Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Percentage Accurate: 98.2% → 98.2%

Time: 9.0s

Alternatives: 14

Speedup: 1.0×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Initial Program: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Alternative 1: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 98.2%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

Alternative 2: 93.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))
   (if (<= t -1.5e+77)
     t_1
     (if (<= t 4.4e-7)
       (/ (* x (* (/ 1.0 a) (exp (- (* (log z) y) b)))) y)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -1.5e+77) {
		tmp = t_1;
	} else if (t <= 4.4e-7) {
		tmp = (x * ((1.0 / a) * exp(((log(z) * y) - b)))) / y;
	} 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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    if (t <= (-1.5d+77)) then
        tmp = t_1
    else if (t <= 4.4d-7) then
        tmp = (x * ((1.0d0 / a) * exp(((log(z) * y) - b)))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -1.5e+77) {
		tmp = t_1;
	} else if (t <= 4.4e-7) {
		tmp = (x * ((1.0 / a) * Math.exp(((Math.log(z) * y) - b)))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	tmp = 0
	if t <= -1.5e+77:
		tmp = t_1
	elif t <= 4.4e-7:
		tmp = (x * ((1.0 / a) * math.exp(((math.log(z) * y) - b)))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y)
	tmp = 0.0
	if (t <= -1.5e+77)
		tmp = t_1;
	elseif (t <= 4.4e-7)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) * exp(Float64(Float64(log(z) * y) - b)))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	tmp = 0.0;
	if (t <= -1.5e+77)
		tmp = t_1;
	elseif (t <= 4.4e-7)
		tmp = (x * ((1.0 / a) * exp(((log(z) * y) - b)))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -1.5e+77], t$95$1, If[LessEqual[t, 4.4e-7], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] * N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4999999999999999e77 or 4.4000000000000002e-7 < t

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\log a \cdot \color{blue}{\left(t - 1\right)} - b}}{y} \]

      2. lift-log.f64 N/A

         \[\leadsto \frac{x \cdot e^{\log a \cdot \left(\color{blue}{t} - 1\right) - b}}{y} \]

      3. lift--.f64 90.3

         \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - \color{blue}{1}\right) - b}}{y} \]

   4. Applied rewrites 90.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]

   if -1.4999999999999999e77 < t < 4.4000000000000002e-7

   1. Initial program 96.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 95.5

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 95.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 93.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))
   (if (<= t -1.5e+77)
     t_1
     (if (<= t 4.4e-7) (/ (/ (* x (exp (- (* y (log z)) b))) y) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -1.5e+77) {
		tmp = t_1;
	} else if (t <= 4.4e-7) {
		tmp = ((x * exp(((y * log(z)) - b))) / y) / a;
	} 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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    if (t <= (-1.5d+77)) then
        tmp = t_1
    else if (t <= 4.4d-7) then
        tmp = ((x * exp(((y * log(z)) - b))) / y) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -1.5e+77) {
		tmp = t_1;
	} else if (t <= 4.4e-7) {
		tmp = ((x * Math.exp(((y * Math.log(z)) - b))) / y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	tmp = 0
	if t <= -1.5e+77:
		tmp = t_1
	elif t <= 4.4e-7:
		tmp = ((x * math.exp(((y * math.log(z)) - b))) / y) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y)
	tmp = 0.0
	if (t <= -1.5e+77)
		tmp = t_1;
	elseif (t <= 4.4e-7)
		tmp = Float64(Float64(Float64(x * exp(Float64(Float64(y * log(z)) - b))) / y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	tmp = 0.0;
	if (t <= -1.5e+77)
		tmp = t_1;
	elseif (t <= 4.4e-7)
		tmp = ((x * exp(((y * log(z)) - b))) / y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -1.5e+77], t$95$1, If[LessEqual[t, 4.4e-7], N[(N[(N[(x * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4999999999999999e77 or 4.4000000000000002e-7 < t

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\log a \cdot \color{blue}{\left(t - 1\right)} - b}}{y} \]

      2. lift-log.f64 N/A

         \[\leadsto \frac{x \cdot e^{\log a \cdot \left(\color{blue}{t} - 1\right) - b}}{y} \]

      3. lift--.f64 90.3

         \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - \color{blue}{1}\right) - b}}{y} \]

