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

Percentage Accurate: 98.5% → 98.5%

Time: 6.8s

Alternatives: 18

Speedup: 1.0×

• 47.6% 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: 98.5% 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: 98.5% 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 98.5%

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

Alternative 2: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+127}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))
   (if (<= t -5e+113)
     t_1
     (if (<= t 1.75e+127)
       (/ (* 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 <= -5e+113) {
		tmp = t_1;
	} else if (t <= 1.75e+127) {
		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 <= (-5d+113)) then
        tmp = t_1
    else if (t <= 1.75d+127) 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 <= -5e+113) {
		tmp = t_1;
	} else if (t <= 1.75e+127) {
		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 <= -5e+113:
		tmp = t_1
	elif t <= 1.75e+127:
		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 <= -5e+113)
		tmp = t_1;
	elseif (t <= 1.75e+127)
		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 <= -5e+113)
		tmp = t_1;
	elseif (t <= 1.75e+127)
		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, -5e+113], t$95$1, If[LessEqual[t, 1.75e+127], 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 < -5e113 or 1.74999999999999989e127 < t

   1. Initial program 98.5%

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

   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 80.5

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

   4. Applied rewrites 80.5%

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

   if -5e113 < t < 1.74999999999999989e127

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

Alternative 3: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))
   (if (<= t -5e+113)
     t_1
     (if (<= t 2e+126)
       (* 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 <= -5e+113) {
		tmp = t_1;
	} else if (t <= 2e+126) {
		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 <= (-5d+113)) then
        tmp = t_1
    else if (t <= 2d+126) 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 <= -5e+113) {
		tmp = t_1;
	} else if (t <= 2e+126) {
		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 <= -5e+113:
		tmp = t_1
	elif t <= 2e+126:
		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 <= -5e+113)
		tmp = t_1;
	elseif (t <= 2e+126)
		tmp = Float64(x * Float64(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 <= -5e+113)
		tmp = t_1;
	elseif (t <= 2e+126)
		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, -5e+113], t$95$1, If[LessEqual[t, 2e+126], N[(x * N[(N[(N[(1.0 / a), $MachinePrecision] * N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5e113 or 1.99999999999999985e126 < t

   1. Initial program 98.5%

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

   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 80.5

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

   4. Applied rewrites 80.5%

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

   if -5e113 < t < 1.99999999999999985e126

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

Alternative 4: 89.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log z \cdot y}}{y}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.04 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (* (log z) y))) y)))
   (if (<= y -4e+112)
     t_1
     (if (<= y 2.04e+28) (/ (* 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 <= -4e+112) {
		tmp = t_1;
	} else if (y <= 2.04e+28) {
		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 <= (-4d+112)) then
        tmp = t_1
    else if (y <= 2.04d+28) 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 <= -4e+112) {
		tmp = t_1;
	} else if (y <= 2.04e+28) {
		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 <= -4e+112:
		tmp = t_1
	elif y <= 2.04e+28:
		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 <= -4e+112)
		tmp = t_1;
	elseif (y <= 2.04e+28)
		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 <= -4e+112)
		tmp = t_1;
	elseif (y <= 2.04e+28)
		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, -4e+112], t$95$1, If[LessEqual[y, 2.04e+28], 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 < -3.9999999999999997e112 or 2.04e28 < y

   1. Initial program 98.5%

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

   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 48.3

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

   4. Applied rewrites 48.3%

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

   if -3.9999999999999997e112 < y < 2.04e28

   1. Initial program 98.5%

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

   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 80.5

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

   4. Applied rewrites 80.5%

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

Alternative 5: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -200:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -4e+41)
     t_2
     (if (<= t_1 -200.0)
       (/ (* x (/ (pow z y) a)) y)
       (if (<= t_1 2e+22) (/ (* 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 <= -4e+41) {
		tmp = t_2;
	} else if (t_1 <= -200.0) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else if (t_1 <= 2e+22) {
		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 <= (-4d+41)) then
        tmp = t_2
    else if (t_1 <= (-200.0d0)) then
        tmp = (x * ((z ** y) / a)) / y
    else if (t_1 <= 2d+22) 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 <= -4e+41) {
		tmp = t_2;
	} else if (t_1 <= -200.0) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else if (t_1 <= 2e+22) {
		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 <= -4e+41:
		tmp = t_2
	elif t_1 <= -200.0:
		tmp = (x * (math.pow(z, y) / a)) / y
	elif t_1 <= 2e+22:
		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 <= -4e+41)
		tmp = t_2;
	elseif (t_1 <= -200.0)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	elseif (t_1 <= 2e+22)
		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 <= -4e+41)
		tmp = t_2;
	elseif (t_1 <= -200.0)
		tmp = (x * ((z ^ y) / a)) / y;
	elseif (t_1 <= 2e+22)
		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, -4e+41], t$95$2, If[LessEqual[t$95$1, -200.0], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+22], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -4.00000000000000002e41 or 2e22 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.5%

