Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 8.3s

Alternatives: 24

Speedup: 1.0×

• could not determine a ground truth

  1. branch1493237 = 1.2084571175267688e+34
  2. NdChar = 2.0870920648700066e+34
  3. Ec = 7.551889930643854e-34
  4. Vef = -6.545147988815178e+176
  5. EDonor = -2.261227403386953e-180
  6. mu = -1.1774597643415433e-226
  7. KbT = 2.204265649973482e+133
  8. NaChar = 1.709249591914431e+227
  9. Ev = -2.136976473617935e-166
  10. EAccept = 1.2672439273885877e+169

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

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

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]

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. Add Preprocessing

Alternative 2: 41.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-305}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
        (t_2 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
   (if (<= t_1 -5e+15)
     t_0
     (if (<= t_1 -1e-305)
       t_2
       (if (<= t_1 0.0)
         (/
          NaChar
          (-
           (+
            2.0
            (/
             (/
              (- (* EAccept EAccept) (* (+ Ev Vef) (+ Ev Vef)))
              (- EAccept (+ Ev Vef)))
             KbT))
           (/ mu KbT)))
         (if (<= t_1 5e-26) t_2 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 = fma(0.5, NaChar, (0.5 * NdChar));
	double t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double t_2 = NaChar / (1.0 + exp((EAccept / KbT)));
	double tmp;
	if (t_1 <= -5e+15) {
		tmp = t_0;
	} else if (t_1 <= -1e-305) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = NaChar / ((2.0 + ((((EAccept * EAccept) - ((Ev + Vef) * (Ev + Vef))) / (EAccept - (Ev + Vef))) / KbT)) - (mu / KbT));
	} else if (t_1 <= 5e-26) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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)))))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))))
	tmp = 0.0
	if (t_1 <= -5e+15)
		tmp = t_0;
	elseif (t_1 <= -1e-305)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(Float64(Float64(EAccept * EAccept) - Float64(Float64(Ev + Vef) * Float64(Ev + Vef))) / Float64(EAccept - Float64(Ev + Vef))) / KbT)) - Float64(mu / KbT)));
	elseif (t_1 <= 5e-26)
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+15], t$95$0, If[LessEqual[t$95$1, -1e-305], t$95$2, If[LessEqual[t$95$1, 0.0], N[(NaChar / N[(N[(2.0 + N[(N[(N[(N[(EAccept * EAccept), $MachinePrecision] - N[(N[(Ev + Vef), $MachinePrecision] * N[(Ev + Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(EAccept - N[(Ev + Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-26], t$95$2, t$95$0]]]]]]]

Derivation

1. Split input into 3 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))))) < -5e15 or 5.00000000000000019e-26 < (+.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 39.5

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

   4. Applied rewrites 39.5%

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

   if -5e15 < (+.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))))) < -9.99999999999999996e-306 or -0.0 < (+.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))))) < 5.00000000000000019e-26

   1. Initial program 100.0%

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

   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. lift-+.f64 50.7

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

   4. Applied rewrites 50.7%

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

   5. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   6. Step-by-step derivation

   7. Applied rewrites 31.8%

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

   if -9.99999999999999996e-306 < (+.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))))) < -0.0

   1. Initial program 99.9%

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

   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. lift-+.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 52.7

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

   7. Applied rewrites 52.7%

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

      1. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. flip-+ N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      11. lift-+.f64 66.2

          \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

   9. Applied rewrites 66.2%

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

Alternative 3: 82.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t\_1\\ t_3 := t\_0 + t\_1\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-283}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{-308}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

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)))))
        (t_1
         (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
        (t_2 (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_1))
        (t_3 (+ t_0 t_1)))
   (if (<= t_3 -1e-283)
     t_2
     (if (<= t_3 1e-308)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))
       (if (<= t_3 5e+257) t_2 (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	double t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	double t_3 = t_0 + t_1;
	double tmp;
	if (t_3 <= -1e-283) {
		tmp = t_2;
	} else if (t_3 <= 1e-308) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else if (t_3 <= 5e+257) {
		tmp = t_2;
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))
    t_1 = nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt)))
    t_2 = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_1
    t_3 = t_0 + t_1
    if (t_3 <= (-1d-283)) then
        tmp = t_2
    else if (t_3 <= 1d-308) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    else if (t_3 <= 5d+257) then
        tmp = t_2
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	double t_2 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_1;
	double t_3 = t_0 + t_1;
	double tmp;
	if (t_3 <= -1e-283) {
		tmp = t_2;
	} else if (t_3 <= 1e-308) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else if (t_3 <= 5e+257) {
		tmp = t_2;
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / 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)))
	t_1 = NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT)))
	t_2 = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_1
	t_3 = t_0 + t_1
	tmp = 0
	if t_3 <= -1e-283:
		tmp = t_2
	elif t_3 <= 1e-308:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)))
	elif t_3 <= 5e+257:
		tmp = t_2
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / 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))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_1)
	t_3 = Float64(t_0 + t_1)
	tmp = 0.0
	if (t_3 <= -1e-283)
		tmp = t_2;
	elseif (t_3 <= 1e-308)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	elseif (t_3 <= 5e+257)
		tmp = t_2;
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	t_1 = NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + t_1;
	t_3 = t_0 + t_1;
	tmp = 0.0;
	if (t_3 <= -1e-283)
		tmp = t_2;
	elseif (t_3 <= 1e-308)
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	elseif (t_3 <= 5e+257)
		tmp = t_2;
	else
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / 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]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-283], t$95$2, If[LessEqual[t$95$3, 1e-308], 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[t$95$3, 5e+257], t$95$2, N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 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))))) < -9.99999999999999947e-284 or 9.9999999999999991e-309 < (+.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))))) < 5.00000000000000028e257

   1. Initial program 100.0%

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

   2. Taylor expanded in mu around inf

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

   4. Applied rewrites 78.5%

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

   if -9.99999999999999947e-284 < (+.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))))) < 9.9999999999999991e-309

   1. Initial program 99.9%

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

   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. lift-+.f64 97.9

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

   4. Applied rewrites 97.9%

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

   if 5.00000000000000028e257 < (+.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 99.9%

