Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C

Percentage Accurate: 99.9% → 100.0%

Time: 5.1s

Alternatives: 11

Speedup: 1.5×

• 20.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / 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 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / 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 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x - z}{y}, 4, 2\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (/ (- x z) y) 4.0 2.0))

C

double code(double x, double y, double z) {
	return fma(((x - z) / y), 4.0, 2.0);
}

Julia

function code(x, y, z)
	return fma(Float64(Float64(x - z) / y), 4.0, 2.0)
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision] * 4.0 + 2.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - z}{y}, 4, 2\right)} \]
6. Add Preprocessing

Alternative 2: 67.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+92}:\\ \;\;\;\;\frac{-4 \cdot z}{y}\\ \mathbf{elif}\;t\_0 \leq -50 \lor \neg \left(t\_0 \leq 10\right):\\ \;\;\;\;\frac{x}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y))))
   (if (<= t_0 -1e+92)
     (/ (* -4.0 z) y)
     (if (or (<= t_0 -50.0) (not (<= t_0 10.0))) (* (/ x y) 4.0) 2.0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	double tmp;
	if (t_0 <= -1e+92) {
		tmp = (-4.0 * z) / y;
	} else if ((t_0 <= -50.0) || !(t_0 <= 10.0)) {
		tmp = (x / y) * 4.0;
	} else {
		tmp = 2.0;
	}
	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 = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
    if (t_0 <= (-1d+92)) then
        tmp = ((-4.0d0) * z) / y
    else if ((t_0 <= (-50.0d0)) .or. (.not. (t_0 <= 10.0d0))) then
        tmp = (x / y) * 4.0d0
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	double tmp;
	if (t_0 <= -1e+92) {
		tmp = (-4.0 * z) / y;
	} else if ((t_0 <= -50.0) || !(t_0 <= 10.0)) {
		tmp = (x / y) * 4.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)
	tmp = 0
	if t_0 <= -1e+92:
		tmp = (-4.0 * z) / y
	elif (t_0 <= -50.0) or not (t_0 <= 10.0):
		tmp = (x / y) * 4.0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
	tmp = 0.0
	if (t_0 <= -1e+92)
		tmp = Float64(Float64(-4.0 * z) / y);
	elseif ((t_0 <= -50.0) || !(t_0 <= 10.0))
		tmp = Float64(Float64(x / y) * 4.0);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	tmp = 0.0;
	if (t_0 <= -1e+92)
		tmp = (-4.0 * z) / y;
	elseif ((t_0 <= -50.0) || ~((t_0 <= 10.0)))
		tmp = (x / y) * 4.0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+92], N[(N[(-4.0 * z), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[t$95$0, -50.0], N[Not[LessEqual[t$95$0, 10.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * 4.0), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < -1e92

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot z}{y}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{-4}{y} \cdot z} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot 1}}{y} \cdot z \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{1}{y}\right)} \cdot z \]

      5. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \frac{1}{y}\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{1}{y}\right) \cdot z} \]

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{-4} \cdot \frac{1}{y}\right) \cdot z \]

      8. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot 1}{y}} \cdot z \]

      9. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{-4}}{y} \cdot z \]

      10. lower-/.f64 58.8

          \[\leadsto \color{blue}{\frac{-4}{y}} \cdot z \]

   5. Applied rewrites 58.8%

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

   7. Applied rewrites 58.9%

      \[\leadsto \frac{-4 \cdot z}{\color{blue}{y}} \]

   if -1e92 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < -50 or 10 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

      3. lower-/.f64 56.7

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot 4 \]