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

   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 47.7

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

   4. Applied rewrites 47.7%

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

   if -4.00000000000000002e41 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -200

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower-pow.f64 59.7

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

   7. Applied rewrites 59.7%

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

   if -200 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e22

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

Alternative 6: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{e^{-b}}{a}\\ t_3 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+41}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq -325:\\ \;\;\;\;\frac{t\_2}{y} \cdot x\\ \mathbf{elif}\;t\_1 \leq -200:\\ \;\;\;\;\frac{x \cdot e^{\log z \cdot y}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\frac{x \cdot t\_2}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a)))
        (t_2 (/ (exp (- b)) a))
        (t_3 (/ (* x (exp (* (log a) t))) y)))
   (if (<= t_1 -4e+41)
     t_3
     (if (<= t_1 -325.0)
       (* (/ t_2 y) x)
       (if (<= t_1 -200.0)
         (/ (* x (exp (* (log z) y))) y)
         (if (<= t_1 2e+22) (/ (* x t_2) y) t_3))))))

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 = exp(-b) / a;
	double t_3 = (x * exp((log(a) * t))) / y;
	double tmp;
	if (t_1 <= -4e+41) {
		tmp = t_3;
	} else if (t_1 <= -325.0) {
		tmp = (t_2 / y) * x;
	} else if (t_1 <= -200.0) {
		tmp = (x * exp((log(z) * y))) / y;
	} else if (t_1 <= 2e+22) {
		tmp = (x * t_2) / y;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (t - 1.0d0) * log(a)
    t_2 = exp(-b) / a
    t_3 = (x * exp((log(a) * t))) / y
    if (t_1 <= (-4d+41)) then
        tmp = t_3
    else if (t_1 <= (-325.0d0)) then
        tmp = (t_2 / y) * x
    else if (t_1 <= (-200.0d0)) then
        tmp = (x * exp((log(z) * y))) / y
    else if (t_1 <= 2d+22) then
        tmp = (x * t_2) / y
    else
        tmp = t_3
    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 = Math.exp(-b) / a;
	double t_3 = (x * Math.exp((Math.log(a) * t))) / y;
	double tmp;
	if (t_1 <= -4e+41) {
		tmp = t_3;
	} else if (t_1 <= -325.0) {
		tmp = (t_2 / y) * x;
	} else if (t_1 <= -200.0) {
		tmp = (x * Math.exp((Math.log(z) * y))) / y;
	} else if (t_1 <= 2e+22) {
		tmp = (x * t_2) / y;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	t_2 = math.exp(-b) / a
	t_3 = (x * math.exp((math.log(a) * t))) / y
	tmp = 0
	if t_1 <= -4e+41:
		tmp = t_3
	elif t_1 <= -325.0:
		tmp = (t_2 / y) * x
	elif t_1 <= -200.0:
		tmp = (x * math.exp((math.log(z) * y))) / y
	elif t_1 <= 2e+22:
		tmp = (x * t_2) / y
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	t_2 = Float64(exp(Float64(-b)) / a)
	t_3 = Float64(Float64(x * exp(Float64(log(a) * t))) / y)
	tmp = 0.0
	if (t_1 <= -4e+41)
		tmp = t_3;
	elseif (t_1 <= -325.0)
		tmp = Float64(Float64(t_2 / y) * x);
	elseif (t_1 <= -200.0)
		tmp = Float64(Float64(x * exp(Float64(log(z) * y))) / y);
	elseif (t_1 <= 2e+22)
		tmp = Float64(Float64(x * t_2) / y);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	t_2 = exp(-b) / a;
	t_3 = (x * exp((log(a) * t))) / y;
	tmp = 0.0;
	if (t_1 <= -4e+41)
		tmp = t_3;
	elseif (t_1 <= -325.0)
		tmp = (t_2 / y) * x;
	elseif (t_1 <= -200.0)
		tmp = (x * exp((log(z) * y))) / y;
	elseif (t_1 <= 2e+22)
		tmp = (x * t_2) / y;
	else
		tmp = t_3;
	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[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[Exp[N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+41], t$95$3, If[LessEqual[t$95$1, -325.0], N[(N[(t$95$2 / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, -200.0], N[(N[(x * N[Exp[N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+22], N[(N[(x * t$95$2), $MachinePrecision] / y), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -4.00000000000000002e41 or 2e22 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.5%