   4. Applied rewrites 90.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]

   if -1.4999999999999999e77 < t < 4.4000000000000002e-7

   1. Initial program 96.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{t \cdot \left(t \cdot \left(\frac{1}{6} \cdot \frac{t \cdot \left(x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{3}\right)\right)}{y} + \frac{1}{2} \cdot \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{2}\right)}{y}\right) + \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(0.16666666666666666 \cdot t, e^{\mathsf{fma}\left(\log \log a, 3, \mathsf{fma}\left(\log z, y, -\log a\right) - b\right)} \cdot x, \left(\left(\left(\log a \cdot \log a\right) \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)\right) \cdot x\right) \cdot 0.5\right)}{y}, x \cdot \frac{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right) \cdot \log a}{y}\right), t, x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto \frac{\frac{1}{6} \cdot \frac{a \cdot \left({t}^{3} \cdot \left(x \cdot e^{\left(3 \cdot \log \log a + y \cdot \log z\right) - \left(b + \log a\right)}\right)\right)}{y} + \left(t \cdot \left(\frac{1}{2} \cdot \frac{t \cdot \left(x \cdot \left(e^{y \cdot \log z - b} \cdot {\log a}^{2}\right)\right)}{y} + \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{y \cdot \log z - b}}{y}\right)}{\color{blue}{a}} \]

   7. Applied rewrites 30.3%

      \[\leadsto \frac{\mathsf{fma}\left(0.16666666666666666, \frac{a \cdot \left(\left(\left(t \cdot t\right) \cdot t\right) \cdot \left(x \cdot e^{\mathsf{fma}\left(3, \log \log a, y \cdot \log z\right) - \left(b + \log a\right)}\right)\right)}{y}, \mathsf{fma}\left(t, \mathsf{fma}\left(0.5, \frac{t \cdot \left(x \cdot \left(e^{y \cdot \log z - b} \cdot \left(\log a \cdot \log a\right)\right)\right)}{y}, \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \log a\right)}{y}\right), \frac{x \cdot e^{y \cdot \log z - b}}{y}\right)\right)}{\color{blue}{a}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]
   9. Step-by-step derivation

      1. lift-log.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      4. lift-exp.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      6. lift-/.f64 95.7

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

   10. Applied rewrites 95.7%

       \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 88.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log z \cdot y}}{y}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+129}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (* (log z) y))) y)))
   (if (<= y -6.2e+60)
     t_1
     (if (<= y 3.1e+129) (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((log(z) * y))) / y;
	double tmp;
	if (y <= -6.2e+60) {
		tmp = t_1;
	} else if (y <= 3.1e+129) {
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	} 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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp((log(z) * y))) / y
    if (y <= (-6.2d+60)) then
        tmp = t_1
    else if (y <= 3.1d+129) then
        tmp = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp((Math.log(z) * y))) / y;
	double tmp;
	if (y <= -6.2e+60) {
		tmp = t_1;
	} else if (y <= 3.1e+129) {
		tmp = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp((math.log(z) * y))) / y
	tmp = 0
	if y <= -6.2e+60:
		tmp = t_1
	elif y <= 3.1e+129:
		tmp = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(log(z) * y))) / y)
	tmp = 0.0
	if (y <= -6.2e+60)
		tmp = t_1;
	elseif (y <= 3.1e+129)
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp((log(z) * y))) / y;
	tmp = 0.0;
	if (y <= -6.2e+60)
		tmp = t_1;
	elseif (y <= 3.1e+129)
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -6.2e+60], t$95$1, If[LessEqual[y, 3.1e+129], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000001e60 or 3.1e129 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z}}}{y} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\log z \cdot \color{blue}{y}}}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\log z \cdot \color{blue}{y}}}{y} \]

      3. lift-log.f64 84.2

         \[\leadsto \frac{x \cdot e^{\log z \cdot y}}{y} \]

   4. Applied rewrites 84.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log z \cdot y}}}{y} \]

   if -6.2000000000000001e60 < y < 3.1e129

   1. Initial program 97.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\log a \cdot \color{blue}{\left(t - 1\right)} - b}}{y} \]

      2. lift-log.f64 N/A

         \[\leadsto \frac{x \cdot e^{\log a \cdot \left(\color{blue}{t} - 1\right) - b}}{y} \]

      3. lift--.f64 90.9

         \[\leadsto \frac{x \cdot e^{\log a \cdot \left(t - \color{blue}{1}\right) - b}}{y} \]

