Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 15

Speedup: N/A×

• could not determine a ground truth

  1. NdChar = -1.3025745278608143e-30
  2. Ec = 5.278989793023217e+213
  3. Vef = 1.5956350784878116e+86
  4. EDonor = 2.7032153428061125e-244
  5. mu = -6.031001497306559e+162
  6. KbT = 4.9142080767970717e-303
  7. NaChar = 2.2252214628724193e-31
  8. Ev = -1.7049961036458754e-165
  9. EAccept = -2.4244852986563357e+269

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. mult-flip N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

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

3. Applied rewrites 100.0%

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

Alternative 2: 93.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -4 \cdot 10^{+141}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.02 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= mu -4e+141)
   (+
    (/ NdChar (+ 1.0 (exp (/ mu KbT))))
    (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
   (if (<= mu 1.02e+86)
     (+
      (/ NaChar (+ 1.0 (exp (/ (+ EAccept (+ Ev Vef)) KbT))))
      (/ NdChar (+ 1.0 (exp (/ (- (+ EDonor Vef) Ec) KbT)))))
     (+
      (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT))))
      (/ NaChar (+ 1.0 (exp (/ (- Vef mu) KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (mu <= -4e+141) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	} else if (mu <= 1.02e+86) {
		tmp = (NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp(((Vef - mu) / KbT))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (mu <= (-4d+141)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    else if (mu <= 1.02d+86) then
        tmp = (nachar / (1.0d0 + exp(((eaccept + (ev + vef)) / kbt)))) + (ndchar / (1.0d0 + exp((((edonor + vef) - ec) / kbt))))
    else
        tmp = (ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))) + (nachar / (1.0d0 + exp(((vef - mu) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (mu <= -4e+141) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	} else if (mu <= 1.02e+86) {
		tmp = (NaChar / (1.0 + Math.exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + Math.exp((((EDonor + Vef) - Ec) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef - mu) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if mu <= -4e+141:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	elif mu <= 1.02e+86:
		tmp = (NaChar / (1.0 + math.exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + math.exp((((EDonor + Vef) - Ec) / KbT))))
	else:
		tmp = (NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp(((Vef - mu) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (mu <= -4e+141)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))));
	elseif (mu <= 1.02e+86)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(EAccept + Float64(Ev + Vef)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(EDonor + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - mu) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (mu <= -4e+141)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	elseif (mu <= 1.02e+86)
		tmp = (NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	else
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp(((Vef - mu) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[mu, -4e+141], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / 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], If[LessEqual[mu, 1.02e+86], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(EDonor + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if mu < -4.00000000000000007e141

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around inf

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

      1. lower-/.f64 69.0

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

   4. Applied rewrites 69.0%

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

   if -4.00000000000000007e141 < mu < 1.01999999999999996e86

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-exp.f64 N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 84.7%

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

   if 1.01999999999999996e86 < mu

   1. Initial program 100.0%

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

   2. Taylor expanded in Vef around inf

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

      1. lower-/.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in EAccept around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 64.6

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

   7. Applied rewrites 64.6%

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

   8. Taylor expanded in Ev around 0

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

      1. lower--.f64 59.2

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

   10. Applied rewrites 59.2%

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

   11. Taylor expanded in EDonor around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 N/A

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

       3. lower-+.f64 76.2

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

   13. Applied rewrites 76.2%

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

Alternative 3: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\\ \mathbf{if}\;Ev \leq -5.7 \cdot 10^{+138}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
   (if (<= Ev -5.7e+138)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= Ev 2.6e-166)
       (+
        (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT))))
        (/ NaChar (+ 1.0 (exp (/ (- Vef mu) 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((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double tmp;
	if (Ev <= -5.7e+138) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Ev <= 2.6e-166) {
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp(((Vef - mu) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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((-(((ec - vef) - edonor) - mu) / kbt)))
    if (ev <= (-5.7d+138)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (ev <= 2.6d-166) then
        tmp = (ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))) + (nachar / (1.0d0 + exp(((vef - mu) / 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((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double tmp;
	if (Ev <= -5.7e+138) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Ev <= 2.6e-166) {
		tmp = (NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef - mu) / 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((-(((Ec - Vef) - EDonor) - mu) / KbT)))
	tmp = 0
	if Ev <= -5.7e+138:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Ev <= 2.6e-166:
		tmp = (NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp(((Vef - mu) / 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(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT))))
	tmp = 0.0
	if (Ev <= -5.7e+138)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Ev <= 2.6e-166)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - mu) / 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((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	tmp = 0.0;
	if (Ev <= -5.7e+138)
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Ev <= 2.6e-166)
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp(((Vef - mu) / 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[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -5.7e+138], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 2.6e-166], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - mu), $MachinePrecision] / KbT), $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 3 regimes