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

   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 47.7

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

   4. Applied rewrites 47.7%

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

   if -4.00000000000000002e41 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -325

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 59.7

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

   9. Applied rewrites 59.7%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 59.7

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

   11. Applied rewrites 59.7%

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

   if -325 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -200

   1. Initial program 98.5%

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

   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 48.3

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

   4. Applied rewrites 48.3%

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

   if -200 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e22

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

Alternative 7: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ t_2 := \left(t - 1\right) \cdot \log a\\ t_3 := \frac{\frac{e^{-b}}{a}}{y} \cdot x\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 380:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 550:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+19}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (* (log a) t))) y))
        (t_2 (* (- t 1.0) (log a)))
        (t_3 (* (/ (/ (exp (- b)) a) y) x)))
   (if (<= t_2 -4e+41)
     t_1
     (if (<= t_2 380.0)
       t_3
       (if (<= t_2 550.0)
         (/ (* (pow z y) x) (* a y))
         (if (<= t_2 2e+19) t_3 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))) / y;
	double t_2 = (t - 1.0) * log(a);
	double t_3 = ((exp(-b) / a) / y) * x;
	double tmp;
	if (t_2 <= -4e+41) {
		tmp = t_1;
	} else if (t_2 <= 380.0) {
		tmp = t_3;
	} else if (t_2 <= 550.0) {
		tmp = (pow(z, y) * x) / (a * y);
	} else if (t_2 <= 2e+19) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * exp((log(a) * t))) / y
    t_2 = (t - 1.0d0) * log(a)
    t_3 = ((exp(-b) / a) / y) * x
    if (t_2 <= (-4d+41)) then
        tmp = t_1
    else if (t_2 <= 380.0d0) then
        tmp = t_3
    else if (t_2 <= 550.0d0) then
        tmp = ((z ** y) * x) / (a * y)
    else if (t_2 <= 2d+19) then
        tmp = t_3
    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))) / y;
	double t_2 = (t - 1.0) * Math.log(a);
	double t_3 = ((Math.exp(-b) / a) / y) * x;
	double tmp;
	if (t_2 <= -4e+41) {
		tmp = t_1;
	} else if (t_2 <= 380.0) {
		tmp = t_3;
	} else if (t_2 <= 550.0) {
		tmp = (Math.pow(z, y) * x) / (a * y);
	} else if (t_2 <= 2e+19) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp((math.log(a) * t))) / y
	t_2 = (t - 1.0) * math.log(a)
	t_3 = ((math.exp(-b) / a) / y) * x
	tmp = 0
	if t_2 <= -4e+41:
		tmp = t_1
	elif t_2 <= 380.0:
		tmp = t_3
	elif t_2 <= 550.0:
		tmp = (math.pow(z, y) * x) / (a * y)
	elif t_2 <= 2e+19:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(log(a) * t))) / y)
	t_2 = Float64(Float64(t - 1.0) * log(a))
	t_3 = Float64(Float64(Float64(exp(Float64(-b)) / a) / y) * x)
	tmp = 0.0
	if (t_2 <= -4e+41)
		tmp = t_1;
	elseif (t_2 <= 380.0)
		tmp = t_3;
	elseif (t_2 <= 550.0)
		tmp = Float64(Float64((z ^ y) * x) / Float64(a * y));
	elseif (t_2 <= 2e+19)
		tmp = t_3;
	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))) / y;
	t_2 = (t - 1.0) * log(a);
	t_3 = ((exp(-b) / a) / y) * x;
	tmp = 0.0;
	if (t_2 <= -4e+41)
		tmp = t_1;
	elseif (t_2 <= 380.0)
		tmp = t_3;
	elseif (t_2 <= 550.0)
		tmp = ((z ^ y) * x) / (a * y);
	elseif (t_2 <= 2e+19)
		tmp = t_3;
	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[a], $MachinePrecision] * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+41], t$95$1, If[LessEqual[t$95$2, 380.0], t$95$3, If[LessEqual[t$95$2, 550.0], N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+19], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -4.00000000000000002e41 or 2e19 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.5%