   4. Applied rewrites 90.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+94}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (/ (* x (exp (* (log a) t))) y)))
   (if (<= t_1 -1e+51)
     t_2
     (if (<= t_1 2e+94) (/ (* x (/ (exp (- b)) a)) y) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double t_2 = (x * exp((log(a) * t))) / y;
	double tmp;
	if (t_1 <= -1e+51) {
		tmp = t_2;
	} else if (t_1 <= 2e+94) {
		tmp = (x * (exp(-b) / a)) / y;
	} else {
		tmp = t_2;
	}
	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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - 1.0d0) * log(a)
    t_2 = (x * exp((log(a) * t))) / y
    if (t_1 <= (-1d+51)) then
        tmp = t_2
    else if (t_1 <= 2d+94) then
        tmp = (x * (exp(-b) / a)) / y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * Math.log(a);
	double t_2 = (x * Math.exp((Math.log(a) * t))) / y;
	double tmp;
	if (t_1 <= -1e+51) {
		tmp = t_2;
	} else if (t_1 <= 2e+94) {
		tmp = (x * (Math.exp(-b) / a)) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	t_2 = (x * math.exp((math.log(a) * t))) / y
	tmp = 0
	if t_1 <= -1e+51:
		tmp = t_2
	elif t_1 <= 2e+94:
		tmp = (x * (math.exp(-b) / a)) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	t_2 = Float64(Float64(x * exp(Float64(log(a) * t))) / y)
	tmp = 0.0
	if (t_1 <= -1e+51)
		tmp = t_2;
	elseif (t_1 <= 2e+94)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	t_2 = (x * exp((log(a) * t))) / y;
	tmp = 0.0;
	if (t_1 <= -1e+51)
		tmp = t_2;
	elseif (t_1 <= 2e+94)
		tmp = (x * (exp(-b) / a)) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Exp[N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+51], t$95$2, If[LessEqual[t$95$1, 2e+94], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1e51 or 2e94 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{t \cdot \log a}}}{y} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\log a \cdot \color{blue}{t}}}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{\log a \cdot \color{blue}{t}}}{y} \]

      3. lift-log.f64 83.3

         \[\leadsto \frac{x \cdot e^{\log a \cdot t}}{y} \]

   4. Applied rewrites 83.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t}}}{y} \]

   if -1e51 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e94

   1. Initial program 97.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 93.0

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 93.0%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{\color{blue}{a}}}{y} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      3. lift-neg.f64 67.3

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 67.3%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 71.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-b}\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x \cdot t\_1}{y}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{t\_1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (- b))))
   (if (<= b -8.5e+48)
     (/ (* x t_1) y)
     (if (<= b 3.1e-11) (/ (* x (pow z y)) (* a y)) (/ (* x (/ t_1 a)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(-b);
	double tmp;
	if (b <= -8.5e+48) {
		tmp = (x * t_1) / y;
	} else if (b <= 3.1e-11) {
		tmp = (x * pow(z, y)) / (a * y);
	} else {
		tmp = (x * (t_1 / a)) / y;
	}
	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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = exp(-b)
    if (b <= (-8.5d+48)) then
        tmp = (x * t_1) / y
    else if (b <= 3.1d-11) then
        tmp = (x * (z ** y)) / (a * y)
    else
        tmp = (x * (t_1 / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.exp(-b);
	double tmp;
	if (b <= -8.5e+48) {
		tmp = (x * t_1) / y;
	} else if (b <= 3.1e-11) {
		tmp = (x * Math.pow(z, y)) / (a * y);
	} else {
		tmp = (x * (t_1 / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp(-b)
	tmp = 0
	if b <= -8.5e+48:
		tmp = (x * t_1) / y
	elif b <= 3.1e-11:
		tmp = (x * math.pow(z, y)) / (a * y)
	else:
		tmp = (x * (t_1 / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(-b))
	tmp = 0.0
	if (b <= -8.5e+48)
		tmp = Float64(Float64(x * t_1) / y);
	elseif (b <= 3.1e-11)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * y));
	else
		tmp = Float64(Float64(x * Float64(t_1 / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp(-b);
	tmp = 0.0;
	if (b <= -8.5e+48)
		tmp = (x * t_1) / y;
	elseif (b <= 3.1e-11)
		tmp = (x * (z ^ y)) / (a * y);
	else
		tmp = (x * (t_1 / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[(-b)], $MachinePrecision]}, If[LessEqual[b, -8.5e+48], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.1e-11], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.5000000000000001e48

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in b around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot e^{\mathsf{neg}\left(b\right)}}{y} \]

      2. lower-neg.f64 80.9

         \[\leadsto \frac{x \cdot e^{-b}}{y} \]

   4. Applied rewrites 80.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   if -8.5000000000000001e48 < b < 3.10000000000000028e-11

   1. Initial program 96.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{t \cdot \left(t \cdot \left(\frac{1}{6} \cdot \frac{t \cdot \left(x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{3}\right)\right)}{y} + \frac{1}{2} \cdot \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{2}\right)}{y}\right) + \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]

   4. Applied rewrites 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(0.16666666666666666 \cdot t, e^{\mathsf{fma}\left(\log \log a, 3, \mathsf{fma}\left(\log z, y, -\log a\right) - b\right)} \cdot x, \left(\left(\left(\log a \cdot \log a\right) \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)\right) \cdot x\right) \cdot 0.5\right)}{y}, x \cdot \frac{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right) \cdot \log a}{y}\right), t, x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot \color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      6. lift-log.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      7. lower-*.f64 67.2

