Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3

Percentage Accurate: 88.7% → 99.9%

Time: 5.4s

Alternatives: 8

Speedup: 1.1×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x + y \cdot \left(z - x\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x (* y (- z x))) z))

C

double code(double x, double y, double z) {
	return (x + (y * (z - x))) / z;
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + (y * (z - x))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x + (y * (z - x))) / z;
}

Python

def code(x, y, z):
	return (x + (y * (z - x))) / z

Julia

function code(x, y, z)
	return Float64(Float64(x + Float64(y * Float64(z - x))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + (y * (z - x))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y \cdot \left(z - x\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x (* y (- z x))) z))

C

double code(double x, double y, double z) {
	return (x + (y * (z - x))) / z;
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + (y * (z - x))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x + (y * (z - x))) / z;
}

Python

def code(x, y, z):
	return (x + (y * (z - x))) / z

Julia

function code(x, y, z)
	return Float64(Float64(x + Float64(y * Float64(z - x))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + (y * (z - x))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{z}, 1 - y, y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (/ x z) (- 1.0 y) y))

C

double code(double x, double y, double z) {
	return fma((x / z), (1.0 - y), y);
}

Julia

function code(x, y, z)
	return fma(Float64(x / z), Float64(1.0 - y), y)
end

Wolfram

code[x_, y_, z_] := N[(N[(x / z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision] + y), $MachinePrecision]

Derivation

1. Initial program 89.3%

   \[\frac{x + y \cdot \left(z - x\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{z}, 1 - y, y\right)} \]
6. Add Preprocessing

Alternative 2: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z} \cdot y\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;\frac{z \cdot y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+15} \lor \neg \left(y \leq 2.85 \cdot 10^{+149}\right):\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (- x) z) y)))
   (if (<= y -4.8e+18)
     t_0
     (if (<= y -1.9e-64)
       (/ (* z y) z)
       (if (<= y 7e-53)
         (/ x z)
         (if (or (<= y 3.5e+15) (not (<= y 2.85e+149))) (* 1.0 y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (-x / z) * y;
	double tmp;
	if (y <= -4.8e+18) {
		tmp = t_0;
	} else if (y <= -1.9e-64) {
		tmp = (z * y) / z;
	} else if (y <= 7e-53) {
		tmp = x / z;
	} else if ((y <= 3.5e+15) || !(y <= 2.85e+149)) {
		tmp = 1.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-x / z) * y
    if (y <= (-4.8d+18)) then
        tmp = t_0
    else if (y <= (-1.9d-64)) then
        tmp = (z * y) / z
    else if (y <= 7d-53) then
        tmp = x / z
    else if ((y <= 3.5d+15) .or. (.not. (y <= 2.85d+149))) then
        tmp = 1.0d0 * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-x / z) * y;
	double tmp;
	if (y <= -4.8e+18) {
		tmp = t_0;
	} else if (y <= -1.9e-64) {
		tmp = (z * y) / z;
	} else if (y <= 7e-53) {
		tmp = x / z;
	} else if ((y <= 3.5e+15) || !(y <= 2.85e+149)) {
		tmp = 1.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-x / z) * y
	tmp = 0
	if y <= -4.8e+18:
		tmp = t_0
	elif y <= -1.9e-64:
		tmp = (z * y) / z
	elif y <= 7e-53:
		tmp = x / z
	elif (y <= 3.5e+15) or not (y <= 2.85e+149):
		tmp = 1.0 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(-x) / z) * y)
	tmp = 0.0
	if (y <= -4.8e+18)
		tmp = t_0;
	elseif (y <= -1.9e-64)
		tmp = Float64(Float64(z * y) / z);
	elseif (y <= 7e-53)
		tmp = Float64(x / z);
	elseif ((y <= 3.5e+15) || !(y <= 2.85e+149))
		tmp = Float64(1.0 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-x / z) * y;
	tmp = 0.0;
	if (y <= -4.8e+18)
		tmp = t_0;
	elseif (y <= -1.9e-64)
		tmp = (z * y) / z;
	elseif (y <= 7e-53)
		tmp = x / z;
	elseif ((y <= 3.5e+15) || ~((y <= 2.85e+149)))
		tmp = 1.0 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[((-x) / z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.8e+18], t$95$0, If[LessEqual[y, -1.9e-64], N[(N[(z * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 7e-53], N[(x / z), $MachinePrecision], If[Or[LessEqual[y, 3.5e+15], N[Not[LessEqual[y, 2.85e+149]], $MachinePrecision]], N[(1.0 * y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.8e18 or 3.5e15 < y < 2.84999999999999983e149