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

   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 47.7

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

   4. Applied rewrites 47.7%

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

   if -4.00000000000000002e41 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 380 or 550 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e19

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 59.7

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

   9. Applied rewrites 59.7%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 59.7

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

   11. Applied rewrites 59.7%

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

   if 380 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 550

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.1

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

   7. Applied rewrites 54.1%

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

Alternative 8: 73.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -7000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 900:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -7000000.0)
     t_1
     (if (<= b 900.0) (/ (* (pow z y) x) (* 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 <= -7000000.0) {
		tmp = t_1;
	} else if (b <= 900.0) {
		tmp = (pow(z, y) * x) / (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 <= (-7000000.0d0)) then
        tmp = t_1
    else if (b <= 900.0d0) then
        tmp = ((z ** y) * x) / (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 <= -7000000.0) {
		tmp = t_1;
	} else if (b <= 900.0) {
		tmp = (Math.pow(z, y) * x) / (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 <= -7000000.0:
		tmp = t_1
	elif b <= 900.0:
		tmp = (math.pow(z, y) * x) / (a * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -7000000.0)
		tmp = t_1;
	elseif (b <= 900.0)
		tmp = Float64(Float64((z ^ y) * x) / Float64(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 <= -7000000.0)
		tmp = t_1;
	elseif (b <= 900.0)
		tmp = ((z ^ y) * x) / (a * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7000000.0], t$95$1, If[LessEqual[b, 900.0], N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7e6 or 900 < b

   1. Initial program 98.5%

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

   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 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 48.7

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

   6. Applied rewrites 48.7%

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

   if -7e6 < b < 900

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.1

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

   7. Applied rewrites 54.1%

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

Alternative 9: 60.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-b}\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{t\_1}{a}}{y} \cdot x\\ \mathbf{elif}\;b \leq 3.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t\_1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (- b))))
   (if (<= b -2.8e-11)
     (* (/ (/ t_1 a) y) x)
     (if (<= b 3.45e+41)
       (/ (/ (fma (* (log z) y) x x) a) y)
       (* x (/ t_1 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 <= -2.8e-11) {
		tmp = ((t_1 / a) / y) * x;
	} else if (b <= 3.45e+41) {
		tmp = (fma((log(z) * y), x, x) / a) / y;
	} else {
		tmp = x * (t_1 / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(-b))
	tmp = 0.0
	if (b <= -2.8e-11)
		tmp = Float64(Float64(Float64(t_1 / a) / y) * x);
	elseif (b <= 3.45e+41)
		tmp = Float64(Float64(fma(Float64(log(z) * y), x, x) / a) / y);
	else
		tmp = Float64(x * Float64(t_1 / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[(-b)], $MachinePrecision]}, If[LessEqual[b, -2.8e-11], N[(N[(N[(t$95$1 / a), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 3.45e+41], N[(N[(N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] * x + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.8e-11

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 59.7

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

   9. Applied rewrites 59.7%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 59.7

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

   11. Applied rewrites 59.7%

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

   if -2.8e-11 < b < 3.4500000000000001e41

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.1

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

   7. Applied rewrites 54.1%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(y \cdot \log z, x, x\right)}{a}}{y} \]

      7. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y} \]

      9. lower-log.f64 31.4

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y} \]

   10. Applied rewrites 31.4%

       \[\leadsto \frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y} \]

   if 3.4500000000000001e41 < b

   1. Initial program 98.5%

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

   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 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 48.7

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

   6. Applied rewrites 48.7%

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

Alternative 10: 59.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -2.1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -2.1)
     t_1
     (if (<= b 3.45e+41) (/ (/ (fma (* (log z) y) x x) 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 <= -2.1) {
		tmp = t_1;
	} else if (b <= 3.45e+41) {
		tmp = (fma((log(z) * y), x, x) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -2.1)
		tmp = t_1;
	elseif (b <= 3.45e+41)
		tmp = Float64(Float64(fma(Float64(log(z) * y), x, x) / a) / y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.1], t$95$1, If[LessEqual[b, 3.45e+41], N[(N[(N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] * x + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.10000000000000009 or 3.4500000000000001e41 < b