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   7. Applied rewrites 67.2%

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]
   9. Step-by-step derivation

      1. lower-pow.f64 65.3

         \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

   10. Applied rewrites 65.3%

       \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

   if 3.10000000000000028e-11 < b

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 88.1

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 88.1%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{\color{blue}{a}}}{y} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      3. lift-neg.f64 77.3

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 77.3%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 59.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1 + b \cdot \left(0.5 \cdot b - 1\right)}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 2e+234)
   (/ (* x (/ (exp (- b)) a)) y)
   (/ (* x (/ (+ 1.0 (* b (- (* 0.5 b) 1.0))) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= 2e+234) {
		tmp = (x * (exp(-b) / a)) / y;
	} else {
		tmp = (x * ((1.0 + (b * ((0.5 * b) - 1.0))) / a)) / y;
	}
	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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t - 1.0d0) * log(a)) <= 2d+234) then
        tmp = (x * (exp(-b) / a)) / y
    else
        tmp = (x * ((1.0d0 + (b * ((0.5d0 * b) - 1.0d0))) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * Math.log(a)) <= 2e+234) {
		tmp = (x * (Math.exp(-b) / a)) / y;
	} else {
		tmp = (x * ((1.0 + (b * ((0.5 * b) - 1.0))) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= 2e+234:
		tmp = (x * (math.exp(-b) / a)) / y
	else:
		tmp = (x * ((1.0 + (b * ((0.5 * b) - 1.0))) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= 2e+234)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64(Float64(1.0 + Float64(b * Float64(Float64(0.5 * b) - 1.0))) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) * log(a)) <= 2e+234)
		tmp = (x * (exp(-b) / a)) / y;
	else
		tmp = (x * ((1.0 + (b * ((0.5 * b) - 1.0))) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], 2e+234], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[(1.0 + N[(b * N[(N[(0.5 * b), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2.00000000000000004e234

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 82.2

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 82.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{\color{blue}{a}}}{y} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      3. lift-neg.f64 59.8

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 59.8%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]

   if 2.00000000000000004e234 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 50.7

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 50.7%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{\color{blue}{a}}}{y} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      3. lift-neg.f64 38.2

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 38.2%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \frac{1 + b \cdot \left(\frac{1}{2} \cdot b - 1\right)}{a}}{y} \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x \cdot \frac{1 + b \cdot \left(\frac{1}{2} \cdot b - 1\right)}{a}}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \frac{1 + b \cdot \left(\frac{1}{2} \cdot b - 1\right)}{a}}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \frac{1 + b \cdot \left(\frac{1}{2} \cdot b - 1\right)}{a}}{y} \]

      4. lower-*.f64 47.2

         \[\leadsto \frac{x \cdot \frac{1 + b \cdot \left(0.5 \cdot b - 1\right)}{a}}{y} \]

   10. Applied rewrites 47.2%

       \[\leadsto \frac{x \cdot \frac{1 + b \cdot \left(0.5 \cdot b - 1\right)}{a}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 58.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 2 \cdot 10^{+236}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + y \cdot \log z\right)}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 2e+236)
   (/ (* x (/ (exp (- b)) a)) y)
   (/ (* x (+ 1.0 (* y (log z)))) (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= 2e+236) {
		tmp = (x * (exp(-b) / a)) / y;
	} else {
		tmp = (x * (1.0 + (y * log(z)))) / (a * y);
	}
	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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t - 1.0d0) * log(a)) <= 2d+236) then
        tmp = (x * (exp(-b) / a)) / y
    else
        tmp = (x * (1.0d0 + (y * log(z)))) / (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * Math.log(a)) <= 2e+236) {
		tmp = (x * (Math.exp(-b) / a)) / y;
	} else {
		tmp = (x * (1.0 + (y * Math.log(z)))) / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= 2e+236:
		tmp = (x * (math.exp(-b) / a)) / y
	else:
		tmp = (x * (1.0 + (y * math.log(z)))) / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= 2e+236)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64(1.0 + Float64(y * log(z)))) / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) * log(a)) <= 2e+236)
		tmp = (x * (exp(-b) / a)) / y;
	else
		tmp = (x * (1.0 + (y * log(z)))) / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], 2e+236], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(1.0 + N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2.00000000000000011e236

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 82.2

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 82.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{\color{blue}{a}}}{y} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      3. lift-neg.f64 59.8

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 59.8%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]

   if 2.00000000000000011e236 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{t \cdot \left(t \cdot \left(\frac{1}{6} \cdot \frac{t \cdot \left(x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{3}\right)\right)}{y} + \frac{1}{2} \cdot \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{2}\right)}{y}\right) + \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]

