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

Percentage Accurate: 98.3% → 98.3%

Time: 15.2s

Alternatives: 24

Speedup: 1.0×

• 47.3% 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: 98.3% 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: 98.3% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Applied rewrites 98.3%

   \[\leadsto \frac{x \cdot e^{\color{blue}{\mathsf{fma}\left(\log a, t, \left(\log z \cdot y - \log a\right) - b\right)}}}{y} \]
4. Add Preprocessing

Alternative 2: 98.3% 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 98.3%

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

Alternative 3: 92.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -5 \cdot 10^{+123}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;t - 1 \leq 10000000000000:\\ \;\;\;\;\frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- t 1.0) -5e+123)
   (/ (* (pow a (- t 1.0)) x) y)
   (if (<= (- t 1.0) 10000000000000.0)
     (/ (* x (* (exp (- (* (log z) y) b)) (/ 1.0 a))) y)
     (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t - 1.0) <= -5e+123) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else if ((t - 1.0) <= 10000000000000.0) {
		tmp = (x * (exp(((log(z) * y) - b)) * (1.0 / a))) / y;
	} else {
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / 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) <= (-5d+123)) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else if ((t - 1.0d0) <= 10000000000000.0d0) then
        tmp = (x * (exp(((log(z) * y) - b)) * (1.0d0 / a))) / y
    else
        tmp = (x * exp(((log(a) * (t - 1.0d0)) - b))) / 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) <= -5e+123) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else if ((t - 1.0) <= 10000000000000.0) {
		tmp = (x * (Math.exp(((Math.log(z) * y) - b)) * (1.0 / a))) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t - 1.0) <= -5e+123:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	elif (t - 1.0) <= 10000000000000.0:
		tmp = (x * (math.exp(((math.log(z) * y) - b)) * (1.0 / a))) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t - 1.0) <= -5e+123)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	elseif (Float64(t - 1.0) <= 10000000000000.0)
		tmp = Float64(Float64(x * Float64(exp(Float64(Float64(log(z) * y) - b)) * Float64(1.0 / a))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t - 1.0) <= -5e+123)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	elseif ((t - 1.0) <= 10000000000000.0)
		tmp = (x * (exp(((log(z) * y) - b)) * (1.0 / a))) / y;
	else
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t - 1.0), $MachinePrecision], -5e+123], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t - 1.0), $MachinePrecision], 10000000000000.0], N[(N[(x * N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -4.99999999999999974e123

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 84.3

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

   4. Applied rewrites 84.3%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lift--.f64 87.0

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

   7. Applied rewrites 87.0%

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

   if -4.99999999999999974e123 < (-.f64 t #s(literal 1 binary64)) < 1e13

   1. Initial program 97.3%

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

   2. Taylor expanded in 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. +-commutative N/A

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

      3. exp-sum N/A

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. inv-pow N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 N/A

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

      13. unpow1 N/A

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

      14. metadata-eval N/A

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

      15. pow-flip N/A

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

      16. inv-pow N/A

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

      17. unpow-1 N/A

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

      18. lower-/.f64 N/A

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

      19. unpow-1 N/A

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

      20. inv-pow N/A

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

   4. Applied rewrites 94.5%

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

   if 1e13 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 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 89.9

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

   4. Applied rewrites 89.9%

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

Alternative 4: 88.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6600000000000:\\ \;\;\;\;\frac{e^{\log z \cdot y - b} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))
   (if (<= t -5.6e-62)
     t_1
     (if (<= t 6600000000000.0)
       (/ (* (exp (- (* (log z) y) b)) 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(((log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -5.6e-62) {
		tmp = t_1;
	} else if (t <= 6600000000000.0) {
		tmp = (exp(((log(z) * y) - b)) * 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(((log(a) * (t - 1.0d0)) - b))) / y
    if (t <= (-5.6d-62)) then
        tmp = t_1
    else if (t <= 6600000000000.0d0) then
        tmp = (exp(((log(z) * y) - b)) * 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(((Math.log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -5.6e-62) {
		tmp = t_1;
	} else if (t <= 6600000000000.0) {
		tmp = (Math.exp(((Math.log(z) * y) - b)) * x) / (a * 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 <= -5.6e-62:
		tmp = t_1
	elif t <= 6600000000000.0:
		tmp = (math.exp(((math.log(z) * y) - b)) * x) / (a * 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 <= -5.6e-62)
		tmp = t_1;
	elseif (t <= 6600000000000.0)
		tmp = Float64(Float64(exp(Float64(Float64(log(z) * y) - b)) * 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(((log(a) * (t - 1.0)) - b))) / y;
	tmp = 0.0;
	if (t <= -5.6e-62)
		tmp = t_1;
	elseif (t <= 6600000000000.0)
		tmp = (exp(((log(z) * y) - b)) * 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[(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, -5.6e-62], t$95$1, If[LessEqual[t, 6600000000000.0], N[(N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.60000000000000005e-62 or 6.6e12 < t

   1. Initial program 99.7%

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

   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 88.1

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

   4. Applied rewrites 88.1%

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

   if -5.60000000000000005e-62 < t < 6.6e12

   1. Initial program 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   6. Applied rewrites 88.6%

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

Alternative 5: 88.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log z \cdot y}}{y}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (* (log z) y))) y)))
   (if (<= y -2.3e+71)
     t_1
     (if (<= y 5.5e+46) (/ (* 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 <= -2.3e+71) {
		tmp = t_1;
	} else if (y <= 5.5e+46) {
		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 <= (-2.3d+71)) then
        tmp = t_1
    else if (y <= 5.5d+46) 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 <= -2.3e+71) {
		tmp = t_1;
	} else if (y <= 5.5e+46) {
		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 <= -2.3e+71:
		tmp = t_1
	elif y <= 5.5e+46:
		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 <= -2.3e+71)
		tmp = t_1;
	elseif (y <= 5.5e+46)
		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 <= -2.3e+71)
		tmp = t_1;
	elseif (y <= 5.5e+46)
		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, -2.3e+71], t$95$1, If[LessEqual[y, 5.5e+46], 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 < -2.3000000000000002e71 or 5.4999999999999998e46 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 82.8

