color{blue}{mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{KbT \cdot mu}\right)}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{2} \]

   8. Taylor expanded in EDonor around inf 36.3%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\frac{EDonor}{KbT}}} + \frac{NaChar}{2} \]

   if 2.35e-35 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 67.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 29.4%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in Ec around -inf 30.0%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{-1 \cdot \left(Ec \cdot \left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right)\right)}} + \frac{NaChar}{2} \]
   8. Step-by-step derivation

      1. mul-1-neg 74.9%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(-Ec \cdot \left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right)\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      2. *-commutative 74.9%

         \[\leadsto \frac{NdChar}{1 + \left(-\color{blue}{\left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right) \cdot Ec}\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      3. distribute-rgt-neg-in 74.9%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right) \cdot \left(-Ec\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      4. +-commutative 74.9%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} + -1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right)} \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      5. mul-1-neg 74.9%

         \[\leadsto \frac{NdChar}{1 + \left(\frac{1}{KbT} + \color{blue}{\left(-\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right)}\right) \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      6. unsub-neg 74.9%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} - \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right)} \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Simplified 30.0%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} - \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right) \cdot \left(-Ec\right)}} + \frac{NaChar}{2} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2 \cdot 10^{+129}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 + \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.25 \cdot 10^{-192}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 2.35 \cdot 10^{-35}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 35.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
4. Add Preprocessing

5. Taylor expanded in EDonor around inf 69.9%

   \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

6. Taylor expanded in KbT around inf 35.5%

   \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\color{blue}{2}} \]
7. Add Preprocessing

Alternative 36: 30.4% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\\ \mathbf{if}\;KbT \leq -2.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{NdChar}{\left(2 + t\_0\right) - \frac{Ec}{KbT}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq -3.9 \cdot 10^{-159}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{elif}\;KbT \leq 4.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{NdChar}{\frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + Ec \cdot \left(\frac{1 + t\_0}{Ec} + \frac{-1}{KbT}\right)} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))))
   (if (<= KbT -2.8e+105)
     (+ (/ NdChar (- (+ 2.0 t_0) (/ Ec KbT))) (/ NaChar (+ (/ Ev KbT) 2.0)))
     (if (<= KbT -3.9e-159)
       (- (/ NaChar 2.0) (/ NdChar (- -1.0 (/ EDonor KbT))))
       (if (<= KbT 4.5e-117)
         (/ NdChar (/ Vef KbT))
         (+
          (/ NdChar (+ 1.0 (* Ec (+ (/ (+ 1.0 t_0) Ec) (/ -1.0 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 t_0 = (EDonor / KbT) + ((Vef / KbT) + (mu / KbT));
	double tmp;
	if (KbT <= -2.8e+105) {
		tmp = (NdChar / ((2.0 + t_0) - (Ec / KbT))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= -3.9e-159) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else if (KbT <= 4.5e-117) {
		tmp = NdChar / (Vef / KbT);
	} else {
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + t_0) / Ec) + (-1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = (edonor / kbt) + ((vef / kbt) + (mu / kbt))
    if (kbt <= (-2.8d+105)) then
        tmp = (ndchar / ((2.0d0 + t_0) - (ec / kbt))) + (nachar / ((ev / kbt) + 2.0d0))
    else if (kbt <= (-3.9d-159)) then
        tmp = (nachar / 2.0d0) - (ndchar / ((-1.0d0) - (edonor / kbt)))
    else if (kbt <= 4.5d-117) then
        tmp = ndchar / (vef / kbt)
    else
        tmp = (ndchar / (1.0d0 + (ec * (((1.0d0 + t_0) / ec) + ((-1.0d0) / 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 t_0 = (EDonor / KbT) + ((Vef / KbT) + (mu / KbT));
	double tmp;
	if (KbT <= -2.8e+105) {
		tmp = (NdChar / ((2.0 + t_0) - (Ec / KbT))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= -3.9e-159) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else if (KbT <= 4.5e-117) {
		tmp = NdChar / (Vef / KbT);
	} else {
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + t_0) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (EDonor / KbT) + ((Vef / KbT) + (mu / KbT))
	tmp = 0
	if KbT <= -2.8e+105:
		tmp = (NdChar / ((2.0 + t_0) - (Ec / KbT))) + (NaChar / ((Ev / KbT) + 2.0))
	elif KbT <= -3.9e-159:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)))
	elif KbT <= 4.5e-117:
		tmp = NdChar / (Vef / KbT)
	else:
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + t_0) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))
	tmp = 0.0
	if (KbT <= -2.8e+105)
		tmp = Float64(Float64(NdChar / Float64(Float64(2.0 + t_0) - Float64(Ec / KbT))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (KbT <= -3.9e-159)
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 - Float64(EDonor / KbT))));
	elseif (KbT <= 4.5e-117)
		tmp = Float64(NdChar / Float64(Vef / KbT));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(1.0 + t_0) / Ec) + Float64(-1.0 / KbT))))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (EDonor / KbT) + ((Vef / KbT) + (mu / KbT));
	tmp = 0.0;
	if (KbT <= -2.8e+105)
		tmp = (NdChar / ((2.0 + t_0) - (Ec / KbT))) + (NaChar / ((Ev / KbT) + 2.0));
	elseif (KbT <= -3.9e-159)
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	elseif (KbT <= 4.5e-117)
		tmp = NdChar / (Vef / KbT);
	else
		tmp = (NdChar / (1.0 + (Ec * (((1.0 + t_0) / Ec) + (-1.0 / KbT))))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -2.8e+105], N[(N[(NdChar / N[(N[(2.0 + t$95$0), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -3.9e-159], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4.5e-117], N[(NdChar / N[(Vef / KbT), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(1.0 + t$95$0), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -2.8000000000000001e105