   4. Applied rewrites 33.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(0.16666666666666666 \cdot t, e^{\mathsf{fma}\left(\log \log a, 3, \mathsf{fma}\left(\log z, y, -\log a\right) - b\right)} \cdot x, \left(\left(\left(\log a \cdot \log a\right) \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)\right) \cdot x\right) \cdot 0.5\right)}{y}, x \cdot \frac{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right) \cdot \log a}{y}\right), t, x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot \color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      6. lift-log.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      7. lower-*.f64 45.6

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   7. Applied rewrites 45.6%

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]
   9. Step-by-step derivation

      1. lower-pow.f64 40.5

         \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

   10. Applied rewrites 40.5%

       \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

   11. Taylor expanded in y around 0

       \[\leadsto \frac{x \cdot \left(1 + y \cdot \log z\right)}{a \cdot y} \]
   12. Step-by-step derivation

       1. lower-+.f64 N/A

          \[\leadsto \frac{x \cdot \left(1 + y \cdot \log z\right)}{a \cdot y} \]

       2. lift-log.f64 N/A

          \[\leadsto \frac{x \cdot \left(1 + y \cdot \log z\right)}{a \cdot y} \]

       3. lift-*.f64 24.7

          \[\leadsto \frac{x \cdot \left(1 + y \cdot \log z\right)}{a \cdot y} \]

   13. Applied rewrites 24.7%

       \[\leadsto \frac{x \cdot \left(1 + y \cdot \log z\right)}{a \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 57.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{-b}\\ \mathbf{if}\;x \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{t\_1}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (- b)))))
   (if (<= x 5e+32) (/ (/ t_1 y) a) (/ t_1 (* a y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp(-b);
	double tmp;
	if (x <= 5e+32) {
		tmp = (t_1 / y) / a;
	} else {
		tmp = t_1 / (a * y);
	}
	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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * exp(-b)
    if (x <= 5d+32) then
        tmp = (t_1 / y) / a
    else
        tmp = t_1 / (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp(-b);
	double tmp;
	if (x <= 5e+32) {
		tmp = (t_1 / y) / a;
	} else {
		tmp = t_1 / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp(-b)
	tmp = 0
	if x <= 5e+32:
		tmp = (t_1 / y) / a
	else:
		tmp = t_1 / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(-b)))
	tmp = 0.0
	if (x <= 5e+32)
		tmp = Float64(Float64(t_1 / y) / a);
	else
		tmp = Float64(t_1 / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp(-b);
	tmp = 0.0;
	if (x <= 5e+32)
		tmp = (t_1 / y) / a;
	else
		tmp = t_1 / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[(-b)], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 5e+32], N[(N[(t$95$1 / y), $MachinePrecision] / a), $MachinePrecision], N[(t$95$1 / N[(a * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 4.9999999999999997e32

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{t \cdot \left(t \cdot \left(\frac{1}{6} \cdot \frac{t \cdot \left(x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{3}\right)\right)}{y} + \frac{1}{2} \cdot \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{2}\right)}{y}\right) + \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]

   4. Applied rewrites 34.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(0.16666666666666666 \cdot t, e^{\mathsf{fma}\left(\log \log a, 3, \mathsf{fma}\left(\log z, y, -\log a\right) - b\right)} \cdot x, \left(\left(\left(\log a \cdot \log a\right) \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)\right) \cdot x\right) \cdot 0.5\right)}{y}, x \cdot \frac{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right) \cdot \log a}{y}\right), t, x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto \frac{\frac{1}{6} \cdot \frac{a \cdot \left({t}^{3} \cdot \left(x \cdot e^{\left(3 \cdot \log \log a + y \cdot \log z\right) - \left(b + \log a\right)}\right)\right)}{y} + \left(t \cdot \left(\frac{1}{2} \cdot \frac{t \cdot \left(x \cdot \left(e^{y \cdot \log z - b} \cdot {\log a}^{2}\right)\right)}{y} + \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{y \cdot \log z - b}}{y}\right)}{\color{blue}{a}} \]

   7. Applied rewrites 26.1%

      \[\leadsto \frac{\mathsf{fma}\left(0.16666666666666666, \frac{a \cdot \left(\left(\left(t \cdot t\right) \cdot t\right) \cdot \left(x \cdot e^{\mathsf{fma}\left(3, \log \log a, y \cdot \log z\right) - \left(b + \log a\right)}\right)\right)}{y}, \mathsf{fma}\left(t, \mathsf{fma}\left(0.5, \frac{t \cdot \left(x \cdot \left(e^{y \cdot \log z - b} \cdot \left(\log a \cdot \log a\right)\right)\right)}{y}, \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \log a\right)}{y}\right), \frac{x \cdot e^{y \cdot \log z - b}}{y}\right)\right)}{\color{blue}{a}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]
   9. Step-by-step derivation