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

   4. Applied rewrites 82.8%

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

   if -2.3000000000000002e71 < y < 5.4999999999999998e46

   1. Initial program 97.2%

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

   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 93.2

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

   4. Applied rewrites 93.2%

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

Alternative 6: 84.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log z \cdot y}}{y}\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+45}:\\ \;\;\;\;e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (* (log z) y))) y)))
   (if (<= y -9.2e+70)
     t_1
     (if (<= y 9e+45) (* (exp (- (* (log a) (- t 1.0)) b)) (/ x 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 <= -9.2e+70) {
		tmp = t_1;
	} else if (y <= 9e+45) {
		tmp = exp(((log(a) * (t - 1.0)) - b)) * (x / 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 <= (-9.2d+70)) then
        tmp = t_1
    else if (y <= 9d+45) then
        tmp = exp(((log(a) * (t - 1.0d0)) - b)) * (x / 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 <= -9.2e+70) {
		tmp = t_1;
	} else if (y <= 9e+45) {
		tmp = Math.exp(((Math.log(a) * (t - 1.0)) - b)) * (x / 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 <= -9.2e+70:
		tmp = t_1
	elif y <= 9e+45:
		tmp = math.exp(((math.log(a) * (t - 1.0)) - b)) * (x / 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 <= -9.2e+70)
		tmp = t_1;
	elseif (y <= 9e+45)
		tmp = Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) * Float64(x / 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 <= -9.2e+70)
		tmp = t_1;
	elseif (y <= 9e+45)
		tmp = exp(((log(a) * (t - 1.0)) - b)) * (x / 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, -9.2e+70], t$95$1, If[LessEqual[y, 9e+45], N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.19999999999999975e70 or 8.9999999999999997e45 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 82.7

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

   4. Applied rewrites 82.7%

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

   if -9.19999999999999975e70 < y < 8.9999999999999997e45

   1. Initial program 97.2%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 85.5

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

   4. Applied rewrites 85.5%

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

Alternative 7: 75.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log z \cdot y}}{y}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \frac{\frac{e^{-b}}{y}}{a}\\ \mathbf{elif}\;y \leq 410000000:\\ \;\;\;\;{a}^{\left(t - 1\right)} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (* (log z) y))) y)))
   (if (<= y -3.8e+46)
     t_1
     (if (<= y 9.2e-139)
       (* x (/ (/ (exp (- b)) y) a))
       (if (<= y 410000000.0) (* (pow a (- t 1.0)) (/ x 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 <= -3.8e+46) {
		tmp = t_1;
	} else if (y <= 9.2e-139) {
		tmp = x * ((exp(-b) / y) / a);
	} else if (y <= 410000000.0) {
		tmp = pow(a, (t - 1.0)) * (x / 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 <= (-3.8d+46)) then
        tmp = t_1
    else if (y <= 9.2d-139) then
        tmp = x * ((exp(-b) / y) / a)
    else if (y <= 410000000.0d0) then
        tmp = (a ** (t - 1.0d0)) * (x / 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 <= -3.8e+46) {
		tmp = t_1;
	} else if (y <= 9.2e-139) {
		tmp = x * ((Math.exp(-b) / y) / a);
	} else if (y <= 410000000.0) {
		tmp = Math.pow(a, (t - 1.0)) * (x / 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 <= -3.8e+46:
		tmp = t_1
	elif y <= 9.2e-139:
		tmp = x * ((math.exp(-b) / y) / a)
	elif y <= 410000000.0:
		tmp = math.pow(a, (t - 1.0)) * (x / 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 <= -3.8e+46)
		tmp = t_1;
	elseif (y <= 9.2e-139)
		tmp = Float64(x * Float64(Float64(exp(Float64(-b)) / y) / a));
	elseif (y <= 410000000.0)
		tmp = Float64((a ^ Float64(t - 1.0)) * Float64(x / 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 <= -3.8e+46)
		tmp = t_1;
	elseif (y <= 9.2e-139)
		tmp = x * ((exp(-b) / y) / a);
	elseif (y <= 410000000.0)
		tmp = (a ^ (t - 1.0)) * (x / 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, -3.8e+46], t$95$1, If[LessEqual[y, 9.2e-139], N[(x * N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 410000000.0], N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999999e46 or 4.1e8 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 80.9

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

   4. Applied rewrites 80.9%

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

   if -3.7999999999999999e46 < y < 9.2000000000000005e-139

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 84.9

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

   4. Applied rewrites 84.9%

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

   5. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. inv-pow N/A

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

      8. associate-/l/ N/A

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

      9. rem-exp-log N/A

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

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

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

      13. rem-exp-log N/A

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

      14. associate-/l/ N/A

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

      15. exp-neg N/A

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

      16. lower-/.f64 N/A

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

      17. lower-exp.f64 N/A

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

      18. lift-neg.f64 71.4

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

   7. Applied rewrites 71.4%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-exp.f64 N/A

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

      4. lift-neg.f64 N/A

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

      5. associate-/l/ N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-neg.f64 N/A

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

      11. lift-exp.f64 71.4

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

   9. Applied rewrites 71.4%

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

   if 9.2000000000000005e-139 < y < 4.1e8

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 91.5

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

   4. Applied rewrites 91.5%

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

   5. Taylor expanded in b around 0

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

      1. exp-to-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. lift--.f64 68.2

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

   7. Applied rewrites 68.2%

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

Alternative 8: 74.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (pow a (- t 1.0)) x) y)))
   (if (<= t -1.8e+113)
     t_1
     (if (<= t 1.8) (/ (* x (/ (exp (- b)) a)) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, (t - 1.0)) * x) / y;
	double tmp;
	if (t <= -1.8e+113) {
		tmp = t_1;
	} else if (t <= 1.8) {
		tmp = (x * (exp(-b) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a ** (t - 1.0d0)) * x) / y
    if (t <= (-1.8d+113)) then
        tmp = t_1
    else if (t <= 1.8d0) then
        tmp = (x * (exp(-b) / a)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.pow(a, (t - 1.0)) * x) / y;
	double tmp;
	if (t <= -1.8e+113) {
		tmp = t_1;
	} else if (t <= 1.8) {
		tmp = (x * (Math.exp(-b) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, (t - 1.0)) * x) / y
	tmp = 0
	if t <= -1.8e+113:
		tmp = t_1
	elif t <= 1.8:
		tmp = (x * (math.exp(-b) / a)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y)
	tmp = 0.0
	if (t <= -1.8e+113)
		tmp = t_1;
	elseif (t <= 1.8)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a ^ (t - 1.0)) * x) / y;
	tmp = 0.0;
	if (t <= -1.8e+113)
		tmp = t_1;
	elseif (t <= 1.8)
		tmp = (x * (exp(-b) / a)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -1.8e+113], t$95$1, If[LessEqual[t, 1.8], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.79999999999999996e113 or 1.80000000000000004 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 81.6

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

   4. Applied rewrites 81.6%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lift--.f64 81.9

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

   7. Applied rewrites 81.9%

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

   if -1.79999999999999996e113 < t < 1.80000000000000004

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0

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

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

      3. exp-sum N/A

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. inv-pow N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 N/A