2. if Ev < -5.69999999999999986e138

   1. Initial program 100.0%

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

   2. Taylor expanded in Ev around inf

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

      1. lower-/.f64 69.0

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

   4. Applied rewrites 69.0%

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

   if -5.69999999999999986e138 < Ev < 2.59999999999999989e-166

   1. Initial program 100.0%

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

   2. Taylor expanded in Vef around inf

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

      1. lower-/.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in EAccept around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 64.6

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

   7. Applied rewrites 64.6%

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

   8. Taylor expanded in Ev around 0

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

      1. lower--.f64 59.2

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

   10. Applied rewrites 59.2%

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

   11. Taylor expanded in EDonor around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 N/A

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

       3. lower-+.f64 76.2

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

   13. Applied rewrites 76.2%

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

   if 2.59999999999999989e-166 < Ev

   1. Initial program 100.0%

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

   2. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 69.1

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

   4. Applied rewrites 69.1%

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

Alternative 4: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -3.5 \cdot 10^{+179}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ev \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -3.5e+179)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ EAccept (+ Ev Vef)) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
   (if (<= Ev 2.6e-166)
     (+
      (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT))))
      (/ NaChar (+ 1.0 (exp (/ (- Vef mu) KbT)))))
     (+
      (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
      (/ 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 tmp;
	if (Ev <= -3.5e+179) {
		tmp = (NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (Ev <= 2.6e-166) {
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp(((Vef - mu) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 <= (-3.5d+179)) then
        tmp = (nachar / (1.0d0 + exp(((eaccept + (ev + vef)) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (ev <= 2.6d-166) then
        tmp = (ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))) + (nachar / (1.0d0 + exp(((vef - mu) / kbt))))
    else
        tmp = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (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 tmp;
	if (Ev <= -3.5e+179) {
		tmp = (NaChar / (1.0 + Math.exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (Ev <= 2.6e-166) {
		tmp = (NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef - mu) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -3.5e+179:
		tmp = (NaChar / (1.0 + math.exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif Ev <= 2.6e-166:
		tmp = (NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp(((Vef - mu) / KbT))))
	else:
		tmp = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -3.5e+179)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(EAccept + Float64(Ev + Vef)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (Ev <= 2.6e-166)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - mu) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + 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)
	tmp = 0.0;
	if (Ev <= -3.5e+179)
		tmp = (NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (Ev <= 2.6e-166)
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp(((Vef - mu) / KbT))));
	else
		tmp = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -3.5e+179], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 2.6e-166], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -3.50000000000000015e179

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-exp.f64 N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 84.7%

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

   5. Taylor expanded in EDonor around inf

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

      1. lower-/.f64 63.6

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

   7. Applied rewrites 63.6%

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

   if -3.50000000000000015e179 < Ev < 2.59999999999999989e-166

   1. Initial program 100.0%

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

   2. Taylor expanded in Vef around inf

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

      1. lower-/.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in EAccept around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 64.6