      1. lift-log.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      4. lift-exp.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

      6. lift-/.f64 80.6

         \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

   10. Applied rewrites 80.6%

       \[\leadsto \frac{\frac{x \cdot e^{y \cdot \log z - b}}{y}}{a} \]

   11. Taylor expanded in y around 0

       \[\leadsto \frac{\frac{x \cdot e^{\mathsf{neg}\left(b\right)}}{y}}{a} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{\frac{x \cdot e^{\mathsf{neg}\left(b\right)}}{y}}{a} \]

       2. lift-neg.f64 N/A

          \[\leadsto \frac{\frac{x \cdot e^{-b}}{y}}{a} \]

       3. lift-exp.f64 59.6

          \[\leadsto \frac{\frac{x \cdot e^{-b}}{y}}{a} \]

   13. Applied rewrites 59.6%

       \[\leadsto \frac{\frac{x \cdot e^{-b}}{y}}{a} \]

   if 4.9999999999999997e32 < x

   1. Initial program 99.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{t \cdot \left(t \cdot \left(\frac{1}{6} \cdot \frac{t \cdot \left(x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{3}\right)\right)}{y} + \frac{1}{2} \cdot \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{2}\right)}{y}\right) + \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]

   4. Applied rewrites 32.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(0.16666666666666666 \cdot t, e^{\mathsf{fma}\left(\log \log a, 3, \mathsf{fma}\left(\log z, y, -\log a\right) - b\right)} \cdot x, \left(\left(\left(\log a \cdot \log a\right) \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)\right) \cdot x\right) \cdot 0.5\right)}{y}, x \cdot \frac{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right) \cdot \log a}{y}\right), t, x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot \color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      6. lift-log.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      7. lower-*.f64 72.1

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   7. Applied rewrites 72.1%

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\mathsf{neg}\left(b\right)}}{a \cdot y} \]
   9. Step-by-step derivation

      1. lift-neg.f64 N/A

         \[\leadsto \frac{x \cdot e^{-b}}{a \cdot y} \]

      2. lift-exp.f64 53.6

         \[\leadsto \frac{x \cdot e^{-b}}{a \cdot y} \]

   10. Applied rewrites 53.6%

       \[\leadsto \frac{x \cdot e^{-b}}{a \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 57.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3:\\ \;\;\;\;\frac{x \cdot \mathsf{fma}\left(-1, \frac{b}{a}, \frac{1}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- b))) y)))
   (if (<= b -1.4e+33)
     t_1
     (if (<= b 3.0) (/ (* x (fma -1.0 (/ b a) (/ 1.0 a))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(-b)) / y;
	double tmp;
	if (b <= -1.4e+33) {
		tmp = t_1;
	} else if (b <= 3.0) {
		tmp = (x * fma(-1.0, (b / a), (1.0 / a))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(-b))) / y)
	tmp = 0.0
	if (b <= -1.4e+33)
		tmp = t_1;
	elseif (b <= 3.0)
		tmp = Float64(Float64(x * fma(-1.0, Float64(b / a), Float64(1.0 / a))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[(-b)], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.4e+33], t$95$1, If[LessEqual[b, 3.0], N[(N[(x * N[(-1.0 * N[(b / a), $MachinePrecision] + N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4e33 or 3 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in b around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot e^{\mathsf{neg}\left(b\right)}}{y} \]

      2. lower-neg.f64 79.0

         \[\leadsto \frac{x \cdot e^{-b}}{y} \]

   4. Applied rewrites 79.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   if -1.4e33 < b < 3

   1. Initial program 96.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 72.5

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 72.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{\color{blue}{a}}}{y} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      3. lift-neg.f64 40.6

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 40.6%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \left(-1 \cdot \frac{b}{a} + \frac{1}{\color{blue}{a}}\right)}{y} \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \frac{x \cdot \mathsf{fma}\left(-1, \frac{b}{a}, \frac{1}{a}\right)}{y} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \mathsf{fma}\left(-1, \frac{b}{a}, \frac{1}{a}\right)}{y} \]

      3. lower-/.f64 38.7

         \[\leadsto \frac{x \cdot \mathsf{fma}\left(-1, \frac{b}{a}, \frac{1}{a}\right)}{y} \]

