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

Percentage Accurate: 88.3% → 99.9%

Time: 3.9s

Alternatives: 7

Speedup: 1.1×

• 22.1% 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: 88.3% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.8%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate-*r/ N/A

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

   3. div-add-rev N/A

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

   4. +-commutative N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. associate-/l* N/A

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

   8. lower-fma.f64 N/A

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

   9. cancel-sign-sub N/A

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

   10. metadata-eval N/A

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

   11. *-lft-identity N/A

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

   12. lower--.f64 N/A

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

   13. lower-/.f64 99.9

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

5. Applied rewrites 99.9%

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

Alternative 2: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-y}{z} \cdot x\\ \mathbf{if}\;y \leq -5 \cdot 10^{+215}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 95000000000:\\ \;\;\;\;\mathsf{fma}\left(1, \frac{x}{z}, y\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+264}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (- y) z) x)))
   (if (<= y -5e+215)
     t_0
     (if (<= y 95000000000.0)
       (fma 1.0 (/ x z) y)
       (if (<= y 1.25e+264) t_0 y)))))

C

double code(double x, double y, double z) {
	double t_0 = (-y / z) * x;
	double tmp;
	if (y <= -5e+215) {
		tmp = t_0;
	} else if (y <= 95000000000.0) {
		tmp = fma(1.0, (x / z), y);
	} else if (y <= 1.25e+264) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(-y) / z) * x)
	tmp = 0.0
	if (y <= -5e+215)
		tmp = t_0;
	elseif (y <= 95000000000.0)
		tmp = fma(1.0, Float64(x / z), y);
	elseif (y <= 1.25e+264)
		tmp = t_0;
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[((-y) / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -5e+215], t$95$0, If[LessEqual[y, 95000000000.0], N[(1.0 * N[(x / z), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[y, 1.25e+264], t$95$0, y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000001e215 or 9.5e10 < y < 1.25000000000000008e264

   1. Initial program 79.1%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. div-add-rev N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 64.1

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

   8. Applied rewrites 64.1%

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

   9. Taylor expanded in y around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. mul-1-neg N/A

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

       4. lower-neg.f64 64.1

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

   11. Applied rewrites 64.1%

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

   if -5.0000000000000001e215 < y < 9.5e10

   1. Initial program 93.3%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. div-add-rev N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.1%

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

   if 1.25000000000000008e264 < y

   1. Initial program 44.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 79.1%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -16000000 \lor \neg \left(y \leq 0.0115\right):\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{x}{z}, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, \frac{x}{z}, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -16000000.0) (not (<= y 0.0115)))
   (fma (- y) (/ x z) y)
   (fma 1.0 (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -16000000.0) || !(y <= 0.0115)) {
		tmp = fma(-y, (x / z), y);
	} else {
		tmp = fma(1.0, (x / z), y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -16000000.0) || !(y <= 0.0115))
		tmp = fma(Float64(-y), Float64(x / z), y);
	else
		tmp = fma(1.0, Float64(x / z), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -16000000.0], N[Not[LessEqual[y, 0.0115]], $MachinePrecision]], N[((-y) * N[(x / z), $MachinePrecision] + y), $MachinePrecision], N[(1.0 * N[(x / z), $MachinePrecision] + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e7 or 0.0115 < y

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. div-add-rev N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 99.3

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

   8. Applied rewrites 99.3%

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

   if -1.6e7 < y < 0.0115

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. div-add-rev N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 99.3%

      \[\leadsto \mathsf{fma}\left(1, \frac{\color{blue}{x}}{z}, y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -16000000 \lor \neg \left(y \leq 0.0115\right):\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{x}{z}, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, \frac{x}{z}, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+37} \lor \neg \left(z \leq 7000\right):\\ \;\;\;\;\mathsf{fma}\left(1, \frac{x}{z}, y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.9e+37) (not (<= z 7000.0)))
   (fma 1.0 (/ x z) y)
   (* (/ x z) (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.9e+37) || !(z <= 7000.0)) {
		tmp = fma(1.0, (x / z), y);
	} else {
		tmp = (x / z) * (1.0 - y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.9e+37) || !(z <= 7000.0))
		tmp = fma(1.0, Float64(x / z), y);
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.9e+37], N[Not[LessEqual[z, 7000.0]], $MachinePrecision]], N[(1.0 * N[(x / z), $MachinePrecision] + y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999978e37 or 7e3 < z

   1. Initial program 74.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. div-add-rev N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.2%

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

   if -2.89999999999999978e37 < z < 7e3

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. div-add-rev N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. cancel-sign-sub N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 87.4

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

   8. Applied rewrites 87.4%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift--.f64 89.1

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

   10. Applied rewrites 89.1%

       \[\leadsto \frac{x}{z} \cdot \left(1 - \color{blue}{y}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+37} \lor \neg \left(z \leq 7000\right):\\ \;\;\;\;\mathsf{fma}\left(1, \frac{x}{z}, y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -740:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -740.0) y (if (<= y 1.72e-121) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -740.0) {
		tmp = y;
	} else if (y <= 1.72e-121) {
		tmp = x / z;
	} else {
		tmp = 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 (y <= (-740.0d0)) then
        tmp = y
    else if (y <= 1.72d-121) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -740.0) {
		tmp = y;
	} else if (y <= 1.72e-121) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -740.0:
		tmp = y
	elif y <= 1.72e-121:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -740.0)
		tmp = y;
	elseif (y <= 1.72e-121)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -740.0)
		tmp = y;
	elseif (y <= 1.72e-121)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -740.0], y, If[LessEqual[y, 1.72e-121], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -740 or 1.72000000000000007e-121 < y

   1. Initial program 78.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 48.9%

      \[\leadsto \color{blue}{y} \]

   if -740 < y < 1.72000000000000007e-121

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 77.9%

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

Alternative 6: 77.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.8%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate-*r/ N/A

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

   3. div-add-rev N/A

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

   4. +-commutative N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. associate-/l* N/A

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

   8. lower-fma.f64 N/A

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

   9. cancel-sign-sub N/A

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

   10. metadata-eval N/A

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

   11. *-lft-identity N/A

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

   12. lower--.f64 N/A

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

   13. lower-/.f64 99.9

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

5. Applied rewrites 99.9%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 74.2%

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

Alternative 7: 39.8% accurate, 23.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = y
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return y
end

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 86.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 38.6%

   \[\leadsto \color{blue}{y} \]
6. Add Preprocessing

Developer Target 1: 93.5% 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 2025037 
(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))