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

   7. Applied rewrites 64.6%

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

   8. Taylor expanded in Ev around 0

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

      1. lower--.f64 59.2

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

   10. Applied rewrites 59.2%

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

   11. Taylor expanded in EDonor around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 N/A

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

       3. lower-+.f64 76.2

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

   13. Applied rewrites 76.2%

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

   if 2.59999999999999989e-166 < Ev

   1. Initial program 100.0%

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

   2. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 69.1

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

   4. Applied rewrites 69.1%

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

Alternative 5: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -3.5 \cdot 10^{+179}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ev \leq 4.8 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -3.5e+179)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ EAccept (+ Ev Vef)) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
   (if (<= Ev 4.8e-166)
     (+
      (/ NdChar (+ 1.0 (exp (/ (- (+ Vef mu) Ec) KbT))))
      (/ NaChar (+ 1.0 (exp (/ (- Vef mu) KbT)))))
     (+
      (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
      (/ NdChar (+ 1.0 (exp (/ (- (+ EDonor Vef) Ec) KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -3.5e+179) {
		tmp = (NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (Ev <= 4.8e-166) {
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp(((Vef - mu) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 <= (-3.5d+179)) then
        tmp = (nachar / (1.0d0 + exp(((eaccept + (ev + vef)) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (ev <= 4.8d-166) then
        tmp = (ndchar / (1.0d0 + exp((((vef + mu) - ec) / kbt)))) + (nachar / (1.0d0 + exp(((vef - mu) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / (1.0d0 + exp((((edonor + vef) - ec) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -3.5e+179) {
		tmp = (NaChar / (1.0 + Math.exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (Ev <= 4.8e-166) {
		tmp = (NdChar / (1.0 + Math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef - mu) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (1.0 + Math.exp((((EDonor + Vef) - Ec) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -3.5e+179:
		tmp = (NaChar / (1.0 + math.exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif Ev <= 4.8e-166:
		tmp = (NdChar / (1.0 + math.exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp(((Vef - mu) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (1.0 + math.exp((((EDonor + Vef) - Ec) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -3.5e+179)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(EAccept + Float64(Ev + Vef)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (Ev <= 4.8e-166)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + mu) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - mu) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(EDonor + Vef) - Ec) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -3.5e+179)
		tmp = (NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (Ev <= 4.8e-166)
		tmp = (NdChar / (1.0 + exp((((Vef + mu) - Ec) / KbT)))) + (NaChar / (1.0 + exp(((Vef - mu) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -3.5e+179], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 4.8e-166], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + mu), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(EDonor + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -3.50000000000000015e179

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-exp.f64 N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 84.7%

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

   5. Taylor expanded in EDonor around inf

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

      1. lower-/.f64 63.6

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

   7. Applied rewrites 63.6%

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

   if -3.50000000000000015e179 < Ev < 4.7999999999999997e-166

   1. Initial program 100.0%

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

   2. Taylor expanded in Vef around inf

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

      1. lower-/.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in EAccept around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 64.6

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

   7. Applied rewrites 64.6%

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

   8. Taylor expanded in Ev around 0

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

      1. lower--.f64 59.2

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

   10. Applied rewrites 59.2%

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

   11. Taylor expanded in EDonor around 0

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 N/A

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

       3. lower-+.f64 76.2

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

   13. Applied rewrites 76.2%

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

   if 4.7999999999999997e-166 < Ev

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-exp.f64 N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 84.7%