   10. Applied rewrites 38.7%

       \[\leadsto \frac{x \cdot \mathsf{fma}\left(-1, \frac{b}{\color{blue}{a}}, \frac{1}{a}\right)}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 57.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3:\\ \;\;\;\;\frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- b))) y)))
   (if (<= b -1.4e+33)
     t_1
     (if (<= b 3.0) (/ (* x (/ (+ 1.0 (* -1.0 b)) a)) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(-b)) / y;
	double tmp;
	if (b <= -1.4e+33) {
		tmp = t_1;
	} else if (b <= 3.0) {
		tmp = (x * ((1.0 + (-1.0 * b)) / a)) / y;
	} 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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp(-b)) / y
    if (b <= (-1.4d+33)) then
        tmp = t_1
    else if (b <= 3.0d0) then
        tmp = (x * ((1.0d0 + ((-1.0d0) * b)) / a)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp(-b)) / y;
	double tmp;
	if (b <= -1.4e+33) {
		tmp = t_1;
	} else if (b <= 3.0) {
		tmp = (x * ((1.0 + (-1.0 * b)) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(-b)) / y
	tmp = 0
	if b <= -1.4e+33:
		tmp = t_1
	elif b <= 3.0:
		tmp = (x * ((1.0 + (-1.0 * b)) / a)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(-b))) / y)
	tmp = 0.0
	if (b <= -1.4e+33)
		tmp = t_1;
	elseif (b <= 3.0)
		tmp = Float64(Float64(x * Float64(Float64(1.0 + Float64(-1.0 * b)) / a)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(-b)) / y;
	tmp = 0.0;
	if (b <= -1.4e+33)
		tmp = t_1;
	elseif (b <= 3.0)
		tmp = (x * ((1.0 + (-1.0 * b)) / a)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[(-b)], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.4e+33], t$95$1, If[LessEqual[b, 3.0], N[(N[(x * N[(N[(1.0 + N[(-1.0 * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4e33 or 3 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in b around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot e^{\mathsf{neg}\left(b\right)}}{y} \]

      2. lower-neg.f64 79.0

         \[\leadsto \frac{x \cdot e^{-b}}{y} \]

   4. Applied rewrites 79.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   if -1.4e33 < b < 3

   1. Initial program 96.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 72.5

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 72.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{\color{blue}{a}}}{y} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      3. lift-neg.f64 40.6

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 40.6%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]

      2. lower-*.f64 38.7

         \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]

   10. Applied rewrites 38.7%

       \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 35.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.4 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 1}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5.4e-39)
   (/ (* x (/ (+ 1.0 (* -1.0 b)) a)) y)
   (/ (* x 1.0) (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.4e-39) {
		tmp = (x * ((1.0 + (-1.0 * b)) / a)) / y;
	} else {
		tmp = (x * 1.0) / (a * y);
	}
	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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 5.4d-39) then
        tmp = (x * ((1.0d0 + ((-1.0d0) * b)) / a)) / y
    else
        tmp = (x * 1.0d0) / (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.4e-39) {
		tmp = (x * ((1.0 + (-1.0 * b)) / a)) / y;
	} else {
		tmp = (x * 1.0) / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5.4e-39:
		tmp = (x * ((1.0 + (-1.0 * b)) / a)) / y
	else:
		tmp = (x * 1.0) / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.4e-39)
		tmp = Float64(Float64(x * Float64(Float64(1.0 + Float64(-1.0 * b)) / a)) / y);
	else
		tmp = Float64(Float64(x * 1.0) / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5.4e-39)
		tmp = (x * ((1.0 + (-1.0 * b)) / a)) / y;
	else
		tmp = (x * 1.0) / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.4e-39], N[(N[(x * N[(N[(1.0 + N[(-1.0 * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * 1.0), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.4000000000000001e-39

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 77.8

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 77.8%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{\color{blue}{a}}}{y} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      3. lift-neg.f64 52.7

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 52.7%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]

      2. lower-*.f64 40.8

         \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]

   10. Applied rewrites 40.8%

       \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]

   if 5.4000000000000001e-39 < b

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{t \cdot \left(t \cdot \left(\frac{1}{6} \cdot \frac{t \cdot \left(x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{3}\right)\right)}{y} + \frac{1}{2} \cdot \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{2}\right)}{y}\right) + \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]

   4. Applied rewrites 41.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(0.16666666666666666 \cdot t, e^{\mathsf{fma}\left(\log \log a, 3, \mathsf{fma}\left(\log z, y, -\log a\right) - b\right)} \cdot x, \left(\left(\left(\log a \cdot \log a\right) \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)\right) \cdot x\right) \cdot 0.5\right)}{y}, x \cdot \frac{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right) \cdot \log a}{y}\right), t, x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot \color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      6. lift-log.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      7. lower-*.f64 73.8

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   7. Applied rewrites 73.8%

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]
   9. Step-by-step derivation