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

   2. Taylor expanded in Ev around inf

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

   4. Applied rewrites 82.3%

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

Alternative 4: 82.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t\_0\\ t_2 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + t\_0\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-308}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
        (t_1 (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_0))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          t_0)))
   (if (<= t_2 -1e-283)
     t_1
     (if (<= t_2 1e-308)
       (/ 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 = NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	double t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + t_0;
	double t_2 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + t_0;
	double tmp;
	if (t_2 <= -1e-283) {
		tmp = t_1;
	} else if (t_2 <= 1e-308) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_0
    t_2 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + t_0
    if (t_2 <= (-1d-283)) then
        tmp = t_1
    else if (t_2 <= 1d-308) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_0;
	double t_2 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + t_0;
	double tmp;
	if (t_2 <= -1e-283) {
		tmp = t_1;
	} else if (t_2 <= 1e-308) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_0
	t_2 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + t_0
	tmp = 0
	if t_2 <= -1e-283:
		tmp = t_1
	elif t_2 <= 1e-308:
		tmp = NaChar / (1.0 + math.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(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_0)
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + t_0)
	tmp = 0.0
	if (t_2 <= -1e-283)
		tmp = t_1;
	elseif (t_2 <= 1e-308)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT)));
	t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + t_0;
	t_2 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + t_0;
	tmp = 0.0;
	if (t_2 <= -1e-283)
		tmp = t_1;
	elseif (t_2 <= 1e-308)
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-283], t$95$1, If[LessEqual[t$95$2, 1e-308], 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))))) < -9.99999999999999947e-284 or 9.9999999999999991e-309 < (+.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 inf

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

   4. Applied rewrites 78.8%

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

   if -9.99999999999999947e-284 < (+.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))))) < 9.9999999999999991e-309

   1. Initial program 99.9%

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

   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. lift-+.f64 97.9

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

   4. Applied rewrites 97.9%

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

Alternative 5: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+15}:\\ \;\;\;\;0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-26}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

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))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_0 -5e+15)
     (+ (* 0.5 NdChar) (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
     (if (<= t_0 5e-26)
       (/ NaChar (+ 1.0 (exp (/ (- Vef mu) KbT))))
       (+ (* 0.5 NdChar) (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_0 <= -5e+15) {
		tmp = (0.5 * NdChar) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (t_0 <= 5e-26) {
		tmp = NaChar / (1.0 + exp(((Vef - mu) / KbT)));
	} else {
		tmp = (0.5 * NdChar) + (NaChar / (1.0 + exp((Ev / 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)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
    if (t_0 <= (-5d+15)) then
        tmp = (0.5d0 * ndchar) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (t_0 <= 5d-26) then
        tmp = nachar / (1.0d0 + exp(((vef - mu) / kbt)))
    else
        tmp = (0.5d0 * ndchar) + (nachar / (1.0d0 + exp((ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	double tmp;
	if (t_0 <= -5e+15) {
		tmp = (0.5 * NdChar) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (t_0 <= 5e-26) {
		tmp = NaChar / (1.0 + Math.exp(((Vef - mu) / KbT)));
	} else {
		tmp = (0.5 * NdChar) + (NaChar / (1.0 + Math.exp((Ev / 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)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
	tmp = 0
	if t_0 <= -5e+15:
		tmp = (0.5 * NdChar) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif t_0 <= 5e-26:
		tmp = NaChar / (1.0 + math.exp(((Vef - mu) / KbT)))
	else:
		tmp = (0.5 * NdChar) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(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_0 <= -5e+15)
		tmp = Float64(Float64(0.5 * NdChar) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (t_0 <= 5e-26)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - mu) / KbT))));
	else
		tmp = Float64(Float64(0.5 * NdChar) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
	tmp = 0.0;
	if (t_0 <= -5e+15)
		tmp = (0.5 * NdChar) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (t_0 <= 5e-26)
		tmp = NaChar / (1.0 + exp(((Vef - mu) / KbT)));
	else
		tmp = (0.5 * NdChar) + (NaChar / (1.0 + exp((Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[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$0, -5e+15], N[(N[(0.5 * NdChar), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-26], N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * NdChar), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.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))))) < -5e15

   1. Initial program 100.0%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-*.f64 64.6

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

   4. Applied rewrites 64.6%

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

   5. Taylor expanded in EAccept around inf

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

   7. Applied rewrites 49.9%

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

   if -5e15 < (+.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))))) < 5.00000000000000019e-26

   1. Initial program 100.0%

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

   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. lift-+.f64 68.4

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

   4. Applied rewrites 68.4%

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

   5. Taylor expanded in Vef around inf

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

   7. Applied rewrites 51.6%

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

   if 5.00000000000000019e-26 < (+.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

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

      1. lower-*.f64 64.9

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

   4. Applied rewrites 64.9%

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

   5. Taylor expanded in Ev around inf

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

   7. Applied rewrites 49.8%

      \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{\color{blue}{Ev}}{KbT}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+227}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ (* 0.5 NdChar) (/ NaChar (+ 1.0 (exp (/ EAccept 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+15)
     t_0
     (if (<= t_1 2e+227) (/ NaChar (+ 1.0 (exp (/ (- 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 = (0.5 * NdChar) + (NaChar / (1.0 + exp((EAccept / 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+15) {
		tmp = t_0;
	} else if (t_1 <= 2e+227) {
		tmp = NaChar / (1.0 + exp(((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 = (0.5d0 * ndchar) + (nachar / (1.0d0 + exp((eaccept / 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+15)) then
        tmp = t_0
    else if (t_1 <= 2d+227) then
        tmp = nachar / (1.0d0 + exp(((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 = (0.5 * NdChar) + (NaChar / (1.0 + Math.exp((EAccept / 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+15) {
		tmp = t_0;
	} else if (t_1 <= 2e+227) {
		tmp = NaChar / (1.0 + Math.exp(((Vef - mu) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (0.5 * NdChar) + (NaChar / (1.0 + math.exp((EAccept / 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+15:
		tmp = t_0
	elif t_1 <= 2e+227:
		tmp = NaChar / (1.0 + math.exp(((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(0.5 * NdChar) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / 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+15)
		tmp = t_0;
	elseif (t_1 <= 2e+227)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(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 = (0.5 * NdChar) + (NaChar / (1.0 + exp((EAccept / 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+15)
		tmp = t_0;
	elseif (t_1 <= 2e+227)
		tmp = NaChar / (1.0 + exp(((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[(0.5 * NdChar), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / 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+15], t$95$0, If[LessEqual[t$95$1, 2e+227], N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - 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))))) < -5e15 or 2.0000000000000002e227 < (+.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