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

   5. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 64.0

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

   7. Applied rewrites 64.0%

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

Alternative 6: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.4 \cdot 10^{+16}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{\left(EAccept + Vef\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -5.5 \cdot 10^{-220}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.65 \cdot 10^{-28}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{\left(Ev + Vef\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT))))))
   (if (<= Vef -1.4e+16)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept Vef) mu) KbT)))))
     (if (<= Vef -5.5e-220)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))
       (if (<= Vef 1.65e-28)
         (+
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
          (/ NdChar (+ 1.0 (exp (/ (- (+ EDonor Vef) Ec) KbT)))))
         (+ t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ Ev Vef) mu) KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((Vef / KbT)));
	double tmp;
	if (Vef <= -1.4e+16) {
		tmp = t_0 + (NaChar / (1.0 + exp((((EAccept + Vef) - mu) / KbT))));
	} else if (Vef <= -5.5e-220) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else if (Vef <= 1.65e-28) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((((Ev + Vef) - mu) / KbT))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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((vef / kbt)))
    if (vef <= (-1.4d+16)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((((eaccept + vef) - mu) / kbt))))
    else if (vef <= (-5.5d-220)) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    else if (vef <= 1.65d-28) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / (1.0d0 + exp((((edonor + vef) - ec) / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((((ev + vef) - mu) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((Vef / KbT)));
	double tmp;
	if (Vef <= -1.4e+16) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((((EAccept + Vef) - mu) / KbT))));
	} else if (Vef <= -5.5e-220) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else if (Vef <= 1.65e-28) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (1.0 + Math.exp((((EDonor + Vef) - Ec) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((((Ev + Vef) - mu) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((Vef / KbT)))
	tmp = 0
	if Vef <= -1.4e+16:
		tmp = t_0 + (NaChar / (1.0 + math.exp((((EAccept + Vef) - mu) / KbT))))
	elif Vef <= -5.5e-220:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	elif Vef <= 1.65e-28:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (1.0 + math.exp((((EDonor + Vef) - Ec) / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((((Ev + Vef) - mu) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	tmp = 0.0
	if (Vef <= -1.4e+16)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Vef) - mu) / KbT)))));
	elseif (Vef <= -5.5e-220)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	elseif (Vef <= 1.65e-28)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(EDonor + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Ev + Vef) - mu) / 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((Vef / KbT)));
	tmp = 0.0;
	if (Vef <= -1.4e+16)
		tmp = t_0 + (NaChar / (1.0 + exp((((EAccept + Vef) - mu) / KbT))));
	elseif (Vef <= -5.5e-220)
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	elseif (Vef <= 1.65e-28)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((((Ev + Vef) - mu) / 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[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -1.4e+16], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + Vef), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, -5.5e-220], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.65e-28], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(EDonor + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Ev + Vef), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -1.4e16

   1. Initial program 100.0%

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

   2. Taylor expanded in Vef around inf

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

      1. lower-/.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in Ev around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 64.3

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

   7. Applied rewrites 64.3%

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

   if -1.4e16 < Vef < -5.4999999999999999e-220

   1. Initial program 100.0%

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

   2. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 60.0

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

   4. Applied rewrites 60.0%

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

   if -5.4999999999999999e-220 < Vef < 1.6500000000000001e-28

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-exp.f64 N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 84.7%

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

   5. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 64.0

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

   7. Applied rewrites 64.0%

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

   if 1.6500000000000001e-28 < Vef

   1. Initial program 100.0%

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

   2. Taylor expanded in Vef around inf

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

      1. lower-/.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in EAccept around 0

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

      1. lower-exp.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 64.6

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

   7. Applied rewrites 64.6%

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

Alternative 7: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-124}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 10^{-59}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
          (/ NdChar (+ 1.0 (exp (/ (- (+ EDonor Vef) Ec) KbT))))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -2e-124)
     t_0
     (if (<= t_1 1e-59)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	double t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -2e-124) {
		tmp = t_0;
	} else if (t_1 <= 1e-59) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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((eaccept / kbt)))) + (ndchar / (1.0d0 + exp((((edonor + vef) - ec) / kbt))))
    t_1 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (t_1 <= (-2d-124)) then
        tmp = t_0
    else if (t_1 <= 1d-59) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (1.0 + Math.exp((((EDonor + Vef) - Ec) / KbT))));
	double t_1 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -2e-124) {
		tmp = t_0;
	} else if (t_1 <= 1e-59) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (1.0 + math.exp((((EDonor + Vef) - Ec) / KbT))))
	t_1 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if t_1 <= -2e-124:
		tmp = t_0
	elif t_1 <= 1e-59:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(EDonor + Vef) - Ec) / KbT)))))
	t_1 = 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)))))
	tmp = 0.0
	if (t_1 <= -2e-124)
		tmp = t_0;
	elseif (t_1 <= 1e-59)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - 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 = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (t_1 <= -2e-124)
		tmp = t_0;
	elseif (t_1 <= 1e-59)
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(EDonor + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -2e-124], t$95$0, If[LessEqual[t$95$1, 1e-59], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999987e-124 or 1e-59 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-exp.f64 N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 84.7%

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

   5. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 64.0

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

   7. Applied rewrites 64.0%

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

   if -1.99999999999999987e-124 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 1e-59