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

      13. unpow1 N/A

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

      14. metadata-eval N/A

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

      15. pow-flip N/A

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

      16. inv-pow N/A

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

      17. unpow-1 N/A

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

      18. lower-/.f64 N/A

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

      19. unpow-1 N/A

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

      20. inv-pow N/A

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

   4. Applied rewrites 95.1%

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

   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 69.4

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

   7. Applied rewrites 69.4%

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

Alternative 9: 71.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{t} \cdot \frac{x}{y}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (pow a t) (/ x y))))
   (if (<= t -2.3e+113)
     t_1
     (if (<= t 2.0) (/ (* x (/ (exp (- b)) a)) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, t) * (x / y);
	double tmp;
	if (t <= -2.3e+113) {
		tmp = t_1;
	} else if (t <= 2.0) {
		tmp = (x * (exp(-b) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a ** t) * (x / y)
    if (t <= (-2.3d+113)) then
        tmp = t_1
    else if (t <= 2.0d0) then
        tmp = (x * (exp(-b) / a)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, t) * (x / y);
	double tmp;
	if (t <= -2.3e+113) {
		tmp = t_1;
	} else if (t <= 2.0) {
		tmp = (x * (Math.exp(-b) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, t) * (x / y)
	tmp = 0
	if t <= -2.3e+113:
		tmp = t_1
	elif t <= 2.0:
		tmp = (x * (math.exp(-b) / a)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64((a ^ t) * Float64(x / y))
	tmp = 0.0
	if (t <= -2.3e+113)
		tmp = t_1;
	elseif (t <= 2.0)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a ^ t) * (x / y);
	tmp = 0.0;
	if (t <= -2.3e+113)
		tmp = t_1;
	elseif (t <= 2.0)
		tmp = (x * (exp(-b) / a)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Power[a, t], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+113], t$95$1, If[LessEqual[t, 2.0], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.29999999999999997e113 or 2 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 81.6

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

   4. Applied rewrites 81.6%

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

   5. Taylor expanded in b around 0

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

      1. exp-to-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. lift--.f64 73.2

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

   7. Applied rewrites 73.2%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 73.2%

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

   if -2.29999999999999997e113 < t < 2

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0

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

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

      3. exp-sum N/A

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. inv-pow N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 N/A

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

      13. unpow1 N/A

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

      14. metadata-eval N/A

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

      15. pow-flip N/A

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

      16. inv-pow N/A

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

      17. unpow-1 N/A

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

      18. lower-/.f64 N/A

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

      19. unpow-1 N/A

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

      20. inv-pow N/A

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

   4. Applied rewrites 95.1%

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

   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 69.4

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

   7. Applied rewrites 69.4%

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

Alternative 10: 60.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-b}\\ t_2 := \left(t - 1\right) \cdot \log a\\ \mathbf{if}\;t\_2 \leq 321.2:\\ \;\;\;\;x \cdot \frac{\frac{t\_1}{a}}{y}\\ \mathbf{elif}\;t\_2 \leq 10^{+114}:\\ \;\;\;\;\frac{t\_1}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\log a, t, 1\right)}{a} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (- b))) (t_2 (* (- t 1.0) (log a))))
   (if (<= t_2 321.2)
     (* x (/ (/ t_1 a) y))
     (if (<= t_2 1e+114)
       (* (/ t_1 y) (/ x a))
       (/ (* (/ (fma (log a) t 1.0) a) x) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(-b);
	double t_2 = (t - 1.0) * log(a);
	double tmp;
	if (t_2 <= 321.2) {
		tmp = x * ((t_1 / a) / y);
	} else if (t_2 <= 1e+114) {
		tmp = (t_1 / y) * (x / a);
	} else {
		tmp = ((fma(log(a), t, 1.0) / a) * x) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(-b))
	t_2 = Float64(Float64(t - 1.0) * log(a))
	tmp = 0.0
	if (t_2 <= 321.2)
		tmp = Float64(x * Float64(Float64(t_1 / a) / y));
	elseif (t_2 <= 1e+114)
		tmp = Float64(Float64(t_1 / y) * Float64(x / a));
	else
		tmp = Float64(Float64(Float64(fma(log(a), t, 1.0) / a) * x) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[(-b)], $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 321.2], N[(x * N[(N[(t$95$1 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+114], N[(N[(t$95$1 / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[Log[a], $MachinePrecision] * t + 1.0), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 321.199999999999989

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 70.3

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

   4. Applied rewrites 70.3%

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

   5. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. inv-pow N/A

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

      8. associate-/l/ N/A

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

      9. rem-exp-log N/A

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

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

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

      13. rem-exp-log N/A

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

      14. associate-/l/ N/A

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

      15. exp-neg N/A

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

      16. lower-/.f64 N/A

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

      17. lower-exp.f64 N/A

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

      18. lift-neg.f64 61.2

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

   7. Applied rewrites 61.2%

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

   if 321.199999999999989 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e114

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 72.1

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

   4. Applied rewrites 72.1%

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

   5. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. inv-pow N/A

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

      8. associate-/l/ N/A

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

      9. rem-exp-log N/A

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

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

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

      13. rem-exp-log N/A

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

      14. associate-/l/ N/A

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

      15. exp-neg N/A

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

      16. lower-/.f64 N/A

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

      17. lower-exp.f64 N/A

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

      18. lift-neg.f64 63.0

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

   7. Applied rewrites 63.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-exp.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. associate-/l/ N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. times-frac N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift-neg.f64 N/A

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

      14. lift-exp.f64 N/A

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

      15. lower-/.f64 61.0

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

   9. Applied rewrites 61.0%

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

   if 1e114 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 85.2

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

   4. Applied rewrites 85.2%

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

   5. Taylor expanded in b around 0

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

      1. exp-to-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. lift--.f64 78.2

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

   7. Applied rewrites 78.2%

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

   8. Taylor expanded in t around 0

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

      1. div-add-rev N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-log.f64 47.7

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

   10. Applied rewrites 47.7%

       \[\leadsto \frac{\mathsf{fma}\left(\log a, t, 1\right)}{a} \cdot \frac{x}{y} \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lower-/.f64 N/A

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

       5. lower-*.f64 51.6

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

   12. Applied rewrites 51.6%

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

Alternative 11: 60.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 10^{+114}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\log a, t, 1\right)}{a} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 1e+114)
   (/ (* x (/ (exp (- b)) a)) y)
   (/ (* (/ (fma (log a) t 1.0) a) x) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= 1e+114) {
		tmp = (x * (exp(-b) / a)) / y;
	} else {
		tmp = ((fma(log(a), t, 1.0) / a) * x) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= 1e+114)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	else
		tmp = Float64(Float64(Float64(fma(log(a), t, 1.0) / a) * x) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], 1e+114], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(N[(N[Log[a], $MachinePrecision] * t + 1.0), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e114

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. exp-sum N/A

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. inv-pow N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 N/A

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

      13. unpow1 N/A

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

      14. metadata-eval N/A

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

      15. pow-flip N/A

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

      16. inv-pow N/A

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

      17. unpow-1 N/A

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

      18. lower-/.f64 N/A

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

      19. unpow-1 N/A

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

      20. inv-pow N/A

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

   4. Applied rewrites 85.0%

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

   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 62.1

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

   7. Applied rewrites 62.1%

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

   if 1e114 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 85.2

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

   4. Applied rewrites 85.2%

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

   5. Taylor expanded in b around 0

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

      1. exp-to-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. lift--.f64 78.2

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

   7. Applied rewrites 78.2%

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

   8. Taylor expanded in t around 0

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

      1. div-add-rev N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-log.f64 47.7