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

      1. lower-*.f64 66.0

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

   4. Applied rewrites 66.0%

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

   5. Taylor expanded in EAccept around inf

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

   7. Applied rewrites 50.4%

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

   if -5e15 < (+.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))))) < 2.0000000000000002e227

   1. Initial program 100.0%

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

   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. lift-+.f64 63.4

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

   4. Applied rewrites 63.4%

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

   5. Taylor expanded in Vef around inf

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

   7. Applied rewrites 48.7%

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

Alternative 7: 39.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-267}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e-207)
     t_0
     (if (<= t_1 2e-267)
       (/
        NaChar
        (-
         (+
          2.0
          (/
           (/
            (- (* EAccept EAccept) (* (+ Ev Vef) (+ Ev Vef)))
            (- EAccept (+ Ev Vef)))
           KbT))
         (/ mu KbT)))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = fma(0.5, NaChar, (0.5 * NdChar));
	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-207) {
		tmp = t_0;
	} else if (t_1 <= 2e-267) {
		tmp = NaChar / ((2.0 + ((((EAccept * EAccept) - ((Ev + Vef) * (Ev + Vef))) / (EAccept - (Ev + Vef))) / KbT)) - (mu / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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-207)
		tmp = t_0;
	elseif (t_1 <= 2e-267)
		tmp = Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(Float64(Float64(EAccept * EAccept) - Float64(Float64(Ev + Vef) * Float64(Ev + Vef))) / Float64(EAccept - Float64(Ev + Vef))) / KbT)) - Float64(mu / KbT)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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-207], t$95$0, If[LessEqual[t$95$1, 2e-267], N[(NaChar / N[(N[(2.0 + N[(N[(N[(N[(EAccept * EAccept), $MachinePrecision] - N[(N[(Ev + Vef), $MachinePrecision] * N[(Ev + Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(EAccept - N[(Ev + Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $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))))) < -5.00000000000000014e-207 or 2e-267 < (+.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 35.2

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

   4. Applied rewrites 35.2%

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

   if -5.00000000000000014e-207 < (+.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))))) < 2e-267

   1. Initial program 99.9%

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

   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. lift-+.f64 87.9

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 42.6

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

   7. Applied rewrites 42.6%

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

      1. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. flip-+ N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lower--.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

      11. lift-+.f64 52.5

          \[\leadsto \frac{NaChar}{\left(2 + \frac{\frac{EAccept \cdot EAccept - \left(Ev + Vef\right) \cdot \left(Ev + Vef\right)}{EAccept - \left(Ev + Vef\right)}}{KbT}\right) - \frac{mu}{KbT}} \]

   9. Applied rewrites 52.5%

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

Alternative 8: 39.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-267}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \frac{EAccept + \frac{Ev \cdot Ev - Vef \cdot Vef}{Ev - Vef}}{KbT}\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e-207)
     t_0
     (if (<= t_1 2e-267)
       (/
        NaChar
        (-
         (+ 2.0 (/ (+ EAccept (/ (- (* Ev Ev) (* Vef Vef)) (- Ev Vef))) KbT))
         (/ mu KbT)))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = fma(0.5, NaChar, (0.5 * NdChar));
	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-207) {
		tmp = t_0;
	} else if (t_1 <= 2e-267) {
		tmp = NaChar / ((2.0 + ((EAccept + (((Ev * Ev) - (Vef * Vef)) / (Ev - Vef))) / KbT)) - (mu / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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-207)
		tmp = t_0;
	elseif (t_1 <= 2e-267)
		tmp = Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept + Float64(Float64(Float64(Ev * Ev) - Float64(Vef * Vef)) / Float64(Ev - Vef))) / KbT)) - Float64(mu / KbT)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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-207], t$95$0, If[LessEqual[t$95$1, 2e-267], N[(NaChar / N[(N[(2.0 + N[(N[(EAccept + N[(N[(N[(Ev * Ev), $MachinePrecision] - N[(Vef * Vef), $MachinePrecision]), $MachinePrecision] / N[(Ev - Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $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))))) < -5.00000000000000014e-207 or 2e-267 < (+.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 35.2

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

   4. Applied rewrites 35.2%

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

   if -5.00000000000000014e-207 < (+.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))))) < 2e-267

   1. Initial program 99.9%

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

   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. lift-+.f64 87.9

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 42.6

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

   7. Applied rewrites 42.6%

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

      1. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      2. flip-+ N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \frac{Ev \cdot Ev - Vef \cdot Vef}{Ev - Vef}}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \frac{Ev \cdot Ev - Vef \cdot Vef}{Ev - Vef}}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \frac{Ev \cdot Ev - Vef \cdot Vef}{Ev - Vef}}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \frac{Ev \cdot Ev - Vef \cdot Vef}{Ev - Vef}}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \frac{Ev \cdot Ev - Vef \cdot Vef}{Ev - Vef}}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lower--.f64 52.7

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \frac{Ev \cdot Ev - Vef \cdot Vef}{Ev - Vef}}{KbT}\right) - \frac{mu}{KbT}} \]

   9. Applied rewrites 52.7%

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

Alternative 9: 39.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-267}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev \cdot \left(1 + \frac{EAccept + Vef}{Ev}\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e-207)
     t_0
     (if (<= t_1 2e-267)
       (/ NaChar (+ 2.0 (/ (* Ev (+ 1.0 (/ (+ EAccept Vef) Ev))) 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 = fma(0.5, NaChar, (0.5 * NdChar));
	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-207) {
		tmp = t_0;
	} else if (t_1 <= 2e-267) {
		tmp = NaChar / (2.0 + ((Ev * (1.0 + ((EAccept + Vef) / Ev))) / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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-207)
		tmp = t_0;
	elseif (t_1 <= 2e-267)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(Ev * Float64(1.0 + Float64(Float64(EAccept + Vef) / Ev))) / KbT)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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-207], t$95$0, If[LessEqual[t$95$1, 2e-267], N[(NaChar / N[(2.0 + N[(N[(Ev * N[(1.0 + N[(N[(EAccept + Vef), $MachinePrecision] / Ev), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $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))))) < -5.00000000000000014e-207 or 2e-267 < (+.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 35.2