   1. Initial program 99.9%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Ev around inf 81.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   6. Taylor expanded in Ev around 0 72.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Ev}{KbT}}} \]

   7. Taylor expanded in KbT around inf 56.8%

      \[\leadsto \frac{NdChar}{\color{blue}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}} \]

   if -2.8000000000000001e105 < KbT < -3.89999999999999977e-159

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 51.6%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 12.9%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in mu around inf 12.6%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \color{blue}{mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{KbT \cdot mu}\right)}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{2} \]

   8. Taylor expanded in EDonor around inf 22.6%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\frac{EDonor}{KbT}}} + \frac{NaChar}{2} \]

   if -3.89999999999999977e-159 < KbT < 4.49999999999999969e-117

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 36.5%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in Vef around inf 39.1%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 34.4%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in EAccept around inf 22.3%

      \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   10. Taylor expanded in EAccept around 0 9.3%

       \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{\color{blue}{2 + \frac{EAccept}{KbT}}} \]
   11. Step-by-step derivation

       1. +-commutative 58.9%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   12. Simplified 9.3%

       \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   13. Taylor expanded in KbT around inf 15.4%

       \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} \]
   14. Step-by-step derivation

       1. associate-*l/ 19.3%

          \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} \]

       2. associate-/r/ 13.8%

          \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} \]

   15. Simplified 13.8%

       \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} \]
   16. Step-by-step derivation

       1. associate-/r/ 19.3%

          \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} \]

   17. Applied egg-rr 19.3%

       \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} \]
   18. Step-by-step derivation

       1. *-commutative 19.3%

          \[\leadsto \color{blue}{NdChar \cdot \frac{KbT}{Vef}} \]

       2. clear-num 19.3%

          \[\leadsto NdChar \cdot \color{blue}{\frac{1}{\frac{Vef}{KbT}}} \]

       3. un-div-inv 19.3%

          \[\leadsto \color{blue}{\frac{NdChar}{\frac{Vef}{KbT}}} \]