   1. Initial program 100.0%

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

   2. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 60.0

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

   4. Applied rewrites 60.0%

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

Alternative 8: 67.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(Ec - Vef\right) - EDonor\\ t_1 := \mathsf{fma}\left(0.5, NaChar, \frac{NdChar}{e^{\frac{mu - t\_0}{KbT}} - -1}\right)\\ t_2 := \frac{NdChar}{1 + e^{\frac{-\left(t\_0 - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 50000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (- (- Ec Vef) EDonor))
        (t_1 (fma 0.5 NaChar (/ NdChar (- (exp (/ (- mu t_0) KbT)) -1.0))))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- t_0 mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_2 -5e+62)
     t_1
     (if (<= t_2 50000.0)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) 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 = (Ec - Vef) - EDonor;
	double t_1 = fma(0.5, NaChar, (NdChar / (exp(((mu - t_0) / KbT)) - -1.0)));
	double t_2 = (NdChar / (1.0 + exp((-(t_0 - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_2 <= -5e+62) {
		tmp = t_1;
	} else if (t_2 <= 50000.0) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(Ec - Vef) - EDonor)
	t_1 = fma(0.5, NaChar, Float64(NdChar / Float64(exp(Float64(Float64(mu - t_0) / KbT)) - -1.0)))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(t_0 - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
	tmp = 0.0
	if (t_2 <= -5e+62)
		tmp = t_1;
	elseif (t_2 <= 50000.0)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision]}, Block[{t$95$1 = N[(0.5 * NaChar + N[(NdChar / N[(N[Exp[N[(N[(mu - t$95$0), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(t$95$0 - 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]}, If[LessEqual[t$95$2, -5e+62], t$95$1, If[LessEqual[t$95$2, 50000.0], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -5.00000000000000029e62 or 5e4 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

      1. lift-exp.f64 N/A

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

      2. exp-fabs N/A

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

      3. lift-exp.f64 N/A

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

      4. rem-sqrt-square-rev N/A

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

      5. sqr-neg-rev N/A

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

      6. lower-*.f32 N/A

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

      7. lower-unsound-*.f32 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-unsound-*.f32 N/A

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

      10. lower-*.f32 N/A

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

      11. sqr-neg-rev N/A

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

   3. Applied rewrites 100.0%

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in KbT around inf

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

   8. Applied rewrites 46.9%

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

   if -5.00000000000000029e62 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 5e4

   1. Initial program 100.0%

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

   2. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 60.0

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

   4. Applied rewrites 60.0%

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

Alternative 9: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{\left(EDonor + Vef\right) - Ec}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 50000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar 2.0)
          (/ NdChar (+ 1.0 (exp (/ (- (+ EDonor Vef) Ec) KbT))))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e+62)
     t_0
     (if (<= t_1 50000.0)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / 2.0) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	double t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -5e+62) {
		tmp = t_0;
	} else if (t_1 <= 50000.0) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 / 2.0d0) + (ndchar / (1.0d0 + exp((((edonor + vef) - ec) / kbt))))
    t_1 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (t_1 <= (-5d+62)) then
        tmp = t_0
    else if (t_1 <= 50000.0d0) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / 2.0) + (NdChar / (1.0 + Math.exp((((EDonor + Vef) - Ec) / KbT))));
	double t_1 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -5e+62) {
		tmp = t_0;
	} else if (t_1 <= 50000.0) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / 2.0) + (NdChar / (1.0 + math.exp((((EDonor + Vef) - Ec) / KbT))))
	t_1 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if t_1 <= -5e+62:
		tmp = t_0
	elif t_1 <= 50000.0:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(EDonor + Vef) - Ec) / KbT)))))
	t_1 = 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)))))
	tmp = 0.0
	if (t_1 <= -5e+62)
		tmp = t_0;
	elseif (t_1 <= 50000.0)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - 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 = (NaChar / 2.0) + (NdChar / (1.0 + exp((((EDonor + Vef) - Ec) / KbT))));
	t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (t_1 <= -5e+62)
		tmp = t_0;
	elseif (t_1 <= 50000.0)
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(EDonor + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -5e+62], t$95$0, If[LessEqual[t$95$1, 50000.0], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -5.00000000000000029e62 or 5e4 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-exp.f64 N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 84.7%

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

   5. Taylor expanded in KbT around inf

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

   7. Applied rewrites 43.7%

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

   if -5.00000000000000029e62 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 5e4