   1. Initial program 86.6%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 61.4%

      \[\leadsto \frac{-x}{z} \cdot y \]

   if -4.8e18 < y < -1.9000000000000001e-64

   1. Initial program 99.8%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{y \cdot z}}{z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 79.0

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

   5. Applied rewrites 79.0%

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

   if -1.9000000000000001e-64 < y < 6.99999999999999987e-53

   1. Initial program 100.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 75.9

         \[\leadsto \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{\frac{x}{z}} \]

   if 6.99999999999999987e-53 < y < 3.5e15 or 2.84999999999999983e149 < y

   1. Initial program 68.2%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 97.6

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 69.1%

      \[\leadsto 1 \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{-x}{z} \cdot y\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;\frac{z \cdot y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+15} \lor \neg \left(y \leq 2.85 \cdot 10^{+149}\right):\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-y}{z} \cdot x\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;\frac{z \cdot y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+23} \lor \neg \left(y \leq 2.3 \cdot 10^{+149}\right):\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (- y) z) x)))
   (if (<= y -1.3e+20)
     t_0
     (if (<= y -1.9e-64)
       (/ (* z y) z)
       (if (<= y 7e-53)
         (/ x z)
         (if (or (<= y 5.6e+23) (not (<= y 2.3e+149))) (* 1.0 y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (-y / z) * x;
	double tmp;
	if (y <= -1.3e+20) {
		tmp = t_0;
	} else if (y <= -1.9e-64) {
		tmp = (z * y) / z;
	} else if (y <= 7e-53) {
		tmp = x / z;
	} else if ((y <= 5.6e+23) || !(y <= 2.3e+149)) {
		tmp = 1.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-y / z) * x
    if (y <= (-1.3d+20)) then
        tmp = t_0
    else if (y <= (-1.9d-64)) then
        tmp = (z * y) / z
    else if (y <= 7d-53) then
        tmp = x / z
    else if ((y <= 5.6d+23) .or. (.not. (y <= 2.3d+149))) then
        tmp = 1.0d0 * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-y / z) * x;
	double tmp;
	if (y <= -1.3e+20) {
		tmp = t_0;
	} else if (y <= -1.9e-64) {
		tmp = (z * y) / z;
	} else if (y <= 7e-53) {
		tmp = x / z;
	} else if ((y <= 5.6e+23) || !(y <= 2.3e+149)) {
		tmp = 1.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-y / z) * x
	tmp = 0
	if y <= -1.3e+20:
		tmp = t_0
	elif y <= -1.9e-64:
		tmp = (z * y) / z
	elif y <= 7e-53:
		tmp = x / z
	elif (y <= 5.6e+23) or not (y <= 2.3e+149):
		tmp = 1.0 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(-y) / z) * x)
	tmp = 0.0
	if (y <= -1.3e+20)
		tmp = t_0;
	elseif (y <= -1.9e-64)
		tmp = Float64(Float64(z * y) / z);
	elseif (y <= 7e-53)
		tmp = Float64(x / z);
	elseif ((y <= 5.6e+23) || !(y <= 2.3e+149))
		tmp = Float64(1.0 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-y / z) * x;
	tmp = 0.0;
	if (y <= -1.3e+20)
		tmp = t_0;
	elseif (y <= -1.9e-64)
		tmp = (z * y) / z;
	elseif (y <= 7e-53)
		tmp = x / z;
	elseif ((y <= 5.6e+23) || ~((y <= 2.3e+149)))
		tmp = 1.0 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[((-y) / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -1.3e+20], t$95$0, If[LessEqual[y, -1.9e-64], N[(N[(z * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 7e-53], N[(x / z), $MachinePrecision], If[Or[LessEqual[y, 5.6e+23], N[Not[LessEqual[y, 2.3e+149]], $MachinePrecision]], N[(1.0 * y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e20 or 5.6e23 < y < 2.2999999999999998e149

   1. Initial program 86.4%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{1 + -1 \cdot y}{z} \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-1 \cdot y + 1}}{z} \cdot x \]

      4. div-add-rev N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot y + 1}{z}} \cdot x \]