   19. Applied egg-rr 19.3%

       \[\leadsto \color{blue}{\frac{NdChar}{\frac{Vef}{KbT}}} \]

   if 4.49999999999999969e-117 < KbT

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 58.3%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 29.9%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in Ec around -inf 30.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{-1 \cdot \left(Ec \cdot \left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right)\right)}} + \frac{NaChar}{2} \]
   8. Step-by-step derivation

      1. mul-1-neg 64.6%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(-Ec \cdot \left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right)\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      2. *-commutative 64.6%

         \[\leadsto \frac{NdChar}{1 + \left(-\color{blue}{\left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right) \cdot Ec}\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      3. distribute-rgt-neg-in 64.6%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(-1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{1}{KbT}\right) \cdot \left(-Ec\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      4. +-commutative 64.6%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} + -1 \cdot \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right)} \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      5. mul-1-neg 64.6%

         \[\leadsto \frac{NdChar}{1 + \left(\frac{1}{KbT} + \color{blue}{\left(-\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right)}\right) \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

      6. unsub-neg 64.6%

         \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} - \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right)} \cdot \left(-Ec\right)} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Simplified 30.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\frac{1}{KbT} - \frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec}\right) \cdot \left(-Ec\right)}} + \frac{NaChar}{2} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq -3.9 \cdot 10^{-159}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{elif}\;KbT \leq 4.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{NdChar}{\frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 30.7% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -4.1 \cdot 10^{+105}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq -3.7 \cdot 10^{-157}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{elif}\;KbT \leq 3.1 \cdot 10^{-119}:\\ \;\;\;\;\frac{NdChar}{\frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -4.1e+105)
   (+
    (/
     NdChar
     (- (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) (/ Ec KbT)))
    (/ NaChar (+ (/ Ev KbT) 2.0)))
   (if (<= KbT -3.7e-157)
     (- (/ NaChar 2.0) (/ NdChar (- -1.0 (/ EDonor KbT))))
     (if (<= KbT 3.1e-119)
       (/ NdChar (/ Vef KbT))
       (+ (/ NaChar 2.0) (* NdChar 0.5))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -4.1e+105) {
		tmp = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= -3.7e-157) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else if (KbT <= 3.1e-119) {
		tmp = NdChar / (Vef / KbT);
	} else {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-4.1d+105)) then
        tmp = (ndchar / ((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt))) + (nachar / ((ev / kbt) + 2.0d0))
    else if (kbt <= (-3.7d-157)) then
        tmp = (nachar / 2.0d0) - (ndchar / ((-1.0d0) - (edonor / kbt)))
    else if (kbt <= 3.1d-119) then
        tmp = ndchar / (vef / kbt)
    else
        tmp = (nachar / 2.0d0) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -4.1e+105) {
		tmp = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= -3.7e-157) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	} else if (KbT <= 3.1e-119) {
		tmp = NdChar / (Vef / KbT);
	} else {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -4.1e+105:
		tmp = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) + (NaChar / ((Ev / KbT) + 2.0))
	elif KbT <= -3.7e-157:
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)))
	elif KbT <= 3.1e-119:
		tmp = NdChar / (Vef / KbT)
	else:
		tmp = (NaChar / 2.0) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -4.1e+105)
		tmp = Float64(Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (KbT <= -3.7e-157)
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 - Float64(EDonor / KbT))));
	elseif (KbT <= 3.1e-119)
		tmp = Float64(NdChar / Float64(Vef / KbT));
	else
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -4.1e+105)
		tmp = (NdChar / ((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT))) + (NaChar / ((Ev / KbT) + 2.0));
	elseif (KbT <= -3.7e-157)
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - (EDonor / KbT)));
	elseif (KbT <= 3.1e-119)
		tmp = NdChar / (Vef / KbT);
	else
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -4.1e+105], N[(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] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -3.7e-157], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 3.1e-119], N[(NdChar / N[(Vef / KbT), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -4.1000000000000002e105

   1. Initial program 99.9%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in Ev around inf 81.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]