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

   4. Applied rewrites 35.2%

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

   if -5.00000000000000014e-207 < (+.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))))) < 2e-267

   1. Initial program 99.9%

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

   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. lift-+.f64 87.9

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 42.6

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

   7. Applied rewrites 42.6%

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

   8. Taylor expanded in mu around 0

      \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \color{blue}{\left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)}\right)} \]
   9. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      6. lift-+.f64 45.5

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

   10. Applied rewrites 45.5%

       \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{\color{blue}{KbT}}} \]

   11. Taylor expanded in Ev around inf

       \[\leadsto \frac{NaChar}{2 + \frac{Ev \cdot \left(1 + \left(\frac{EAccept}{Ev} + \frac{Vef}{Ev}\right)\right)}{KbT}} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{NaChar}{2 + \frac{Ev \cdot \left(1 + \left(\frac{EAccept}{Ev} + \frac{Vef}{Ev}\right)\right)}{KbT}} \]

       2. lower-+.f64 N/A

          \[\leadsto \frac{NaChar}{2 + \frac{Ev \cdot \left(1 + \left(\frac{EAccept}{Ev} + \frac{Vef}{Ev}\right)\right)}{KbT}} \]

       3. div-add-rev N/A

          \[\leadsto \frac{NaChar}{2 + \frac{Ev \cdot \left(1 + \frac{EAccept + Vef}{Ev}\right)}{KbT}} \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{NaChar}{2 + \frac{Ev \cdot \left(1 + \frac{EAccept + Vef}{Ev}\right)}{KbT}} \]

       5. lower-+.f64 53.3

          \[\leadsto \frac{NaChar}{2 + \frac{Ev \cdot \left(1 + \frac{EAccept + Vef}{Ev}\right)}{KbT}} \]

   13. Applied rewrites 53.3%

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

Alternative 10: 39.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-265}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-267}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept \cdot \left(1 + \frac{Ev + Vef}{EAccept}\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -4e-265)
     t_0
     (if (<= t_1 2e-267)
       (/ NaChar (+ 2.0 (/ (* EAccept (+ 1.0 (/ (+ Ev Vef) EAccept))) KbT)))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = fma(0.5, NaChar, (0.5 * NdChar));
	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 <= -4e-265) {
		tmp = t_0;
	} else if (t_1 <= 2e-267) {
		tmp = NaChar / (2.0 + ((EAccept * (1.0 + ((Ev + Vef) / EAccept))) / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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 <= -4e-265)
		tmp = t_0;
	elseif (t_1 <= 2e-267)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(EAccept * Float64(1.0 + Float64(Float64(Ev + Vef) / EAccept))) / KbT)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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, -4e-265], t$95$0, If[LessEqual[t$95$1, 2e-267], N[(NaChar / N[(2.0 + N[(N[(EAccept * N[(1.0 + N[(N[(Ev + Vef), $MachinePrecision] / EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $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))))) < -3.99999999999999994e-265 or 2e-267 < (+.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 34.4

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

   4. Applied rewrites 34.4%

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

   if -3.99999999999999994e-265 < (+.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))))) < 2e-267

   1. Initial program 99.9%

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

   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. lift-+.f64 92.7

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

   4. Applied rewrites 92.7%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 46.7

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

   7. Applied rewrites 46.7%

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

   8. Taylor expanded in mu around 0

      \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \color{blue}{\left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)}\right)} \]
   9. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      6. lift-+.f64 49.8

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

   10. Applied rewrites 49.8%

       \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{\color{blue}{KbT}}} \]

   11. Taylor expanded in EAccept around inf

       \[\leadsto \frac{NaChar}{2 + \frac{EAccept \cdot \left(1 + \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{NaChar}{2 + \frac{EAccept \cdot \left(1 + \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}} \]

       2. lower-+.f64 N/A

          \[\leadsto \frac{NaChar}{2 + \frac{EAccept \cdot \left(1 + \left(\frac{Ev}{EAccept} + \frac{Vef}{EAccept}\right)\right)}{KbT}} \]

       3. div-add-rev N/A

          \[\leadsto \frac{NaChar}{2 + \frac{EAccept \cdot \left(1 + \frac{Ev + Vef}{EAccept}\right)}{KbT}} \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{NaChar}{2 + \frac{EAccept \cdot \left(1 + \frac{Ev + Vef}{EAccept}\right)}{KbT}} \]

       5. lift-+.f64 58.9

          \[\leadsto \frac{NaChar}{2 + \frac{EAccept \cdot \left(1 + \frac{Ev + Vef}{EAccept}\right)}{KbT}} \]

   13. Applied rewrites 58.9%

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

Alternative 11: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-267}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e-207)
     t_0
     (if (<= t_1 2e-267)
       (/ NaChar (+ 2.0 (/ (+ EAccept (+ Ev Vef)) 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 = fma(0.5, NaChar, (0.5 * NdChar));
	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-207) {
		tmp = t_0;
	} else if (t_1 <= 2e-267) {
		tmp = NaChar / (2.0 + ((EAccept + (Ev + Vef)) / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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-207)
		tmp = t_0;
	elseif (t_1 <= 2e-267)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(EAccept + Float64(Ev + Vef)) / KbT)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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-207], t$95$0, If[LessEqual[t$95$1, 2e-267], N[(NaChar / N[(2.0 + N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] / KbT), $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))))) < -5.00000000000000014e-207 or 2e-267 < (+.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 35.2

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

   4. Applied rewrites 35.2%

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

   if -5.00000000000000014e-207 < (+.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))))) < 2e-267

   1. Initial program 99.9%

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

   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. lift-+.f64 87.9

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 42.6

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

   7. Applied rewrites 42.6%

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

   8. Taylor expanded in mu around 0

      \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \color{blue}{\left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)}\right)} \]
   9. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      6. lift-+.f64 45.5