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

   10. Applied rewrites 47.7%

       \[\leadsto \frac{\mathsf{fma}\left(\log a, t, 1\right)}{a} \cdot \frac{x}{y} \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lower-/.f64 N/A

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

       5. lower-*.f64 51.6

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

   12. Applied rewrites 51.6%

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

Alternative 12: 59.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1200000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\log a, t, 1\right)}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -6.5e-51)
     t_1
     (if (<= b 1200000.0) (/ (* (/ (fma (log a) t 1.0) a) x) 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 <= -6.5e-51) {
		tmp = t_1;
	} else if (b <= 1200000.0) {
		tmp = ((fma(log(a), t, 1.0) / a) * x) / 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 <= -6.5e-51)
		tmp = t_1;
	elseif (b <= 1200000.0)
		tmp = Float64(Float64(Float64(fma(log(a), t, 1.0) / a) * x) / 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, -6.5e-51], t$95$1, If[LessEqual[b, 1200000.0], N[(N[(N[(N[(N[Log[a], $MachinePrecision] * t + 1.0), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5000000000000003e-51 or 1.2e6 < b

   1. Initial program 99.7%

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

   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 74.9

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

   4. Applied rewrites 74.9%

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

   6. Applied rewrites 74.9%

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

   if -6.5000000000000003e-51 < b < 1.2e6

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 66.7

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

   4. Applied rewrites 66.7%

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

   5. Taylor expanded in b around 0

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

      1. exp-to-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. lift--.f64 67.5

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

   7. Applied rewrites 67.5%

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

   8. Taylor expanded in t around 0

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

      1. div-add-rev N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-log.f64 42.1

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

   10. Applied rewrites 42.1%

       \[\leadsto \frac{\mathsf{fma}\left(\log a, t, 1\right)}{a} \cdot \frac{x}{y} \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lower-/.f64 N/A

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

       5. lower-*.f64 41.9

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

   12. Applied rewrites 41.9%

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

Alternative 13: 59.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 10^{+114}:\\ \;\;\;\;x \cdot \frac{\frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\log a, t, 1\right)}{a} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 1e+114)
   (* x (/ (/ (exp (- b)) a) y))
   (/ (* (/ (fma (log a) t 1.0) a) x) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= 1e+114) {
		tmp = x * ((exp(-b) / a) / y);
	} else {
		tmp = ((fma(log(a), t, 1.0) / a) * x) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= 1e+114)
		tmp = Float64(x * Float64(Float64(exp(Float64(-b)) / a) / y));
	else
		tmp = Float64(Float64(Float64(fma(log(a), t, 1.0) / a) * x) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], 1e+114], N[(x * N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[Log[a], $MachinePrecision] * t + 1.0), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e114

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 70.8

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

   4. Applied rewrites 70.8%

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

   5. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. inv-pow N/A

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

      8. associate-/l/ N/A

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

      9. rem-exp-log N/A

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

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

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

      13. rem-exp-log N/A

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

      14. associate-/l/ N/A

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

      15. exp-neg N/A

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

      16. lower-/.f64 N/A

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

      17. lower-exp.f64 N/A

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

      18. lift-neg.f64 61.7

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

   7. Applied rewrites 61.7%

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

   if 1e114 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 85.2

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

   4. Applied rewrites 85.2%

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

   5. Taylor expanded in b around 0

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

      1. exp-to-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. lift--.f64 78.2

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

   7. Applied rewrites 78.2%

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

   8. Taylor expanded in t around 0

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

      1. div-add-rev N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-log.f64 47.7

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

   10. Applied rewrites 47.7%

       \[\leadsto \frac{\mathsf{fma}\left(\log a, t, 1\right)}{a} \cdot \frac{x}{y} \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lower-/.f64 N/A

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

       5. lower-*.f64 51.6

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

   12. Applied rewrites 51.6%

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

Alternative 14: 58.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1200000:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -6.5e-51) t_1 (if (<= b 1200000.0) (/ (/ 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 <= -6.5e-51) {
		tmp = t_1;
	} else if (b <= 1200000.0) {
		tmp = (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 <= (-6.5d-51)) then
        tmp = t_1
    else if (b <= 1200000.0d0) then
        tmp = (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 <= -6.5e-51) {
		tmp = t_1;
	} else if (b <= 1200000.0) {
		tmp = (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 <= -6.5e-51:
		tmp = t_1
	elif b <= 1200000.0:
		tmp = (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 <= -6.5e-51)
		tmp = t_1;
	elseif (b <= 1200000.0)
		tmp = Float64(Float64(x / 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 <= -6.5e-51)
		tmp = t_1;
	elseif (b <= 1200000.0)
		tmp = (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, -6.5e-51], t$95$1, If[LessEqual[b, 1200000.0], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5000000000000003e-51 or 1.2e6 < b

   1. Initial program 99.7%

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

   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 74.9

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

   4. Applied rewrites 74.9%

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

   6. Applied rewrites 74.9%

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

   if -6.5000000000000003e-51 < b < 1.2e6

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 66.7

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

   4. Applied rewrites 66.7%

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

   5. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. inv-pow N/A

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

      8. associate-/l/ N/A

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

      9. rem-exp-log N/A

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

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

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

      13. rem-exp-log N/A

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

      14. associate-/l/ N/A

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

      15. exp-neg N/A

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

      16. lower-/.f64 N/A

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

      17. lower-exp.f64 N/A

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

      18. lift-neg.f64 39.6

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

   7. Applied rewrites 39.6%

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

   8. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 39.4

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

   10. Applied rewrites 39.4%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-/r* N/A

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

       4. lower-/.f64 N/A

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

       5. lower-/.f64 39.4

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

   12. Applied rewrites 39.4%

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

Alternative 15: 36.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ \mathbf{if}\;t\_1 \leq 310:\\ \;\;\;\;x \cdot \frac{1 - b}{a \cdot y}\\ \mathbf{elif}\;t\_1 \leq 20000000000000:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-x, b, x\right)}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))))
   (if (<= t_1 310.0)
     (* x (/ (- 1.0 b) (* a y)))
     (if (<= t_1 20000000000000.0)
       (/ (* x (/ 1.0 a)) y)
       (/ (fma (- x) b x) (* a y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double tmp;
	if (t_1 <= 310.0) {
		tmp = x * ((1.0 - b) / (a * y));
	} else if (t_1 <= 20000000000000.0) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = fma(-x, b, x) / (a * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	tmp = 0.0
	if (t_1 <= 310.0)
		tmp = Float64(x * Float64(Float64(1.0 - b) / Float64(a * y)));
	elseif (t_1 <= 20000000000000.0)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(fma(Float64(-x), b, x) / Float64(a * y));
	end
	return 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]}, If[LessEqual[t$95$1, 310.0], N[(x * N[(N[(1.0 - b), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 20000000000000.0], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[((-x) * b + x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 310