   1. Initial program 100.0%

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

   2. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 60.0

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

   4. Applied rewrites 60.0%

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

Alternative 10: 61.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.05 \cdot 10^{+196}:\\ \;\;\;\;\left(NaChar + NdChar\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.05e+196)
   (* (+ NaChar NdChar) 0.5)
   (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.05e+196) {
		tmp = (NaChar + NdChar) * 0.5;
	} else {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-1.05d+196)) then
        tmp = (nachar + ndchar) * 0.5d0
    else
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.05e+196) {
		tmp = (NaChar + NdChar) * 0.5;
	} else {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -1.05e+196:
		tmp = (NaChar + NdChar) * 0.5
	else:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -1.05e+196)
		tmp = Float64(Float64(NaChar + NdChar) * 0.5);
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -1.05e+196)
		tmp = (NaChar + NdChar) * 0.5;
	else
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -1.05e+196], N[(N[(NaChar + NdChar), $MachinePrecision] * 0.5), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -1.05000000000000007e196

   1. Initial program 100.0%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 27.3

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 27.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot \color{blue}{NdChar} \]

      3. distribute-lft-out N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NaChar + NdChar\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(NaChar + NdChar\right) \cdot \color{blue}{\frac{1}{2}} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(NaChar + NdChar\right) \cdot \color{blue}{\frac{1}{2}} \]

      6. lower-+.f64 27.3

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

   6. Applied rewrites 27.3%

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

   if -1.05000000000000007e196 < KbT

   1. Initial program 100.0%

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

   2. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 60.0

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

   4. Applied rewrites 60.0%

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

Alternative 11: 55.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -9.1 \cdot 10^{+195}:\\ \;\;\;\;\left(NaChar + NdChar\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept + \left(Ev + Vef\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -9.1e+195)
   (* (+ NaChar NdChar) 0.5)
   (/ NaChar (+ 1.0 (exp (/ (+ EAccept (+ Ev Vef)) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -9.1e+195) {
		tmp = (NaChar + NdChar) * 0.5;
	} else {
		tmp = NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 <= (-9.1d+195)) then
        tmp = (nachar + ndchar) * 0.5d0
    else
        tmp = nachar / (1.0d0 + exp(((eaccept + (ev + vef)) / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -9.1e+195) {
		tmp = (NaChar + NdChar) * 0.5;
	} else {
		tmp = NaChar / (1.0 + Math.exp(((EAccept + (Ev + Vef)) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -9.1e+195:
		tmp = (NaChar + NdChar) * 0.5
	else:
		tmp = NaChar / (1.0 + math.exp(((EAccept + (Ev + Vef)) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -9.1e+195)
		tmp = Float64(Float64(NaChar + NdChar) * 0.5);
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(EAccept + Float64(Ev + Vef)) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -9.1e+195)
		tmp = (NaChar + NdChar) * 0.5;
	else
		tmp = NaChar / (1.0 + exp(((EAccept + (Ev + Vef)) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -9.1e+195], N[(N[(NaChar + NdChar), $MachinePrecision] * 0.5), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -9.0999999999999998e195

   1. Initial program 100.0%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 27.3

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 27.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot \color{blue}{NdChar} \]

      3. distribute-lft-out N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NaChar + NdChar\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(NaChar + NdChar\right) \cdot \color{blue}{\frac{1}{2}} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(NaChar + NdChar\right) \cdot \color{blue}{\frac{1}{2}} \]

      6. lower-+.f64 27.3

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

   6. Applied rewrites 27.3%

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

   if -9.0999999999999998e195 < KbT

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-exp.f64 N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 84.7%