   6. Taylor expanded in Ev around 0 72.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Ev}{KbT}}} \]

   7. Taylor expanded in KbT around inf 56.8%

      \[\leadsto \frac{NdChar}{\color{blue}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}} \]

   if -4.1000000000000002e105 < KbT < -3.6999999999999998e-157

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 51.6%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 12.9%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in mu around inf 12.6%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \color{blue}{mu \cdot \left(\frac{1}{KbT} + \frac{Vef}{KbT \cdot mu}\right)}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{2} \]

   8. Taylor expanded in EDonor around inf 22.6%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\frac{EDonor}{KbT}}} + \frac{NaChar}{2} \]

   if -3.6999999999999998e-157 < KbT < 3.09999999999999978e-119

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 36.5%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in Vef around inf 39.1%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 34.4%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in EAccept around inf 22.3%

      \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   10. Taylor expanded in EAccept around 0 9.3%

       \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{\color{blue}{2 + \frac{EAccept}{KbT}}} \]
   11. Step-by-step derivation

       1. +-commutative 58.9%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   12. Simplified 9.3%

       \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   13. Taylor expanded in KbT around inf 15.4%

       \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} \]
   14. Step-by-step derivation

       1. associate-*l/ 19.3%

          \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} \]

       2. associate-/r/ 13.8%

          \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} \]

   15. Simplified 13.8%

       \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} \]
   16. Step-by-step derivation

       1. associate-/r/ 19.3%

          \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} \]

   17. Applied egg-rr 19.3%

       \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} \]
   18. Step-by-step derivation

       1. *-commutative 19.3%

          \[\leadsto \color{blue}{NdChar \cdot \frac{KbT}{Vef}} \]

       2. clear-num 19.3%

          \[\leadsto NdChar \cdot \color{blue}{\frac{1}{\frac{Vef}{KbT}}} \]

       3. un-div-inv 19.3%

          \[\leadsto \color{blue}{\frac{NdChar}{\frac{Vef}{KbT}}} \]

   19. Applied egg-rr 19.3%

       \[\leadsto \color{blue}{\frac{NdChar}{\frac{Vef}{KbT}}} \]

   if 3.09999999999999978e-119 < KbT

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 58.3%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 29.9%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in KbT around inf 30.3%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{2} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.1 \cdot 10^{+105}:\\ \;\;\;\;\frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq -3.7 \cdot 10^{-157}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - \frac{EDonor}{KbT}}\\ \mathbf{elif}\;KbT \leq 3.1 \cdot 10^{-119}:\\ \;\;\;\;\frac{NdChar}{\frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 26.9% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{-254} \lor \neg \left(NaChar \leq 6.1 \cdot 10^{-280}\right):\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar \cdot \left(EDonor \cdot 0.5\right)}{EDonor}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.7e-254) (not (<= NaChar 6.1e-280)))
   (+ (/ NaChar 2.0) (* NdChar 0.5))
   (/ (* NaChar (* EDonor 0.5)) EDonor)))

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 <= -2.7e-254) || !(NaChar <= 6.1e-280)) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else {
		tmp = (NaChar * (EDonor * 0.5)) / EDonor;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-2.7d-254)) .or. (.not. (nachar <= 6.1d-280))) then
        tmp = (nachar / 2.0d0) + (ndchar * 0.5d0)
    else
        tmp = (nachar * (edonor * 0.5d0)) / edonor
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.7e-254) || !(NaChar <= 6.1e-280)) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else {
		tmp = (NaChar * (EDonor * 0.5)) / EDonor;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2.7e-254) or not (NaChar <= 6.1e-280):
		tmp = (NaChar / 2.0) + (NdChar * 0.5)
	else:
		tmp = (NaChar * (EDonor * 0.5)) / EDonor
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -2.7e-254) || !(NaChar <= 6.1e-280))
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NaChar * Float64(EDonor * 0.5)) / EDonor);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -2.7e-254) || ~((NaChar <= 6.1e-280)))
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	else
		tmp = (NaChar * (EDonor * 0.5)) / EDonor;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -2.7e-254], N[Not[LessEqual[NaChar, 6.1e-280]], $MachinePrecision]], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar * N[(EDonor * 0.5), $MachinePrecision]), $MachinePrecision] / EDonor), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.70000000000000007e-254 or 6.10000000000000008e-280 < NaChar