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 70.4

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

   4. Applied rewrites 70.4%

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

   5. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. inv-pow N/A

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

      8. associate-/l/ N/A

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

      9. rem-exp-log N/A

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

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

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

      13. rem-exp-log N/A

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

      14. associate-/l/ N/A

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

      15. exp-neg N/A

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

      16. lower-/.f64 N/A

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

      17. lower-exp.f64 N/A

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

      18. lift-neg.f64 61.3

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

   7. Applied rewrites 61.3%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. div-add-rev N/A

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

      6. lift-neg.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 34.4

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

   10. Applied rewrites 34.4%

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

   if 310 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e13

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0

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

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

      3. exp-sum N/A

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. inv-pow N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 N/A

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

      13. unpow1 N/A

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

      14. metadata-eval N/A

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

      15. pow-flip N/A

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

      16. inv-pow N/A

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

      17. unpow-1 N/A

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

      18. lower-/.f64 N/A

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

      19. unpow-1 N/A

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

      20. inv-pow N/A

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

   4. Applied rewrites 98.6%

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

   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 72.5

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 42.3%

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

   if 2e13 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 82.5

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

   4. Applied rewrites 82.5%

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

   5. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. inv-pow N/A

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

      8. associate-/l/ N/A

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

      9. rem-exp-log N/A

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

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

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

      13. rem-exp-log N/A

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

      14. associate-/l/ N/A

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

      15. exp-neg N/A

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

      16. lower-/.f64 N/A

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

      17. lower-exp.f64 N/A

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

      18. lift-neg.f64 50.8

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

   7. Applied rewrites 50.8%

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

   8. Taylor expanded in b around 0

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

      1. associate-*r/ N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 27.2

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

   10. Applied rewrites 27.2%

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

Alternative 16: 36.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 288:\\ \;\;\;\;x \cdot \frac{1 - b}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 288.0)
   (* x (/ (- 1.0 b) (* a y)))
   (/ (* x (/ (- 1.0 b) 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)) <= 288.0) {
		tmp = x * ((1.0 - b) / (a * y));
	} else {
		tmp = (x * ((1.0 - b) / 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)) <= 288.0d0) then
        tmp = x * ((1.0d0 - b) / (a * y))
    else
        tmp = (x * ((1.0d0 - b) / 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)) <= 288.0) {
		tmp = x * ((1.0 - b) / (a * y));
	} else {
		tmp = (x * ((1.0 - b) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= 288.0:
		tmp = x * ((1.0 - b) / (a * y))
	else:
		tmp = (x * ((1.0 - b) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= 288.0)
		tmp = Float64(x * Float64(Float64(1.0 - b) / Float64(a * y)));
	else
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / 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)) <= 288.0)
		tmp = x * ((1.0 - b) / (a * y));
	else
		tmp = (x * ((1.0 - b) / 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], 288.0], N[(x * N[(N[(1.0 - b), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 288

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 70.6

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. inv-pow N/A

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

      8. associate-/l/ N/A

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

      9. rem-exp-log N/A

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

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

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

      13. rem-exp-log N/A

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

      14. associate-/l/ N/A

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

      15. exp-neg N/A

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

      16. lower-/.f64 N/A

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

      17. lower-exp.f64 N/A

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

      18. lift-neg.f64 61.3

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

   7. Applied rewrites 61.3%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. div-add-rev N/A

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

      6. lift-neg.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 34.3

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

   10. Applied rewrites 34.3%

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

   if 288 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0

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

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

      3. exp-sum N/A

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. inv-pow N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 N/A

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

      13. unpow1 N/A

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

      14. metadata-eval N/A

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

      15. pow-flip N/A

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

      16. inv-pow N/A

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

      17. unpow-1 N/A

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

      18. lower-/.f64 N/A

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

      19. unpow-1 N/A

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

      20. inv-pow N/A

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-exp.f64 N/A

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

      3. lift-neg.f64 59.0

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

   7. Applied rewrites 59.0%

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

   8. Taylor expanded in b around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 35.8

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

   10. Applied rewrites 35.8%

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

Alternative 17: 35.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 285:\\ \;\;\;\;x \cdot \frac{1 - b}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - b}{a} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 285.0)
   (* x (/ (- 1.0 b) (* a y)))
   (* (/ (- 1.0 b) a) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= 285.0) {
		tmp = x * ((1.0 - b) / (a * y));
	} else {
		tmp = ((1.0 - b) / a) * (x / 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)) <= 285.0d0) then
        tmp = x * ((1.0d0 - b) / (a * y))
    else
        tmp = ((1.0d0 - b) / a) * (x / 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)) <= 285.0) {
		tmp = x * ((1.0 - b) / (a * y));
	} else {
		tmp = ((1.0 - b) / a) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= 285.0:
		tmp = x * ((1.0 - b) / (a * y))
	else:
		tmp = ((1.0 - b) / a) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= 285.0)
		tmp = Float64(x * Float64(Float64(1.0 - b) / Float64(a * y)));
	else
		tmp = Float64(Float64(Float64(1.0 - b) / a) * Float64(x / 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)) <= 285.0)
		tmp = x * ((1.0 - b) / (a * y));
	else
		tmp = ((1.0 - b) / a) * (x / 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], 285.0], N[(x * N[(N[(1.0 - b), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - b), $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 285

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 70.6

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. inv-pow N/A

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

      8. associate-/l/ N/A

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

      9. rem-exp-log N/A

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

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

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

      13. rem-exp-log N/A

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

      14. associate-/l/ N/A

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

      15. exp-neg N/A

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

      16. lower-/.f64 N/A

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

      17. lower-exp.f64 N/A

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

      18. lift-neg.f64 61.3

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

   7. Applied rewrites 61.3%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. lift-neg.f64 N/A

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

      5. div-add-rev N/A

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

      6. lift-neg.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 34.3

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

   10. Applied rewrites 34.3%

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

   if 285 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0

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

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

      3. exp-sum N/A

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. inv-pow N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 N/A

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

      13. unpow1 N/A

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

      14. metadata-eval N/A

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

      15. pow-flip N/A

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

      16. inv-pow N/A

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

      17. unpow-1 N/A

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

      18. lower-/.f64 N/A

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

      19. unpow-1 N/A

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

      20. inv-pow N/A

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

   4. Applied rewrites 79.4%

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

   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 58.9

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

   7. Applied rewrites 58.9%

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

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]
   9. Step-by-step derivation

      1. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{x \cdot \frac{1 - \left(\mathsf{neg}\left(-1\right)\right) \cdot b}{a}}{y} \]

      2. metadata-eval N/A

         \[\leadsto \frac{x \cdot \frac{1 - 1 \cdot b}{a}}{y} \]

      3. *-lft-identity N/A

         \[\leadsto \frac{x \cdot \frac{1 - b}{a}}{y} \]

      4. lower--.f64 35.8

         \[\leadsto \frac{x \cdot \frac{1 - b}{a}}{y} \]