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

   5. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 53.8

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

   7. Applied rewrites 53.8%

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

Alternative 12: 29.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(NaChar + NdChar\right) \cdot 0.5\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-179}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-231}:\\ \;\;\;\;-0.25 \cdot \frac{EAccept \cdot NaChar}{KbT}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* (+ NaChar NdChar) 0.5))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e-179)
     t_0
     (if (<= t_1 5e-231) (* -0.25 (/ (* EAccept NaChar) 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 + NdChar) * 0.5;
	double t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -5e-179) {
		tmp = t_0;
	} else if (t_1 <= 5e-231) {
		tmp = -0.25 * ((EAccept * NaChar) / KbT);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 + ndchar) * 0.5d0
    t_1 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (t_1 <= (-5d-179)) then
        tmp = t_0
    else if (t_1 <= 5d-231) then
        tmp = (-0.25d0) * ((eaccept * nachar) / kbt)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar + NdChar) * 0.5;
	double t_1 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_1 <= -5e-179) {
		tmp = t_0;
	} else if (t_1 <= 5e-231) {
		tmp = -0.25 * ((EAccept * NaChar) / KbT);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar + NdChar) * 0.5
	t_1 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if t_1 <= -5e-179:
		tmp = t_0
	elif t_1 <= 5e-231:
		tmp = -0.25 * ((EAccept * NaChar) / KbT)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar + NdChar) * 0.5)
	t_1 = 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)))))
	tmp = 0.0
	if (t_1 <= -5e-179)
		tmp = t_0;
	elseif (t_1 <= 5e-231)
		tmp = Float64(-0.25 * Float64(Float64(EAccept * NaChar) / KbT));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar + NdChar) * 0.5;
	t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (t_1 <= -5e-179)
		tmp = t_0;
	elseif (t_1 <= 5e-231)
		tmp = -0.25 * ((EAccept * NaChar) / KbT);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar + NdChar), $MachinePrecision] * 0.5), $MachinePrecision]}, Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -5e-179], t$95$0, If[LessEqual[t$95$1, 5e-231], N[(-0.25 * N[(N[(EAccept * NaChar), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -4.9999999999999998e-179 or 5.00000000000000023e-231 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 27.3

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 27.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot \color{blue}{NdChar} \]

      3. distribute-lft-out N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NaChar + NdChar\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(NaChar + NdChar\right) \cdot \color{blue}{\frac{1}{2}} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(NaChar + NdChar\right) \cdot \color{blue}{\frac{1}{2}} \]

      6. lower-+.f64 27.3

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

   6. Applied rewrites 27.3%

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

   if -4.9999999999999998e-179 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 5.00000000000000023e-231

   1. Initial program 100.0%

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

   2. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{1}{4} \cdot \left(NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)\right) + \frac{1}{4} \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)}{KbT} + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-1, \color{blue}{\frac{\frac{1}{4} \cdot \left(NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)\right) + \frac{1}{4} \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)}{KbT}}, \frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \]

   4. Applied rewrites 14.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{\mathsf{fma}\left(0.25, NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right), 0.25 \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)\right)}{KbT}, \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\right)} \]

   5. Taylor expanded in EAccept around inf

      \[\leadsto \frac{-1}{4} \cdot \color{blue}{\frac{EAccept \cdot NaChar}{KbT}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{4} \cdot \frac{EAccept \cdot NaChar}{\color{blue}{KbT}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{-1}{4} \cdot \frac{EAccept \cdot NaChar}{KbT} \]

      3. lower-*.f64 5.9

         \[\leadsto -0.25 \cdot \frac{EAccept \cdot NaChar}{KbT} \]

   7. Applied rewrites 5.9%

      \[\leadsto -0.25 \cdot \color{blue}{\frac{EAccept \cdot NaChar}{KbT}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 27.3% accurate, 9.1× speedup

Math

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

FPCore

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 + 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 + NdChar) * 0.5;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in KbT around inf

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

   1. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

   2. lower-*.f64 27.3

      \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

4. Applied rewrites 27.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)} \]
5. Step-by-step derivation

   1. lift-fma.f64 N/A

      \[\leadsto \frac{1}{2} \cdot NaChar + \color{blue}{\frac{1}{2} \cdot NdChar} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot \color{blue}{NdChar} \]

   3. distribute-lft-out N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(NaChar + NdChar\right)} \]

   4. *-commutative N/A

      \[\leadsto \left(NaChar + NdChar\right) \cdot \color{blue}{\frac{1}{2}} \]

   5. lower-*.f64 N/A

      \[\leadsto \left(NaChar + NdChar\right) \cdot \color{blue}{\frac{1}{2}} \]