      9. +-commutative N/A

         \[\leadsto \frac{\color{blue}{1 + -1 \cdot y}}{z} \cdot x \]

      10. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{1 + -1 \cdot y}{z}} \cdot x \]

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

          \[\leadsto \frac{\color{blue}{1 - \left(\mathsf{neg}\left(-1\right)\right) \cdot y}}{z} \cdot x \]

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. lower--.f64 58.9

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

   5. Applied rewrites 58.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 58.9%

      \[\leadsto \frac{-y}{z} \cdot x \]

   if -1.3e20 < y < -1.9000000000000001e-64

   1. Initial program 99.8%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{y \cdot z}}{z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 79.0

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

   5. Applied rewrites 79.0%

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

   if -1.9000000000000001e-64 < y < 6.99999999999999987e-53

   1. Initial program 100.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 75.9

         \[\leadsto \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{\frac{x}{z}} \]

   if 6.99999999999999987e-53 < y < 5.6e23 or 2.2999999999999998e149 < y

   1. Initial program 69.7%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 97.8

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 68.3%

      \[\leadsto 1 \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;\frac{-y}{z} \cdot x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;\frac{z \cdot y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+23} \lor \neg \left(y \leq 2.3 \cdot 10^{+149}\right):\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-64} \lor \neg \left(y \leq 7 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{z - x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e-64) (not (<= y 7e-53))) (* (/ (- z x) z) y) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e-64) || !(y <= 7e-53)) {
		tmp = ((z - x) / z) * y;
	} else {
		tmp = x / z;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.8d-64)) .or. (.not. (y <= 7d-53))) then
        tmp = ((z - x) / z) * y
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e-64) || !(y <= 7e-53)) {
		tmp = ((z - x) / z) * y;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e-64) or not (y <= 7e-53):
		tmp = ((z - x) / z) * y
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e-64) || !(y <= 7e-53))
		tmp = Float64(Float64(Float64(z - x) / z) * y);
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e-64) || ~((y <= 7e-53)))
		tmp = ((z - x) / z) * y;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e-64], N[Not[LessEqual[y, 7e-53]], $MachinePrecision]], N[(N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e-64 or 6.99999999999999987e-53 < y

   1. Initial program 83.1%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 97.6

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

   5. Applied rewrites 97.6%

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

   if -1.7999999999999999e-64 < y < 6.99999999999999987e-53

   1. Initial program 100.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 75.9

         \[\leadsto \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-64} \lor \neg \left(y \leq 7 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{z - x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-140} \lor \neg \left(x \leq 6.4 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{1 - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.5e-140) (not (<= x 6.4e-32)))
   (* (/ (- 1.0 y) z) x)
   (* 1.0 y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e-140) || !(x <= 6.4e-32)) {
		tmp = ((1.0 - y) / z) * x;
	} else {
		tmp = 1.0 * 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.5d-140)) .or. (.not. (x <= 6.4d-32))) then
        tmp = ((1.0d0 - y) / z) * x
    else
        tmp = 1.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e-140) || !(x <= 6.4e-32)) {
		tmp = ((1.0 - y) / z) * x;
	} else {
		tmp = 1.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.5e-140) or not (x <= 6.4e-32):
		tmp = ((1.0 - y) / z) * x
	else:
		tmp = 1.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.5e-140) || !(x <= 6.4e-32))
		tmp = Float64(Float64(Float64(1.0 - y) / z) * x);
	else
		tmp = Float64(1.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.5e-140) || ~((x <= 6.4e-32)))
		tmp = ((1.0 - y) / z) * x;
	else
		tmp = 1.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.5e-140], N[Not[LessEqual[x, 6.4e-32]], $MachinePrecision]], N[(N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.50000000000000007e-140 or 6.4000000000000004e-32 < x

   1. Initial program 90.1%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{1 + -1 \cdot y}{z} \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-1 \cdot y + 1}}{z} \cdot x \]

      4. div-add-rev N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot y + 1}{z}} \cdot x \]

      9. +-commutative N/A

         \[\leadsto \frac{\color{blue}{1 + -1 \cdot y}}{z} \cdot x \]

      10. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{1 + -1 \cdot y}{z}} \cdot x \]

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

          \[\leadsto \frac{\color{blue}{1 - \left(\mathsf{neg}\left(-1\right)\right) \cdot y}}{z} \cdot x \]