   10. Applied rewrites 35.8%

       \[\leadsto \frac{x \cdot \frac{1 - b}{a}}{y} \]
   11. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1 - b}{a}}{y}} \]

       2. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1 - b}{a}}}{y} \]

       3. *-commutative N/A

          \[\leadsto \frac{\color{blue}{\frac{1 - b}{a} \cdot x}}{y} \]

       4. associate-/l* N/A

          \[\leadsto \color{blue}{\frac{1 - b}{a} \cdot \frac{x}{y}} \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{1 - b}{a} \cdot \frac{x}{y}} \]

   12. Applied rewrites 36.4%

       \[\leadsto \color{blue}{\frac{1 - b}{a} \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 35.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.8 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \frac{\frac{1 - b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8.8e-137) (* x (/ (/ (- 1.0 b) a) y)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.8e-137) {
		tmp = x * (((1.0 - b) / 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 <= 8.8d-137) then
        tmp = x * (((1.0d0 - b) / 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 <= 8.8e-137) {
		tmp = x * (((1.0 - b) / a) / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8.8e-137:
		tmp = x * (((1.0 - b) / a) / y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8.8e-137)
		tmp = Float64(x * Float64(Float64(Float64(1.0 - b) / a) / y));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8.8e-137)
		tmp = x * (((1.0 - b) / a) / y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8.8e-137], N[(x * N[(N[(N[(1.0 - b), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.8000000000000005e-137

   1. Initial program 98.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 72.2

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 72.2%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 55.1

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 55.1%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto x \cdot \frac{\frac{1 + -1 \cdot b}{a}}{y} \]
   9. Step-by-step derivation

      1. fp-cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \frac{\frac{1 - \left(\mathsf{neg}\left(-1\right)\right) \cdot b}{a}}{y} \]

      2. metadata-eval N/A

         \[\leadsto x \cdot \frac{\frac{1 - 1 \cdot b}{a}}{y} \]

      3. *-lft-identity N/A

         \[\leadsto x \cdot \frac{\frac{1 - b}{a}}{y} \]

      4. lower--.f64 42.2

         \[\leadsto x \cdot \frac{\frac{1 - b}{a}}{y} \]

   10. Applied rewrites 42.2%

       \[\leadsto x \cdot \frac{\frac{1 - b}{a}}{y} \]

   if 8.8000000000000005e-137 < b

   1. Initial program 98.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 74.7

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 74.7%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 67.5

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 67.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{a \cdot y} \]

      2. lower-*.f64 26.0

         \[\leadsto \frac{x}{a \cdot y} \]

   10. Applied rewrites 26.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{x}{a \cdot y} \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{x}{a \cdot y} \]

       3. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{a}}{y} \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{\frac{x}{a}}{y} \]

       5. lower-/.f64 26.1

          \[\leadsto \frac{\frac{x}{a}}{y} \]

   12. Applied rewrites 26.1%

       \[\leadsto \frac{\frac{x}{a}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 34.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.8 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \frac{1 - b}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8.8e-137) (* x (/ (- 1.0 b) (* a y))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.8e-137) {
		tmp = x * ((1.0 - b) / (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 <= 8.8d-137) then
        tmp = x * ((1.0d0 - b) / (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 <= 8.8e-137) {
		tmp = x * ((1.0 - b) / (a * y));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8.8e-137:
		tmp = x * ((1.0 - b) / (a * y))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8.8e-137)
		tmp = Float64(x * Float64(Float64(1.0 - b) / Float64(a * y)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8.8e-137)
		tmp = x * ((1.0 - b) / (a * y));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8.8e-137], N[(x * N[(N[(1.0 - b), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.8000000000000005e-137

   1. Initial program 98.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 72.2

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 72.2%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 55.1

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 55.1%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{\color{blue}{a \cdot y}}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x \cdot \left(\frac{1}{a \cdot y} + -1 \cdot \frac{b}{\color{blue}{a \cdot y}}\right) \]

      2. associate-*r/ N/A

         \[\leadsto x \cdot \left(\frac{1}{a \cdot y} + \frac{-1 \cdot b}{a \cdot y}\right) \]

      3. mul-1-neg N/A

         \[\leadsto x \cdot \left(\frac{1}{a \cdot y} + \frac{\mathsf{neg}\left(b\right)}{a \cdot y}\right) \]

      4. lift-neg.f64 N/A

         \[\leadsto x \cdot \left(\frac{1}{a \cdot y} + \frac{-b}{a \cdot y}\right) \]

      5. div-add-rev N/A

         \[\leadsto x \cdot \frac{1 + \left(-b\right)}{a \cdot y} \]

      6. lift-neg.f64 N/A

         \[\leadsto x \cdot \frac{1 + \left(\mathsf{neg}\left(b\right)\right)}{a \cdot y} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{1 + -1 \cdot b}{a \cdot y} \]

      8. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{1 + -1 \cdot b}{a \cdot y} \]

      9. fp-cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \frac{1 - \left(\mathsf{neg}\left(-1\right)\right) \cdot b}{a \cdot y} \]

      10. metadata-eval N/A

          \[\leadsto x \cdot \frac{1 - 1 \cdot b}{a \cdot y} \]

      11. *-lft-identity N/A

          \[\leadsto x \cdot \frac{1 - b}{a \cdot y} \]

      12. lower--.f64 N/A

          \[\leadsto x \cdot \frac{1 - b}{a \cdot y} \]

      13. lower-*.f64 41.5

          \[\leadsto x \cdot \frac{1 - b}{a \cdot y} \]

   10. Applied rewrites 41.5%

       \[\leadsto x \cdot \frac{1 - b}{a \cdot \color{blue}{y}} \]

   if 8.8000000000000005e-137 < b

   1. Initial program 98.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 74.7

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 74.7%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 67.5

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 67.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{a \cdot y} \]

      2. lower-*.f64 26.0

         \[\leadsto \frac{x}{a \cdot y} \]

   10. Applied rewrites 26.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{x}{a \cdot y} \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{x}{a \cdot y} \]

       3. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{a}}{y} \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{\frac{x}{a}}{y} \]

       5. lower-/.f64 26.1

          \[\leadsto \frac{\frac{x}{a}}{y} \]

   12. Applied rewrites 26.1%

       \[\leadsto \frac{\frac{x}{a}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 33.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.5e-51) (/ (* x (/ (- b) a)) y) (/ x (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e-51) {
		tmp = (x * (-b / 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 <= (-6.5d-51)) then
        tmp = (x * (-b / 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 <= -6.5e-51) {
		tmp = (x * (-b / a)) / y;
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.5e-51:
		tmp = (x * (-b / a)) / y
	else:
		tmp = x / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.5e-51)
		tmp = Float64(Float64(x * Float64(Float64(-b) / 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 <= -6.5e-51)
		tmp = (x * (-b / a)) / y;
	else
		tmp = x / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.5e-51], N[(N[(x * N[((-b) / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5000000000000003e-51