   6. lower-+.f64 27.3

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

6. Applied rewrites 27.3%

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

Alternative 14: 22.4% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.55 \cdot 10^{+90}:\\ \;\;\;\;0.5 \cdot NaChar\\ \mathbf{elif}\;NaChar \leq 5.8 \cdot 10^{+130}:\\ \;\;\;\;NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NaChar\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -1.55e+90)
   (* 0.5 NaChar)
   (if (<= NaChar 5.8e+130) (* NdChar 0.5) (* 0.5 NaChar))))

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 <= -1.55e+90) {
		tmp = 0.5 * NaChar;
	} else if (NaChar <= 5.8e+130) {
		tmp = NdChar * 0.5;
	} else {
		tmp = 0.5 * NaChar;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 <= (-1.55d+90)) then
        tmp = 0.5d0 * nachar
    else if (nachar <= 5.8d+130) then
        tmp = ndchar * 0.5d0
    else
        tmp = 0.5d0 * nachar
    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 <= -1.55e+90) {
		tmp = 0.5 * NaChar;
	} else if (NaChar <= 5.8e+130) {
		tmp = NdChar * 0.5;
	} else {
		tmp = 0.5 * NaChar;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -1.55e+90:
		tmp = 0.5 * NaChar
	elif NaChar <= 5.8e+130:
		tmp = NdChar * 0.5
	else:
		tmp = 0.5 * NaChar
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -1.55e+90)
		tmp = Float64(0.5 * NaChar);
	elseif (NaChar <= 5.8e+130)
		tmp = Float64(NdChar * 0.5);
	else
		tmp = Float64(0.5 * NaChar);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -1.55e+90)
		tmp = 0.5 * NaChar;
	elseif (NaChar <= 5.8e+130)
		tmp = NdChar * 0.5;
	else
		tmp = 0.5 * NaChar;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -1.55e+90], N[(0.5 * NaChar), $MachinePrecision], If[LessEqual[NaChar, 5.8e+130], N[(NdChar * 0.5), $MachinePrecision], N[(0.5 * NaChar), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.54999999999999994e90 or 5.7999999999999998e130 < NaChar

   1. Initial program 100.0%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 27.3

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 27.3%

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

   5. Taylor expanded in NdChar around 0

      \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
   6. Step-by-step derivation

      1. lower-*.f64 18.1

         \[\leadsto 0.5 \cdot NaChar \]

   7. Applied rewrites 18.1%

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

   if -1.54999999999999994e90 < NaChar < 5.7999999999999998e130

   1. Initial program 100.0%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

      2. lower-*.f64 27.3

         \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

   4. Applied rewrites 27.3%

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

   5. Taylor expanded in NdChar around inf

      \[\leadsto NdChar \cdot \color{blue}{\left(\frac{1}{2} + \frac{1}{2} \cdot \frac{NaChar}{NdChar}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto NdChar \cdot \left(\frac{1}{2} + \color{blue}{\frac{1}{2} \cdot \frac{NaChar}{NdChar}}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto NdChar \cdot \left(\frac{1}{2} + \frac{1}{2} \cdot \color{blue}{\frac{NaChar}{NdChar}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto NdChar \cdot \left(\frac{1}{2} + \frac{1}{2} \cdot \frac{NaChar}{\color{blue}{NdChar}}\right) \]

      4. lower-/.f64 24.4

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

   7. Applied rewrites 24.4%

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

   8. Taylor expanded in NdChar around inf

      \[\leadsto NdChar \cdot \frac{1}{2} \]
   9. Step-by-step derivation

   10. Applied rewrites 18.1%

       \[\leadsto NdChar \cdot 0.5 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 18.1% accurate, 15.4× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in KbT around inf

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

   1. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{1}{2}, \color{blue}{NaChar}, \frac{1}{2} \cdot NdChar\right) \]

   2. lower-*.f64 27.3

      \[\leadsto \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right) \]

4. Applied rewrites 27.3%

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

5. Taylor expanded in NdChar around 0

   \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
6. Step-by-step derivation

   1. lower-*.f64 18.1

      \[\leadsto 0.5 \cdot NaChar \]

7. Applied rewrites 18.1%

   \[\leadsto 0.5 \cdot \color{blue}{NaChar} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025155 
(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))))))