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

   10. Applied rewrites 45.5%

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

Alternative 12: 35.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 10^{-192}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept + Ev}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e-207)
     t_0
     (if (<= t_1 1e-192) (/ NaChar (+ 2.0 (/ (+ EAccept Ev) 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 = fma(0.5, NaChar, (0.5 * NdChar));
	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-207) {
		tmp = t_0;
	} else if (t_1 <= 1e-192) {
		tmp = NaChar / (2.0 + ((EAccept + Ev) / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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-207)
		tmp = t_0;
	elseif (t_1 <= 1e-192)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(EAccept + Ev) / KbT)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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-207], t$95$0, If[LessEqual[t$95$1, 1e-192], N[(NaChar / N[(2.0 + N[(N[(EAccept + Ev), $MachinePrecision] / KbT), $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))))) < -5.00000000000000014e-207 or 1.0000000000000001e-192 < (+.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 36.1

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

   4. Applied rewrites 36.1%

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

   if -5.00000000000000014e-207 < (+.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))))) < 1.0000000000000001e-192

   1. Initial program 99.9%

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

   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. lift-+.f64 83.2

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

   4. Applied rewrites 83.2%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 39.1

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

   7. Applied rewrites 39.1%

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

   8. Taylor expanded in mu around 0

      \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \color{blue}{\left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)}\right)} \]
   9. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      6. lift-+.f64 41.7

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

   10. Applied rewrites 41.7%

       \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{\color{blue}{KbT}}} \]

   11. Taylor expanded in Vef around 0

       \[\leadsto \frac{NaChar}{2 + \frac{EAccept + Ev}{KbT}} \]
   12. Step-by-step derivation

   13. Applied rewrites 32.9%

       \[\leadsto \frac{NaChar}{2 + \frac{EAccept + Ev}{KbT}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 34.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-265}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 10^{-192}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -4e-265)
     t_0
     (if (<= t_1 1e-192) (/ NaChar (+ 2.0 (/ Vef 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 = fma(0.5, NaChar, (0.5 * NdChar));
	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 <= -4e-265) {
		tmp = t_0;
	} else if (t_1 <= 1e-192) {
		tmp = NaChar / (2.0 + (Vef / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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 <= -4e-265)
		tmp = t_0;
	elseif (t_1 <= 1e-192)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Vef / KbT)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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, -4e-265], t$95$0, If[LessEqual[t$95$1, 1e-192], N[(NaChar / N[(2.0 + N[(Vef / KbT), $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))))) < -3.99999999999999994e-265 or 1.0000000000000001e-192 < (+.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 35.3

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

   4. Applied rewrites 35.3%

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

   if -3.99999999999999994e-265 < (+.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))))) < 1.0000000000000001e-192

   1. Initial program 99.9%

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

   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. lift-+.f64 86.8

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

   4. Applied rewrites 86.8%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 42.2

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in mu around 0

      \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \color{blue}{\left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)}\right)} \]
   9. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

      6. lift-+.f64 45.0

         \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}} \]

   10. Applied rewrites 45.0%

       \[\leadsto \frac{NaChar}{2 + \frac{EAccept + \left(Ev + Vef\right)}{\color{blue}{KbT}}} \]

   11. Taylor expanded in Vef around inf

       \[\leadsto \frac{NaChar}{2 + \frac{Vef}{KbT}} \]
   12. Step-by-step derivation

   13. Applied rewrites 32.4%

       \[\leadsto \frac{NaChar}{2 + \frac{Vef}{KbT}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 34.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-265}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -4e-265) t_0 (if (<= t_1 0.0) (/ NaChar (/ Vef 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 = fma(0.5, NaChar, (0.5 * NdChar));
	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 <= -4e-265) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = NaChar / (Vef / KbT);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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 <= -4e-265)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = Float64(NaChar / Float64(Vef / KbT));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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, -4e-265], t$95$0, If[LessEqual[t$95$1, 0.0], N[(NaChar / N[(Vef / 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))))) < -3.99999999999999994e-265 or -0.0 < (+.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 33.8

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

   4. Applied rewrites 33.8%

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

   if -3.99999999999999994e-265 < (+.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))))) < -0.0

   1. Initial program 99.9%

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

   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. lift-+.f64 96.4

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

   4. Applied rewrites 96.4%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 49.7

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

   7. Applied rewrites 49.7%

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

   8. Taylor expanded in Vef around inf

      \[\leadsto \frac{NaChar}{\frac{Vef}{KbT}} \]
   9. Step-by-step derivation

      1. lower-/.f64 36.2

         \[\leadsto \frac{NaChar}{\frac{Vef}{KbT}} \]

   10. Applied rewrites 36.2%

       \[\leadsto \frac{NaChar}{\frac{Vef}{KbT}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 32.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-265}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -4e-265) t_0 (if (<= t_1 0.0) (/ NaChar (/ Ev 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 = fma(0.5, NaChar, (0.5 * NdChar));
	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 <= -4e-265) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = NaChar / (Ev / KbT);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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 <= -4e-265)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = Float64(NaChar / Float64(Ev / KbT));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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, -4e-265], t$95$0, If[LessEqual[t$95$1, 0.0], N[(NaChar / N[(Ev / 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))))) < -3.99999999999999994e-265 or -0.0 < (+.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 33.8

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

   4. Applied rewrites 33.8%

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

   if -3.99999999999999994e-265 < (+.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))))) < -0.0

   1. Initial program 99.9%

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

   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. lift-+.f64 96.4

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

   4. Applied rewrites 96.4%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 49.7

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

   7. Applied rewrites 49.7%

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

   8. Taylor expanded in Ev around inf

      \[\leadsto \frac{NaChar}{\frac{Ev}{KbT}} \]
   9. Step-by-step derivation

      1. lower-/.f64 27.1

         \[\leadsto \frac{NaChar}{\frac{Ev}{KbT}} \]

   10. Applied rewrites 27.1%

       \[\leadsto \frac{NaChar}{\frac{Ev}{KbT}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 32.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (fma 0.5 NaChar (* 0.5 NdChar)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))))
   (if (<= t_1 -5e-207) t_0 (if (<= t_1 0.0) (/ NaChar (/ EAccept KbT)) t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = fma(0.5, NaChar, (0.5 * NdChar));
	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-207) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = NaChar / (EAccept / KbT);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = fma(0.5, NaChar, Float64(0.5 * NdChar))
	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-207)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = Float64(NaChar / Float64(EAccept / KbT));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * NaChar + N[(0.5 * NdChar), $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-207], t$95$0, If[LessEqual[t$95$1, 0.0], N[(NaChar / N[(EAccept / 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))))) < -5.00000000000000014e-207 or -0.0 < (+.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 34.6