   1. Initial program 99.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   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. +-commutative N/A

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z - b\right) + -1 \cdot \log a}}{y} \]

      3. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \color{blue}{e^{-1 \cdot \log a}}\right)}{y} \]

      4. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot e^{\log a \cdot -1}\right)}{y} \]

      5. exp-to-pow N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot {a}^{\color{blue}{-1}}\right)}{y} \]

      6. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \frac{1}{\color{blue}{a}}\right)}{y} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \color{blue}{\frac{1}{a}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \frac{\color{blue}{1}}{a}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \frac{1}{a}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{a}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{a}\right)}{y} \]

      12. lift-log.f64 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{a}\right)}{y} \]

      13. unpow1 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{{a}^{\color{blue}{1}}}\right)}{y} \]

      14. metadata-eval N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{{a}^{\left(\mathsf{neg}\left(-1\right)\right)}}\right)}{y} \]

      15. pow-flip N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\frac{1}{\color{blue}{{a}^{-1}}}}\right)}{y} \]

      16. inv-pow N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\frac{1}{\frac{1}{\color{blue}{a}}}}\right)}{y} \]

      17. unpow-1 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{{\left(\frac{1}{a}\right)}^{\color{blue}{-1}}}\right)}{y} \]

      18. lower-/.f64 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\color{blue}{{\left(\frac{1}{a}\right)}^{-1}}}\right)}{y} \]

      19. unpow-1 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\frac{1}{\color{blue}{\frac{1}{a}}}}\right)}{y} \]

      20. inv-pow N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\frac{1}{{a}^{\color{blue}{-1}}}}\right)}{y} \]

   4. Applied rewrites 86.7%

      \[\leadsto \frac{x \cdot \color{blue}{\left(e^{\log z \cdot y - b} \cdot \frac{1}{a}\right)}}{y} \]

   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 74.3

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 74.3%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \frac{1 + -1 \cdot b}{a}}{y} \]
   9. Step-by-step derivation

      1. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{x \cdot \frac{1 - \left(\mathsf{neg}\left(-1\right)\right) \cdot b}{a}}{y} \]

      2. metadata-eval N/A

         \[\leadsto \frac{x \cdot \frac{1 - 1 \cdot b}{a}}{y} \]

      3. *-lft-identity N/A

         \[\leadsto \frac{x \cdot \frac{1 - b}{a}}{y} \]

      4. lower--.f64 44.2

         \[\leadsto \frac{x \cdot \frac{1 - b}{a}}{y} \]

   10. Applied rewrites 44.2%

       \[\leadsto \frac{x \cdot \frac{1 - b}{a}}{y} \]

   11. Taylor expanded in b around inf

       \[\leadsto \frac{x \cdot \frac{-1 \cdot b}{a}}{y} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \frac{x \cdot \frac{\mathsf{neg}\left(b\right)}{a}}{y} \]

       2. lower-neg.f64 42.7

          \[\leadsto \frac{x \cdot \frac{-b}{a}}{y} \]

   13. Applied rewrites 42.7%

       \[\leadsto \frac{x \cdot \frac{-b}{a}}{y} \]

   if -6.5000000000000003e-51 < b

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 70.7

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 70.7%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 53.5

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 53.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{a \cdot y} \]

      2. lower-*.f64 32.8

         \[\leadsto \frac{x}{a \cdot y} \]

   10. Applied rewrites 32.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 32.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 320:\\ \;\;\;\;x \cdot \frac{1}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 320.0)
   (* x (/ 1.0 (* a y)))
   (/ (* x (/ 1.0 a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= 320.0) {
		tmp = x * (1.0 / (a * y));
	} else {
		tmp = (x * (1.0 / a)) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t - 1.0d0) * log(a)) <= 320.0d0) then
        tmp = x * (1.0d0 / (a * y))
    else
        tmp = (x * (1.0d0 / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * Math.log(a)) <= 320.0) {
		tmp = x * (1.0 / (a * y));
	} else {
		tmp = (x * (1.0 / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= 320.0:
		tmp = x * (1.0 / (a * y))
	else:
		tmp = (x * (1.0 / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= 320.0)
		tmp = Float64(x * Float64(1.0 / Float64(a * y)));
	else
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) * log(a)) <= 320.0)
		tmp = x * (1.0 / (a * y));
	else
		tmp = (x * (1.0 / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], 320.0], N[(x * N[(1.0 / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 320

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 70.3

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 70.3%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 61.3

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 61.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto x \cdot \frac{1}{a \cdot \color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{1}{a \cdot y} \]

      2. lower-*.f64 32.4

         \[\leadsto x \cdot \frac{1}{a \cdot y} \]

   10. Applied rewrites 32.4%

       \[\leadsto x \cdot \frac{1}{a \cdot \color{blue}{y}} \]

   if 320 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \frac{x \cdot e^{-1 \cdot \log a + \left(y \cdot \log z - b\right)}}{y} \]

      2. +-commutative N/A

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z - b\right) + -1 \cdot \log a}}{y} \]

      3. exp-sum N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \color{blue}{e^{-1 \cdot \log a}}\right)}{y} \]

      4. *-commutative N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot e^{\log a \cdot -1}\right)}{y} \]

      5. exp-to-pow N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot {a}^{\color{blue}{-1}}\right)}{y} \]

      6. inv-pow N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \frac{1}{\color{blue}{a}}\right)}{y} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \color{blue}{\frac{1}{a}}\right)}{y} \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \frac{\color{blue}{1}}{a}\right)}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x \cdot \left(e^{y \cdot \log z - b} \cdot \frac{1}{a}\right)}{y} \]

      10. *-commutative N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{a}\right)}{y} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{a}\right)}{y} \]

      12. lift-log.f64 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{a}\right)}{y} \]

      13. unpow1 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{{a}^{\color{blue}{1}}}\right)}{y} \]

      14. metadata-eval N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{{a}^{\left(\mathsf{neg}\left(-1\right)\right)}}\right)}{y} \]

      15. pow-flip N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\frac{1}{\color{blue}{{a}^{-1}}}}\right)}{y} \]

      16. inv-pow N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\frac{1}{\frac{1}{\color{blue}{a}}}}\right)}{y} \]

      17. unpow-1 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{{\left(\frac{1}{a}\right)}^{\color{blue}{-1}}}\right)}{y} \]

      18. lower-/.f64 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\color{blue}{{\left(\frac{1}{a}\right)}^{-1}}}\right)}{y} \]

      19. unpow-1 N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\frac{1}{\color{blue}{\frac{1}{a}}}}\right)}{y} \]

      20. inv-pow N/A

          \[\leadsto \frac{x \cdot \left(e^{\log z \cdot y - b} \cdot \frac{1}{\frac{1}{{a}^{\color{blue}{-1}}}}\right)}{y} \]

   4. Applied rewrites 78.6%

      \[\leadsto \frac{x \cdot \color{blue}{\left(e^{\log z \cdot y - b} \cdot \frac{1}{a}\right)}}{y} \]