      1. lower-pow.f64 40.1

         \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

   10. Applied rewrites 40.1%

       \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

   11. Taylor expanded in y around 0

       \[\leadsto \frac{x \cdot 1}{a \cdot y} \]
   12. Step-by-step derivation

   13. Applied rewrites 21.6%

       \[\leadsto \frac{x \cdot 1}{a \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 31.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.05 \cdot 10^{-95}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 1}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.05e-95) (/ (* x (/ 1.0 a)) y) (/ (* x 1.0) (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.05e-95) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = (x * 1.0) / (a * y);
	}
	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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1.05d-95) then
        tmp = (x * (1.0d0 / a)) / y
    else
        tmp = (x * 1.0d0) / (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.05e-95) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = (x * 1.0) / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.05e-95:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = (x * 1.0) / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.05e-95)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(Float64(x * 1.0) / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.05e-95)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = (x * 1.0) / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.05e-95], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * 1.0), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.05e-95

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{-1 \cdot \log a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      3. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{\log a \cdot -1} \cdot e^{\color{blue}{y \cdot \log z} - b}\right)}{y} \]

      4. pow-to-exp N/A

         \[\leadsto \frac{x \cdot \left({a}^{-1} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      5. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot \color{blue}{e^{y \cdot \log z - b}}\right)}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\color{blue}{y \cdot \log z - b}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{y \cdot \log z - b}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

      12. lift-log.f64 80.5

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y} \]

   4. Applied rewrites 80.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{\color{blue}{a}}}{y} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      3. lift-neg.f64 59.1

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 59.1%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
   9. Step-by-step derivation

   10. Applied rewrites 31.7%

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]

   if 1.05e-95 < x

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{t \cdot \left(t \cdot \left(\frac{1}{6} \cdot \frac{t \cdot \left(x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{3}\right)\right)}{y} + \frac{1}{2} \cdot \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{2}\right)}{y}\right) + \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]

   4. Applied rewrites 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(0.16666666666666666 \cdot t, e^{\mathsf{fma}\left(\log \log a, 3, \mathsf{fma}\left(\log z, y, -\log a\right) - b\right)} \cdot x, \left(\left(\left(\log a \cdot \log a\right) \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)\right) \cdot x\right) \cdot 0.5\right)}{y}, x \cdot \frac{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right) \cdot \log a}{y}\right), t, x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot \color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      6. lift-log.f64 N/A

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

      7. lower-*.f64 71.4

         \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   7. Applied rewrites 71.4%

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]
   9. Step-by-step derivation

      1. lower-pow.f64 54.8

         \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

   10. Applied rewrites 54.8%

       \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

   11. Taylor expanded in y around 0

       \[\leadsto \frac{x \cdot 1}{a \cdot y} \]
   12. Step-by-step derivation

   13. Applied rewrites 30.9%

       \[\leadsto \frac{x \cdot 1}{a \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 31.2% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 1}{a \cdot y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (* x 1.0) (* a y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * 1.0) / (a * y);
}

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(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * 1.0d0) / (a * y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * 1.0) / (a * y);
}

Python

def code(x, y, z, t, a, b):
	return (x * 1.0) / (a * y)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * 1.0) / Float64(a * y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * 1.0) / (a * y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * 1.0), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.2%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in t around 0

   \[\leadsto \color{blue}{t \cdot \left(t \cdot \left(\frac{1}{6} \cdot \frac{t \cdot \left(x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{3}\right)\right)}{y} + \frac{1}{2} \cdot \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot {\log a}^{2}\right)}{y}\right) + \frac{x \cdot \left(e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b} \cdot \log a\right)}{y}\right) + \frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]

4. Applied rewrites 34.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(0.16666666666666666 \cdot t, e^{\mathsf{fma}\left(\log \log a, 3, \mathsf{fma}\left(\log z, y, -\log a\right) - b\right)} \cdot x, \left(\left(\left(\log a \cdot \log a\right) \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)\right) \cdot x\right) \cdot 0.5\right)}{y}, x \cdot \frac{\left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right) \cdot \log a}{y}\right), t, x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\right)} \]

5. Taylor expanded in t around 0

   \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]
6. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot \color{blue}{y}} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   3. lower-exp.f64 N/A

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   4. lower--.f64 N/A

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   5. lower-*.f64 N/A

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   6. lift-log.f64 N/A

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

   7. lower-*.f64 72.3

      \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{a \cdot y} \]

7. Applied rewrites 72.3%

   \[\leadsto \frac{x \cdot e^{y \cdot \log z - b}}{\color{blue}{a \cdot y}} \]

8. Taylor expanded in b around 0

   \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]
9. Step-by-step derivation

   1. lower-pow.f64 54.0

      \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

10. Applied rewrites 54.0%

    \[\leadsto \frac{x \cdot {z}^{y}}{a \cdot y} \]

11. Taylor expanded in y around 0

    \[\leadsto \frac{x \cdot 1}{a \cdot y} \]
12. Step-by-step derivation

13. Applied rewrites 31.2%

    \[\leadsto \frac{x \cdot 1}{a \cdot y} \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2025114 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))