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

   4. Applied rewrites 34.6%

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

   if -5.00000000000000014e-207 < (+.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))))) < -0.0

   1. Initial program 99.9%

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

   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. lift-+.f64 90.8

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

   4. Applied rewrites 90.8%

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

   5. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

         \[\leadsto \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \frac{Ev + Vef}{KbT}\right)\right) - \frac{mu}{KbT}} \]

      2. div-add N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}} \]

      8. lift--.f64 45.0

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

   7. Applied rewrites 45.0%

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

   8. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NaChar}{\frac{EAccept}{KbT}} \]
   9. Step-by-step derivation

      1. lower-/.f64 24.7

         \[\leadsto \frac{NaChar}{\frac{EAccept}{KbT}} \]

   10. Applied rewrites 24.7%

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

Alternative 17: 69.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))))
   (if (<= NaChar -4.2e+106)
     t_0
     (if (<= NaChar 1.2e+34)
       (/ NdChar (+ 1.0 (exp (/ (- (+ EDonor (+ Vef mu)) Ec) KbT))))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	double tmp;
	if (NaChar <= -4.2e+106) {
		tmp = t_0;
	} else if (NaChar <= 1.2e+34) {
		tmp = NdChar / (1.0 + exp((((EDonor + (Vef + mu)) - Ec) / 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) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (ev + vef)) - mu) / kbt)))
    if (nachar <= (-4.2d+106)) then
        tmp = t_0
    else if (nachar <= 1.2d+34) then
        tmp = ndchar / (1.0d0 + exp((((edonor + (vef + mu)) - ec) / kbt)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	double tmp;
	if (NaChar <= -4.2e+106) {
		tmp = t_0;
	} else if (NaChar <= 1.2e+34) {
		tmp = NdChar / (1.0 + Math.exp((((EDonor + (Vef + mu)) - Ec) / 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 + (Ev + Vef)) - mu) / KbT)))
	tmp = 0
	if NaChar <= -4.2e+106:
		tmp = t_0
	elif NaChar <= 1.2e+34:
		tmp = NdChar / (1.0 + math.exp((((EDonor + (Vef + mu)) - Ec) / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))))
	tmp = 0.0
	if (NaChar <= -4.2e+106)
		tmp = t_0;
	elseif (NaChar <= 1.2e+34)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(EDonor + Float64(Vef + mu)) - Ec) / KbT))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	tmp = 0.0;
	if (NaChar <= -4.2e+106)
		tmp = t_0;
	elseif (NaChar <= 1.2e+34)
		tmp = NdChar / (1.0 + exp((((EDonor + (Vef + mu)) - Ec) / KbT)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -4.2e+106], t$95$0, If[LessEqual[NaChar, 1.2e+34], N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(EDonor + N[(Vef + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.2000000000000001e106 or 1.19999999999999993e34 < NaChar

   1. Initial program 99.9%

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

   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. lift-+.f64 70.9

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

   4. Applied rewrites 70.9%

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

   if -4.2000000000000001e106 < NaChar < 1.19999999999999993e34

   1. Initial program 100.0%

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

   2. Taylor expanded in NdChar around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 68.3

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

   4. Applied rewrites 68.3%

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

Alternative 18: 62.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.65 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ \mathbf{elif}\;KbT \leq 2.9 \cdot 10^{+205}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.65e+224)
   (fma 0.5 NaChar (* 0.5 NdChar))
   (if (<= KbT 2.9e+205)
     (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT))))
     (+ (* 0.5 NdChar) (/ 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 (KbT <= -1.65e+224) {
		tmp = fma(0.5, NaChar, (0.5 * NdChar));
	} else if (KbT <= 2.9e+205) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Ev + Vef)) - mu) / KbT)));
	} else {
		tmp = (0.5 * NdChar) + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -1.65e+224)
		tmp = fma(0.5, NaChar, Float64(0.5 * NdChar));
	elseif (KbT <= 2.9e+205)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT))));
	else
		tmp = Float64(Float64(0.5 * NdChar) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -1.65e+224], N[(0.5 * NaChar + N[(0.5 * NdChar), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.9e+205], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * NdChar), $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 KbT < -1.64999999999999998e224