   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 58.7

         \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 58.7%

      \[\leadsto \frac{x \cdot \frac{e^{-b}}{\color{blue}{a}}}{y} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
   9. Step-by-step derivation

   10. Applied rewrites 32.5%

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 32.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 288:\\ \;\;\;\;x \cdot \frac{1}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 288.0) (* 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)) <= 288.0) {
		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)) <= 288.0d0) 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)) <= 288.0) {
		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)) <= 288.0:
		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)) <= 288.0)
		tmp = Float64(x * Float64(1.0 / Float64(a * y)));
	else
		tmp = Float64(Float64(x / 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)) <= 288.0)
		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], 288.0], N[(x * N[(1.0 / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 288

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 70.6

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 70.6%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 61.3

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 61.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto x \cdot \frac{1}{a \cdot \color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{1}{a \cdot y} \]

      2. lower-*.f64 32.5

         \[\leadsto x \cdot \frac{1}{a \cdot y} \]

   10. Applied rewrites 32.5%

       \[\leadsto x \cdot \frac{1}{a \cdot \color{blue}{y}} \]

   if 288 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 76.9

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 76.9%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 56.9

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 56.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{a \cdot y} \]

      2. lower-*.f64 31.0

         \[\leadsto \frac{x}{a \cdot y} \]

   10. Applied rewrites 31.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{x}{a \cdot y} \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{x}{a \cdot y} \]

       3. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{a}}{y} \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{\frac{x}{a}}{y} \]

       5. lower-/.f64 32.7

          \[\leadsto \frac{\frac{x}{a}}{y} \]

   12. Applied rewrites 32.7%

       \[\leadsto \frac{\frac{x}{a}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 32.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 320:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 320.0) (/ x (* 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)) <= 320.0) {
		tmp = x / (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)) <= 320.0d0) then
        tmp = x / (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)) <= 320.0) {
		tmp = x / (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)) <= 320.0:
		tmp = x / (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)) <= 320.0)
		tmp = Float64(x / Float64(a * y));
	else
		tmp = Float64(Float64(x / 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)) <= 320.0)
		tmp = x / (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], 320.0], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 320

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 70.3

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 70.3%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 61.3

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 61.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{a \cdot y} \]

      2. lower-*.f64 32.5

         \[\leadsto \frac{x}{a \cdot y} \]

   10. Applied rewrites 32.5%

       \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]

   if 320 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

      2. associate-/l* N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      3. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

      4. lower-exp.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

      5. lower--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      7. lift-log.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      8. lift--.f64 N/A

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

      9. lower-/.f64 77.5

         \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

   4. Applied rewrites 77.5%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

      4. div-exp N/A

         \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

      5. *-commutative N/A

         \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

      6. exp-to-pow N/A

         \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

      7. inv-pow N/A

         \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

      8. associate-/l/ N/A

         \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

      9. rem-exp-log N/A

         \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

      10. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

      11. +-commutative N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

      12. exp-sum N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

      13. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

      14. associate-/l/ N/A

          \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

      15. exp-neg N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      16. lower-/.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      17. lower-exp.f64 N/A

          \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

      18. lift-neg.f64 56.8

          \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

   7. Applied rewrites 56.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{a \cdot y} \]

      2. lower-*.f64 31.0

         \[\leadsto \frac{x}{a \cdot y} \]

   10. Applied rewrites 31.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{x}{a \cdot y} \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{x}{a \cdot y} \]

       3. associate-/r* N/A

          \[\leadsto \frac{\frac{x}{a}}{y} \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{\frac{x}{a}}{y} \]

       5. lower-/.f64 32.5

          \[\leadsto \frac{\frac{x}{a}}{y} \]

   12. Applied rewrites 32.5%

       \[\leadsto \frac{\frac{x}{a}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 31.9% 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 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
3. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y} \]

   2. associate-/l* N/A

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

   3. lower-*.f64 N/A

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \color{blue}{\frac{x}{y}} \]

   4. lower-exp.f64 N/A

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{\color{blue}{x}}{y} \]

   5. lower--.f64 N/A

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

   6. lower-*.f64 N/A

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

   7. lift-log.f64 N/A

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

   8. lift--.f64 N/A

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y} \]

   9. lower-/.f64 73.1

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{\color{blue}{y}} \]

4. Applied rewrites 73.1%

   \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot \frac{x}{y}} \]

5. Taylor expanded in t around 0

   \[\leadsto \frac{x \cdot e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]
6. Step-by-step derivation

   1. associate-/l* N/A

      \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

   2. lower-*.f64 N/A

      \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{\color{blue}{y}} \]

   3. lower-/.f64 N/A

      \[\leadsto x \cdot \frac{e^{-1 \cdot \log a - b}}{y} \]

   4. div-exp N/A

      \[\leadsto x \cdot \frac{\frac{e^{-1 \cdot \log a}}{e^{b}}}{y} \]

   5. *-commutative N/A

      \[\leadsto x \cdot \frac{\frac{e^{\log a \cdot -1}}{e^{b}}}{y} \]

   6. exp-to-pow N/A

      \[\leadsto x \cdot \frac{\frac{{a}^{-1}}{e^{b}}}{y} \]

   7. inv-pow N/A

      \[\leadsto x \cdot \frac{\frac{\frac{1}{a}}{e^{b}}}{y} \]

   8. associate-/l/ N/A

      \[\leadsto x \cdot \frac{\frac{1}{a \cdot e^{b}}}{y} \]

   9. rem-exp-log N/A

      \[\leadsto x \cdot \frac{\frac{1}{e^{\log a} \cdot e^{b}}}{y} \]

   10. exp-sum N/A

       \[\leadsto x \cdot \frac{\frac{1}{e^{\log a + b}}}{y} \]

   11. +-commutative N/A

       \[\leadsto x \cdot \frac{\frac{1}{e^{b + \log a}}}{y} \]

   12. exp-sum N/A

       \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot e^{\log a}}}{y} \]

   13. rem-exp-log N/A

       \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot a}}{y} \]

   14. associate-/l/ N/A

       \[\leadsto x \cdot \frac{\frac{\frac{1}{e^{b}}}{a}}{y} \]

   15. exp-neg N/A

       \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

   16. lower-/.f64 N/A

       \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

   17. lower-exp.f64 N/A

       \[\leadsto x \cdot \frac{\frac{e^{\mathsf{neg}\left(b\right)}}{a}}{y} \]

   18. lift-neg.f64 59.5

       \[\leadsto x \cdot \frac{\frac{e^{-b}}{a}}{y} \]

7. Applied rewrites 59.5%

   \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{a}}{y}} \]

8. Taylor expanded in b around 0

   \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
9. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{x}{a \cdot y} \]

   2. lower-*.f64 31.9

      \[\leadsto \frac{x}{a \cdot y} \]

10. Applied rewrites 31.9%

    \[\leadsto \frac{x}{a \cdot \color{blue}{y}} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025130 
(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))