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. lower--.f64 80.8

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

   5. Applied rewrites 80.8%

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

   if -2.50000000000000007e-140 < x < 6.4000000000000004e-32

   1. Initial program 88.1%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 83.4

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 77.7%

      \[\leadsto 1 \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-140} \lor \neg \left(x \leq 6.4 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{1 - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-64}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, -y, y\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e-64)
   (fma (/ x z) (- y) y)
   (if (<= y 7e-53) (/ x z) (* (/ (- z x) z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e-64) {
		tmp = fma((x / z), -y, y);
	} else if (y <= 7e-53) {
		tmp = x / z;
	} else {
		tmp = ((z - x) / z) * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e-64)
		tmp = fma(Float64(x / z), Float64(-y), y);
	elseif (y <= 7e-53)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(Float64(z - x) / z) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.8e-64], N[(N[(x / z), $MachinePrecision] * (-y) + y), $MachinePrecision], If[LessEqual[y, 7e-53], N[(x / z), $MachinePrecision], N[(N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7999999999999999e-64

   1. Initial program 88.6%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{z}, 1 - y, y\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{x}{z}, -1 \cdot \color{blue}{y}, y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 96.6%

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

   if -1.7999999999999999e-64 < y < 6.99999999999999987e-53

   1. Initial program 100.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 75.9

         \[\leadsto \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{\frac{x}{z}} \]

   if 6.99999999999999987e-53 < y

   1. Initial program 77.4%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 98.7

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

   5. Applied rewrites 98.7%

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

Alternative 7: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-64} \lor \neg \left(y \leq 7 \cdot 10^{-53}\right):\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e-64) (not (<= y 7e-53))) (* 1.0 y) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e-64) || !(y <= 7e-53)) {
		tmp = 1.0 * y;
	} else {
		tmp = x / z;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.9d-64)) .or. (.not. (y <= 7d-53))) then
        tmp = 1.0d0 * y
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e-64) || !(y <= 7e-53)) {
		tmp = 1.0 * y;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.9e-64) or not (y <= 7e-53):
		tmp = 1.0 * y
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.9e-64) || !(y <= 7e-53))
		tmp = Float64(1.0 * y);
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.9e-64) || ~((y <= 7e-53)))
		tmp = 1.0 * y;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.9e-64], N[Not[LessEqual[y, 7e-53]], $MachinePrecision]], N[(1.0 * y), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000001e-64 or 6.99999999999999987e-53 < y

   1. Initial program 83.1%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 97.6

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 51.3%

      \[\leadsto 1 \cdot y \]

   if -1.9000000000000001e-64 < y < 6.99999999999999987e-53

   1. Initial program 100.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 75.9

         \[\leadsto \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-64} \lor \neg \left(y \leq 7 \cdot 10^{-53}\right):\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.0% accurate, 3.8× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* 1.0 y))

C

double code(double x, double y, double z) {
	return 1.0 * 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 * y
end function

Java

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

Python

def code(x, y, z):
	return 1.0 * y

Julia

function code(x, y, z)
	return Float64(1.0 * y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 * y;
end

Wolfram

code[x_, y_, z_] := N[(1.0 * y), $MachinePrecision]

Derivation

1. Initial program 89.3%

   \[\frac{x + y \cdot \left(z - x\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
4. Step-by-step derivation

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower--.f64 71.9

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

5. Applied rewrites 71.9%

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

6. Taylor expanded in x around 0

   \[\leadsto 1 \cdot y \]
7. Step-by-step derivation

8. Applied rewrites 41.9%

   \[\leadsto 1 \cdot y \]
9. Add Preprocessing

Developer Target 1: 94.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ y (/ x z)) (/ y (/ z x))))

C

double code(double x, double y, double z) {
	return (y + (x / z)) - (y / (z / x));
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y + (x / z)) - (y / (z / x))
end function

Java

public static double code(double x, double y, double z) {
	return (y + (x / z)) - (y / (z / x));
}

Python

def code(x, y, z):
	return (y + (x / z)) - (y / (z / x))

Julia

function code(x, y, z)
	return Float64(Float64(y + Float64(x / z)) - Float64(y / Float64(z / x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y + (x / z)) - (y / (z / x));
end

Wolfram

code[x_, y_, z_] := N[(N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision] - N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024356 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ y (/ x z)) (/ y (/ z x))))

  (/ (+ x (* y (- z x))) z))