   1. Initial program 99.9%

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

   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 76.3

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

   4. Applied rewrites 76.3%

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

   if -1.64999999999999998e224 < KbT < 2.9000000000000001e205

   1. Initial program 100.0%

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

   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. lift-+.f64 60.5

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

   4. Applied rewrites 60.5%

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

   if 2.9000000000000001e205 < KbT

   1. Initial program 99.9%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-*.f64 81.1

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

   4. Applied rewrites 81.1%

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

   5. Taylor expanded in EAccept around inf

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

   7. Applied rewrites 74.6%

      \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{\color{blue}{EAccept}}{KbT}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 41.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot NdChar + \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}}\\ \mathbf{if}\;KbT \leq -1.4 \cdot 10^{+141}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 1.56 \cdot 10^{-285}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 3.2 \cdot 10^{+111}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (* 0.5 NdChar)
          (/ NaChar (- (+ 2.0 (/ (+ EAccept (+ Ev Vef)) KbT)) (/ mu KbT))))))
   (if (<= KbT -1.4e+141)
     t_0
     (if (<= KbT 1.56e-285)
       (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
       (if (<= KbT 3.2e+111) (/ NaChar (+ 1.0 (exp (/ Vef 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 = (0.5 * NdChar) + (NaChar / ((2.0 + ((EAccept + (Ev + Vef)) / KbT)) - (mu / KbT)));
	double tmp;
	if (KbT <= -1.4e+141) {
		tmp = t_0;
	} else if (KbT <= 1.56e-285) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else if (KbT <= 3.2e+111) {
		tmp = NaChar / (1.0 + exp((Vef / 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) :: tmp
    t_0 = (0.5d0 * ndchar) + (nachar / ((2.0d0 + ((eaccept + (ev + vef)) / kbt)) - (mu / kbt)))
    if (kbt <= (-1.4d+141)) then
        tmp = t_0
    else if (kbt <= 1.56d-285) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else if (kbt <= 3.2d+111) then
        tmp = nachar / (1.0d0 + exp((vef / 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 = (0.5 * NdChar) + (NaChar / ((2.0 + ((EAccept + (Ev + Vef)) / KbT)) - (mu / KbT)));
	double tmp;
	if (KbT <= -1.4e+141) {
		tmp = t_0;
	} else if (KbT <= 1.56e-285) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else if (KbT <= 3.2e+111) {
		tmp = NaChar / (1.0 + Math.exp((Vef / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (0.5 * NdChar) + (NaChar / ((2.0 + ((EAccept + (Ev + Vef)) / KbT)) - (mu / KbT)))
	tmp = 0
	if KbT <= -1.4e+141:
		tmp = t_0
	elif KbT <= 1.56e-285:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	elif KbT <= 3.2e+111:
		tmp = NaChar / (1.0 + math.exp((Vef / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(0.5 * NdChar) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept + Float64(Ev + Vef)) / KbT)) - Float64(mu / KbT))))
	tmp = 0.0
	if (KbT <= -1.4e+141)
		tmp = t_0;
	elseif (KbT <= 1.56e-285)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	elseif (KbT <= 3.2e+111)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Vef / 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 = (0.5 * NdChar) + (NaChar / ((2.0 + ((EAccept + (Ev + Vef)) / KbT)) - (mu / KbT)));
	tmp = 0.0;
	if (KbT <= -1.4e+141)
		tmp = t_0;
	elseif (KbT <= 1.56e-285)
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	elseif (KbT <= 3.2e+111)
		tmp = NaChar / (1.0 + exp((Vef / 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[(0.5 * NdChar), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -1.4e+141], t$95$0, If[LessEqual[KbT, 1.56e-285], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 3.2e+111], N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.39999999999999996e141 or 3.2000000000000001e111 < KbT

   1. Initial program 99.9%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in Vef around inf

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

   7. Applied rewrites 62.6%

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

   8. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

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

      2. div-add N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift--.f64 59.4

         \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \color{blue}{\frac{mu}{KbT}}} \]

   10. Applied rewrites 59.4%

       \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{\color{blue}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}}} \]

   if -1.39999999999999996e141 < KbT < 1.55999999999999998e-285

   1. Initial program 100.0%

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

   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. lift-+.f64 61.3

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

   4. Applied rewrites 61.3%

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

   5. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

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

   if 1.55999999999999998e-285 < KbT < 3.2000000000000001e111

   1. Initial program 100.0%

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

   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. lift-+.f64 62.5

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

   4. Applied rewrites 62.5%

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

   5. Taylor expanded in Vef around inf

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

   7. Applied rewrites 35.5%

      \[\leadsto \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 41.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot NdChar + \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}}\\ \mathbf{if}\;KbT \leq -1.4 \cdot 10^{+141}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq -1.45 \cdot 10^{-281}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (* 0.5 NdChar)
          (/ NaChar (- (+ 2.0 (/ (+ EAccept (+ Ev Vef)) KbT)) (/ mu KbT))))))
   (if (<= KbT -1.4e+141)
     t_0
     (if (<= KbT -1.45e-281)
       (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
       (if (<= KbT 1.6e+50) (/ NaChar (+ 1.0 (exp (/ Ev 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 = (0.5 * NdChar) + (NaChar / ((2.0 + ((EAccept + (Ev + Vef)) / KbT)) - (mu / KbT)));
	double tmp;
	if (KbT <= -1.4e+141) {
		tmp = t_0;
	} else if (KbT <= -1.45e-281) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else if (KbT <= 1.6e+50) {
		tmp = NaChar / (1.0 + exp((Ev / 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) :: tmp
    t_0 = (0.5d0 * ndchar) + (nachar / ((2.0d0 + ((eaccept + (ev + vef)) / kbt)) - (mu / kbt)))
    if (kbt <= (-1.4d+141)) then
        tmp = t_0
    else if (kbt <= (-1.45d-281)) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else if (kbt <= 1.6d+50) then
        tmp = nachar / (1.0d0 + exp((ev / 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 = (0.5 * NdChar) + (NaChar / ((2.0 + ((EAccept + (Ev + Vef)) / KbT)) - (mu / KbT)));
	double tmp;
	if (KbT <= -1.4e+141) {
		tmp = t_0;
	} else if (KbT <= -1.45e-281) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else if (KbT <= 1.6e+50) {
		tmp = NaChar / (1.0 + Math.exp((Ev / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (0.5 * NdChar) + (NaChar / ((2.0 + ((EAccept + (Ev + Vef)) / KbT)) - (mu / KbT)))
	tmp = 0
	if KbT <= -1.4e+141:
		tmp = t_0
	elif KbT <= -1.45e-281:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	elif KbT <= 1.6e+50:
		tmp = NaChar / (1.0 + math.exp((Ev / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(0.5 * NdChar) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept + Float64(Ev + Vef)) / KbT)) - Float64(mu / KbT))))
	tmp = 0.0
	if (KbT <= -1.4e+141)
		tmp = t_0;
	elseif (KbT <= -1.45e-281)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	elseif (KbT <= 1.6e+50)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Ev / 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 = (0.5 * NdChar) + (NaChar / ((2.0 + ((EAccept + (Ev + Vef)) / KbT)) - (mu / KbT)));
	tmp = 0.0;
	if (KbT <= -1.4e+141)
		tmp = t_0;
	elseif (KbT <= -1.45e-281)
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	elseif (KbT <= 1.6e+50)
		tmp = NaChar / (1.0 + exp((Ev / 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[(0.5 * NdChar), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -1.4e+141], t$95$0, If[LessEqual[KbT, -1.45e-281], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.6e+50], N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.39999999999999996e141 or 1.59999999999999991e50 < KbT

   1. Initial program 99.9%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-*.f64 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in Vef around inf

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

   7. Applied rewrites 57.7%

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

   8. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

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

      2. div-add N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift--.f64 53.8

         \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \color{blue}{\frac{mu}{KbT}}} \]