   1. Initial program 98.5%

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

   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 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 48.7

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

   6. Applied rewrites 48.7%

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

   if -2.10000000000000009 < b < 3.4500000000000001e41

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.1

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

   7. Applied rewrites 54.1%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(y \cdot \log z, x, x\right)}{a}}{y} \]

      7. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y} \]

      9. lower-log.f64 31.4

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y} \]

   10. Applied rewrites 31.4%

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

Alternative 11: 59.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.85:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 350:\\ \;\;\;\;\frac{\mathsf{fma}\left(\log z, y, 1\right) \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -1.85)
     t_1
     (if (<= b 350.0) (/ (* (fma (log z) y 1.0) x) (* 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 <= -1.85) {
		tmp = t_1;
	} else if (b <= 350.0) {
		tmp = (fma(log(z), y, 1.0) * x) / (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -1.85)
		tmp = t_1;
	elseif (b <= 350.0)
		tmp = Float64(Float64(fma(log(z), y, 1.0) * x) / Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.85], t$95$1, If[LessEqual[b, 350.0], N[(N[(N[(N[Log[z], $MachinePrecision] * y + 1.0), $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8500000000000001 or 350 < b

   1. Initial program 98.5%

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

   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 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 48.7

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

   6. Applied rewrites 48.7%

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

   if -1.8500000000000001 < b < 350

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.1

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

   7. Applied rewrites 54.1%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 29.7

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

   10. Applied rewrites 29.7%

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

Alternative 12: 59.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.85:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -1.85) t_1 (if (<= b 4.7e-14) (/ (* x (/ 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 <= -1.85) {
		tmp = t_1;
	} else if (b <= 4.7e-14) {
		tmp = (x * (1.0 / 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 <= (-1.85d0)) then
        tmp = t_1
    else if (b <= 4.7d-14) then
        tmp = (x * (1.0d0 / 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 <= -1.85) {
		tmp = t_1;
	} else if (b <= 4.7e-14) {
		tmp = (x * (1.0 / 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 <= -1.85:
		tmp = t_1
	elif b <= 4.7e-14:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -1.85)
		tmp = t_1;
	elseif (b <= 4.7e-14)
		tmp = Float64(Float64(x * Float64(1.0 / 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 <= -1.85)
		tmp = t_1;
	elseif (b <= 4.7e-14)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.85], t$95$1, If[LessEqual[b, 4.7e-14], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8500000000000001 or 4.7000000000000002e-14 < b

   1. Initial program 98.5%

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

   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 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 48.7

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

   6. Applied rewrites 48.7%

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

   if -1.8500000000000001 < b < 4.7000000000000002e-14

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 31.1%

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

Alternative 13: 59.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \frac{e^{-b}}{a}}{y} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * (exp(-b) / 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 * (exp(-b) / a)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

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 81.5

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

4. Applied rewrites 81.5%

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

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 60.1

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

7. Applied rewrites 60.1%

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

Alternative 14: 38.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-285}:\\ \;\;\;\;\frac{x \cdot \frac{\left(b \cdot b\right) \cdot 0.5}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.5e-285) (/ (* x (/ (* (* b b) 0.5) a)) y) (/ x (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.5e-285) {
		tmp = (x * (((b * b) * 0.5) / a)) / y;
	} else {
		tmp = x / (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 <= (-8.5d-285)) then
        tmp = (x * (((b * b) * 0.5d0) / a)) / y
    else
        tmp = x / (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 <= -8.5e-285) {
		tmp = (x * (((b * b) * 0.5) / a)) / y;
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.5e-285:
		tmp = (x * (((b * b) * 0.5) / a)) / y
	else:
		tmp = x / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.5e-285)
		tmp = Float64(Float64(x * Float64(Float64(Float64(b * b) * 0.5) / a)) / y);
	else
		tmp = Float64(x / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.5e-285)
		tmp = (x * (((b * b) * 0.5) / a)) / y;
	else
		tmp = x / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.5e-285], N[(N[(x * N[(N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.49999999999999979e-285