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 54.8%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 25.8%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in KbT around inf 27.6%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{2} \]

   if -2.70000000000000007e-254 < NaChar < 6.10000000000000008e-280

   1. Initial program 99.7%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 27.1%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 7.4%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in EDonor around inf 4.5%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{EDonor}} + \frac{NaChar}{2} \]
   8. Step-by-step derivation

      1. associate-/l* 4.6%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} + \frac{NaChar}{2} \]

   9. Simplified 4.6%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} + \frac{NaChar}{2} \]

   10. Taylor expanded in EDonor around 0 4.5%

       \[\leadsto \color{blue}{\frac{0.5 \cdot \left(EDonor \cdot NaChar\right) + KbT \cdot NdChar}{EDonor}} \]

   11. Taylor expanded in EDonor around inf 36.4%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(EDonor \cdot NaChar\right)}}{EDonor} \]
   12. Step-by-step derivation

       1. *-commutative 36.4%

          \[\leadsto \frac{\color{blue}{\left(EDonor \cdot NaChar\right) \cdot 0.5}}{EDonor} \]

       2. *-commutative 36.4%

          \[\leadsto \frac{\color{blue}{\left(NaChar \cdot EDonor\right)} \cdot 0.5}{EDonor} \]

       3. associate-*r* 36.4%

          \[\leadsto \frac{\color{blue}{NaChar \cdot \left(EDonor \cdot 0.5\right)}}{EDonor} \]

   13. Simplified 36.4%

       \[\leadsto \frac{\color{blue}{NaChar \cdot \left(EDonor \cdot 0.5\right)}}{EDonor} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{-254} \lor \neg \left(NaChar \leq 6.1 \cdot 10^{-280}\right):\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar \cdot \left(EDonor \cdot 0.5\right)}{EDonor}\\ \end{array} \]
5. Add Preprocessing

Alternative 39: 19.4% accurate, 22.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq 5 \cdot 10^{+152}:\\ \;\;\;\;NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{Vef}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Vef 5e+152) (* NaChar 0.5) (* KbT (/ NdChar Vef))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Vef <= 5e+152) {
		tmp = NaChar * 0.5;
	} else {
		tmp = KbT * (NdChar / Vef);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (vef <= 5d+152) then
        tmp = nachar * 0.5d0
    else
        tmp = kbt * (ndchar / vef)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Vef <= 5e+152) {
		tmp = NaChar * 0.5;
	} else {
		tmp = KbT * (NdChar / Vef);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Vef <= 5e+152:
		tmp = NaChar * 0.5
	else:
		tmp = KbT * (NdChar / Vef)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Vef <= 5e+152)
		tmp = Float64(NaChar * 0.5);
	else
		tmp = Float64(KbT * Float64(NdChar / Vef));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Vef <= 5e+152)
		tmp = NaChar * 0.5;
	else
		tmp = KbT * (NdChar / Vef);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Vef, 5e+152], N[(NaChar * 0.5), $MachinePrecision], N[(KbT * N[(NdChar / Vef), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < 5e152

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 56.2%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in KbT around inf 26.4%

      \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

   7. Taylor expanded in EDonor around inf 11.8%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{EDonor}} + \frac{NaChar}{2} \]
   8. Step-by-step derivation

      1. associate-/l* 11.7%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} + \frac{NaChar}{2} \]

   9. Simplified 11.7%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} + \frac{NaChar}{2} \]

   10. Taylor expanded in KbT around 0 22.2%

       \[\leadsto \color{blue}{0.5 \cdot NaChar} \]

   if 5e152 < Vef

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in KbT around inf 28.5%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   6. Taylor expanded in Vef around inf 26.1%

      \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
   7. Step-by-step derivation

      1. associate-/l* 38.8%

         \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   8. Simplified 38.8%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{Vef}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