   10. Applied rewrites 53.8%

       \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{\color{blue}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}}} \]

   if -1.39999999999999996e141 < KbT < -1.44999999999999995e-281

   1. Initial program 99.9%

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

   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. lift-+.f64 61.2

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

   4. Applied rewrites 61.2%

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

   5. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
   6. Step-by-step derivation

   7. Applied rewrites 32.8%

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

   if -1.44999999999999995e-281 < KbT < 1.59999999999999991e50

   1. Initial program 100.0%

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

   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. lift-+.f64 62.4

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

   4. Applied rewrites 62.4%

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

   5. Taylor expanded in Ev around inf

      \[\leadsto \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

      \[\leadsto \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 50.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.05 \cdot 10^{+221}:\\ \;\;\;\;\mathsf{fma}\left(0.5, NaChar, 0.5 \cdot NdChar\right)\\ \mathbf{elif}\;KbT \leq 2.9 \cdot 10^{+222}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NdChar + \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2.05e+221)
   (fma 0.5 NaChar (* 0.5 NdChar))
   (if (<= KbT 2.9e+222)
     (/ NaChar (+ 1.0 (exp (/ (- Vef mu) KbT))))
     (+
      (* 0.5 NdChar)
      (/ NaChar (- (+ 2.0 (/ (+ EAccept (+ Ev Vef)) KbT)) (/ 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 <= -2.05e+221) {
		tmp = fma(0.5, NaChar, (0.5 * NdChar));
	} else if (KbT <= 2.9e+222) {
		tmp = NaChar / (1.0 + exp(((Vef - mu) / KbT)));
	} else {
		tmp = (0.5 * NdChar) + (NaChar / ((2.0 + ((EAccept + (Ev + Vef)) / KbT)) - (mu / KbT)));
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -2.05e+221)
		tmp = fma(0.5, NaChar, Float64(0.5 * NdChar));
	elseif (KbT <= 2.9e+222)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - mu) / KbT))));
	else
		tmp = Float64(Float64(0.5 * NdChar) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept + Float64(Ev + Vef)) / KbT)) - Float64(mu / KbT))));
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -2.05e+221], N[(0.5 * NaChar + N[(0.5 * NdChar), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.9e+222], N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * NdChar), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -2.04999999999999985e221

   1. Initial program 99.9%

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

   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 75.9

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

   4. Applied rewrites 75.9%

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

   if -2.04999999999999985e221 < KbT < 2.89999999999999981e222

   1. Initial program 100.0%

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

   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. lift-+.f64 60.3

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in Vef around inf

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

   7. Applied rewrites 45.7%

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

   if 2.89999999999999981e222 < KbT

   1. Initial program 99.9%

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

   2. Taylor expanded in KbT around inf

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

      1. lower-*.f64 83.1

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

   4. Applied rewrites 83.1%

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

   5. Taylor expanded in Vef around inf

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

   7. Applied rewrites 76.6%

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

   8. Taylor expanded in KbT around inf

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

      1. div-add-rev N/A

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

      2. div-add N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift--.f64 75.9

         \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \color{blue}{\frac{mu}{KbT}}} \]

   10. Applied rewrites 75.9%

       \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{\color{blue}{\left(2 + \frac{EAccept + \left(Ev + Vef\right)}{KbT}\right) - \frac{mu}{KbT}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 23.3% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -3.6 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot NaChar\\ \mathbf{elif}\;NaChar \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;0.5 \cdot NdChar\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NaChar\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -3.6e+106)
   (* 0.5 NaChar)
   (if (<= NaChar 2.7e+34) (* 0.5 NdChar) (* 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 <= -3.6e+106) {
		tmp = 0.5 * NaChar;
	} else if (NaChar <= 2.7e+34) {
		tmp = 0.5 * NdChar;
	} 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 <= (-3.6d+106)) then
        tmp = 0.5d0 * nachar
    else if (nachar <= 2.7d+34) then
        tmp = 0.5d0 * ndchar
    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 <= -3.6e+106) {
		tmp = 0.5 * NaChar;
	} else if (NaChar <= 2.7e+34) {
		tmp = 0.5 * NdChar;
	} else {
		tmp = 0.5 * NaChar;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -3.6e+106:
		tmp = 0.5 * NaChar
	elif NaChar <= 2.7e+34:
		tmp = 0.5 * NdChar
	else:
		tmp = 0.5 * NaChar
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -3.6e+106)
		tmp = Float64(0.5 * NaChar);
	elseif (NaChar <= 2.7e+34)
		tmp = Float64(0.5 * NdChar);
	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 <= -3.6e+106)
		tmp = 0.5 * NaChar;
	elseif (NaChar <= 2.7e+34)
		tmp = 0.5 * NdChar;
	else
		tmp = 0.5 * NaChar;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -3.6e+106], N[(0.5 * NaChar), $MachinePrecision], If[LessEqual[NaChar, 2.7e+34], N[(0.5 * NdChar), $MachinePrecision], N[(0.5 * NaChar), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -3.6000000000000001e106 or 2.7e34 < NaChar

   1. Initial program 99.9%

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

   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. lift-+.f64 71.0

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

   4. Applied rewrites 71.0%

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

   5. Taylor expanded in KbT around inf

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

      1. lower-*.f64 23.6

         \[\leadsto 0.5 \cdot NaChar \]

   7. Applied rewrites 23.6%

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

   if -3.6000000000000001e106 < NaChar < 2.7e34

   1. Initial program 100.0%

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

   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 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in NdChar around inf

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

      1. lift-*.f64 23.0

         \[\leadsto 0.5 \cdot NdChar \]

   7. Applied rewrites 23.0%

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

Alternative 23: 28.0% accurate, 23.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(0.5 * NaChar + N[(0.5 * NdChar), $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. 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 28.0

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

4. Applied rewrites 28.0%

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

Alternative 24: 18.9% accurate, 46.0× speedup

Math

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

FPCore

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

C

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

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 * ndchar
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(0.5 * NdChar), $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 28.0

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

4. Applied rewrites 28.0%

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

5. Taylor expanded in NdChar around inf

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

   1. lift-*.f64 18.9

      \[\leadsto 0.5 \cdot NdChar \]

7. Applied rewrites 18.9%

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

Reproduce

herbie shell --seed 2025093 
(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))))))