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 39.4

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

   10. Applied rewrites 39.4%

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

   11. Taylor expanded in b around inf

       \[\leadsto \frac{x \cdot \frac{\frac{1}{2} \cdot {b}^{2}}{a}}{y} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{x \cdot \frac{{b}^{2} \cdot \frac{1}{2}}{a}}{y} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \frac{{b}^{2} \cdot \frac{1}{2}}{a}}{y} \]

       3. unpow2 N/A

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

       4. lower-*.f64 36.7

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

   13. Applied rewrites 36.7%

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

   if -8.49999999999999979e-285 < b

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.1

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

   7. Applied rewrites 54.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 30.9%

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

Alternative 15: 35.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{x \cdot \frac{\left(-b\right) + 1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.8e-105) (/ (* x (/ (+ (- b) 1.0) a)) y) (/ x (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.8e-105) {
		tmp = (x * ((-b + 1.0) / a)) / y;
	} else {
		tmp = x / (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 <= (-3.8d-105)) then
        tmp = (x * ((-b + 1.0d0) / a)) / y
    else
        tmp = x / (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 <= -3.8e-105) {
		tmp = (x * ((-b + 1.0) / a)) / y;
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.8e-105:
		tmp = (x * ((-b + 1.0) / a)) / y
	else:
		tmp = x / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.8e-105)
		tmp = Float64(Float64(x * Float64(Float64(Float64(-b) + 1.0) / a)) / y);
	else
		tmp = Float64(x / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.8e-105)
		tmp = (x * ((-b + 1.0) / a)) / y;
	else
		tmp = x / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.8e-105], N[(N[(x * N[(N[((-b) + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.7999999999999998e-105

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

   8. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 32.4

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

   10. Applied rewrites 32.4%

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

   if -3.7999999999999998e-105 < b

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.1

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

   7. Applied rewrites 54.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 30.9%

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

Alternative 16: 35.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{\frac{\left(-b\right) + 1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.15e+18) (* x (/ (/ (+ (- b) 1.0) a) y)) (/ x (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.15e+18) {
		tmp = x * (((-b + 1.0) / a) / y);
	} else {
		tmp = x / (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 <= (-2.15d+18)) then
        tmp = x * (((-b + 1.0d0) / a) / y)
    else
        tmp = x / (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 <= -2.15e+18) {
		tmp = x * (((-b + 1.0) / a) / y);
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.15e+18:
		tmp = x * (((-b + 1.0) / a) / y)
	else:
		tmp = x / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.15e+18)
		tmp = Float64(x * Float64(Float64(Float64(Float64(-b) + 1.0) / a) / y));
	else
		tmp = Float64(x / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.15e+18)
		tmp = x * (((-b + 1.0) / a) / y);
	else
		tmp = x / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.15e+18], N[(x * N[(N[(N[((-b) + 1.0), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.15e18

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 59.7

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

   9. Applied rewrites 59.7%

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

   10. Taylor expanded in b around 0

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

       1. mul-1-neg N/A

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

       2. lift-neg.f64 N/A

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

       3. +-commutative N/A

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

       4. lower-+.f64 32.2

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

   12. Applied rewrites 32.2%

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

   if -2.15e18 < b

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.1

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

   7. Applied rewrites 54.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 30.9%

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

Alternative 17: 31.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -5 \cdot 10^{+90}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) -5e+90) (/ (* x (/ 1.0 a)) y) (/ x (* 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)) <= -5e+90) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x / (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)) <= (-5d+90)) then
        tmp = (x * (1.0d0 / a)) / y
    else
        tmp = x / (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)) <= -5e+90) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= -5e+90:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = x / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= -5e+90)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(x / 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)) <= -5e+90)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = x / (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], -5e+90], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5.0000000000000004e90

   1. Initial program 98.5%

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

   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 81.5

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

   4. Applied rewrites 81.5%

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

   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 60.1

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

   7. Applied rewrites 60.1%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 31.1%

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

   if -5.0000000000000004e90 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.1

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

   7. Applied rewrites 54.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 30.9%

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

Alternative 18: 30.9% accurate, 5.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (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 / (a * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

2. Taylor expanded in t around 0

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

   1. associate-/l* N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

4. Applied rewrites 81.4%

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

5. Taylor expanded in b around 0

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower-pow.f64 N/A

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

   5. lower-*.f64 54.1

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

7. Applied rewrites 54.1%

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

8. Taylor expanded in y around 0

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

10. Applied rewrites 30.9%

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

Reproduce

herbie shell --seed 2025123 
(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))