   9. Taylor expanded in EAccept around inf 17.9%

      \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   10. Taylor expanded in EAccept around 0 14.6%

       \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{\color{blue}{2 + \frac{EAccept}{KbT}}} \]
   11. Step-by-step derivation

       1. +-commutative 47.6%

          \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   12. Simplified 14.6%

       \[\leadsto KbT \cdot \frac{NdChar}{Vef} + \frac{NaChar}{\color{blue}{\frac{EAccept}{KbT} + 2}} \]

   13. Taylor expanded in KbT around inf 13.3%

       \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{Vef}} \]
   14. Step-by-step derivation

       1. associate-*l/ 16.5%

          \[\leadsto \color{blue}{\frac{KbT}{Vef} \cdot NdChar} \]

       2. associate-/r/ 22.9%

          \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} \]

   15. Simplified 22.9%

       \[\leadsto \color{blue}{\frac{KbT}{\frac{Vef}{NdChar}}} \]
   16. Step-by-step derivation

       1. clear-num 22.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{\frac{Vef}{NdChar}}{KbT}}} \]

       2. associate-/r/ 22.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{Vef}{NdChar}} \cdot KbT} \]

       3. clear-num 22.9%

          \[\leadsto \color{blue}{\frac{NdChar}{Vef}} \cdot KbT \]

   17. Applied egg-rr 22.9%

       \[\leadsto \color{blue}{\frac{NdChar}{Vef} \cdot KbT} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq 5 \cdot 10^{+152}:\\ \;\;\;\;NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;KbT \cdot \frac{NdChar}{Vef}\\ \end{array} \]
5. Add Preprocessing

Alternative 40: 27.7% accurate, 32.7× speedup

Math

\[\begin{array}{l} \\ \frac{NaChar}{2} + NdChar \cdot 0.5 \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (/ NaChar 2.0) (* NdChar 0.5)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / 2.0) + (NdChar * 0.5);
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (nachar / 2.0d0) + (ndchar * 0.5d0)
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / 2.0) + (NdChar * 0.5);
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NaChar / 2.0) + (NdChar * 0.5)

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NaChar / 2.0) + Float64(NdChar * 0.5))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar / 2.0) + (NdChar * 0.5);
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
4. Add Preprocessing

5. Taylor expanded in KbT around inf 52.9%

   \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

6. Taylor expanded in KbT around inf 24.6%

   \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

7. Taylor expanded in KbT around inf 26.2%

   \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{2} \]

8. Final simplification 26.2%

   \[\leadsto \frac{NaChar}{2} + NdChar \cdot 0.5 \]
9. Add Preprocessing

Alternative 41: 18.3% accurate, 76.3× speedup

Math

\[\begin{array}{l} \\ NaChar \cdot 0.5 \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (* NaChar 0.5))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return NaChar * 0.5;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = nachar * 0.5d0
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return NaChar * 0.5;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return NaChar * 0.5

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(NaChar * 0.5)
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = NaChar * 0.5;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(NaChar * 0.5), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}} \]
4. Add Preprocessing

5. Taylor expanded in KbT around inf 52.9%

   \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]

6. Taylor expanded in KbT around inf 24.6%

   \[\leadsto \frac{NdChar}{1 + \left(\left(1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\color{blue}{2}} \]

7. Taylor expanded in EDonor around inf 11.1%

   \[\leadsto \color{blue}{\frac{KbT \cdot NdChar}{EDonor}} + \frac{NaChar}{2} \]
8. Step-by-step derivation

   1. associate-/l* 11.0%

      \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} + \frac{NaChar}{2} \]

9. Simplified 11.0%

   \[\leadsto \color{blue}{KbT \cdot \frac{NdChar}{EDonor}} + \frac{NaChar}{2} \]

10. Taylor expanded in KbT around 0 20.7%

    \[\leadsto \color{blue}{0.5 \cdot NaChar} \]

11. Final simplification 20.7%

    \[\leadsto NaChar \cdot 0.5 \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(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))))))