   5. Applied rewrites 56.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

   if -50 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < 10

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq -1 \cdot 10^{+92}:\\ \;\;\;\;\frac{-4 \cdot z}{y}\\ \mathbf{elif}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq -50 \lor \neg \left(1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq 10\right):\\ \;\;\;\;\frac{x}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+92}:\\ \;\;\;\;\frac{-4}{y} \cdot z\\ \mathbf{elif}\;t\_0 \leq -50 \lor \neg \left(t\_0 \leq 10\right):\\ \;\;\;\;\frac{x}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y))))
   (if (<= t_0 -1e+92)
     (* (/ -4.0 y) z)
     (if (or (<= t_0 -50.0) (not (<= t_0 10.0))) (* (/ x y) 4.0) 2.0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	double tmp;
	if (t_0 <= -1e+92) {
		tmp = (-4.0 / y) * z;
	} else if ((t_0 <= -50.0) || !(t_0 <= 10.0)) {
		tmp = (x / y) * 4.0;
	} else {
		tmp = 2.0;
	}
	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 = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
    if (t_0 <= (-1d+92)) then
        tmp = ((-4.0d0) / y) * z
    else if ((t_0 <= (-50.0d0)) .or. (.not. (t_0 <= 10.0d0))) then
        tmp = (x / y) * 4.0d0
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	double tmp;
	if (t_0 <= -1e+92) {
		tmp = (-4.0 / y) * z;
	} else if ((t_0 <= -50.0) || !(t_0 <= 10.0)) {
		tmp = (x / y) * 4.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)
	tmp = 0
	if t_0 <= -1e+92:
		tmp = (-4.0 / y) * z
	elif (t_0 <= -50.0) or not (t_0 <= 10.0):
		tmp = (x / y) * 4.0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
	tmp = 0.0
	if (t_0 <= -1e+92)
		tmp = Float64(Float64(-4.0 / y) * z);
	elseif ((t_0 <= -50.0) || !(t_0 <= 10.0))
		tmp = Float64(Float64(x / y) * 4.0);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	tmp = 0.0;
	if (t_0 <= -1e+92)
		tmp = (-4.0 / y) * z;
	elseif ((t_0 <= -50.0) || ~((t_0 <= 10.0)))
		tmp = (x / y) * 4.0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+92], N[(N[(-4.0 / y), $MachinePrecision] * z), $MachinePrecision], If[Or[LessEqual[t$95$0, -50.0], N[Not[LessEqual[t$95$0, 10.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * 4.0), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < -1e92

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot z}{y}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{-4}{y} \cdot z} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot 1}}{y} \cdot z \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{1}{y}\right)} \cdot z \]

      5. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \frac{1}{y}\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{1}{y}\right) \cdot z} \]

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{-4} \cdot \frac{1}{y}\right) \cdot z \]

      8. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot 1}{y}} \cdot z \]

      9. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{-4}}{y} \cdot z \]

      10. lower-/.f64 58.8

          \[\leadsto \color{blue}{\frac{-4}{y}} \cdot z \]

   5. Applied rewrites 58.8%

      \[\leadsto \color{blue}{\frac{-4}{y} \cdot z} \]

   if -1e92 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < -50 or 10 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

      3. lower-/.f64 56.7

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot 4 \]

   5. Applied rewrites 56.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

   if -50 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < 10

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq -1 \cdot 10^{+92}:\\ \;\;\;\;\frac{-4}{y} \cdot z\\ \mathbf{elif}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq -50 \lor \neg \left(1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq 10\right):\\ \;\;\;\;\frac{x}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+92}:\\ \;\;\;\;\frac{-4}{y} \cdot z\\ \mathbf{elif}\;t\_0 \leq -50 \lor \neg \left(t\_0 \leq 10\right):\\ \;\;\;\;\frac{4}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y))))
   (if (<= t_0 -1e+92)
     (* (/ -4.0 y) z)
     (if (or (<= t_0 -50.0) (not (<= t_0 10.0))) (* (/ 4.0 y) x) 2.0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	double tmp;
	if (t_0 <= -1e+92) {
		tmp = (-4.0 / y) * z;
	} else if ((t_0 <= -50.0) || !(t_0 <= 10.0)) {
		tmp = (4.0 / y) * x;
	} else {
		tmp = 2.0;
	}
	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 = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
    if (t_0 <= (-1d+92)) then
        tmp = ((-4.0d0) / y) * z
    else if ((t_0 <= (-50.0d0)) .or. (.not. (t_0 <= 10.0d0))) then
        tmp = (4.0d0 / y) * x
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	double tmp;
	if (t_0 <= -1e+92) {
		tmp = (-4.0 / y) * z;
	} else if ((t_0 <= -50.0) || !(t_0 <= 10.0)) {
		tmp = (4.0 / y) * x;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)
	tmp = 0
	if t_0 <= -1e+92:
		tmp = (-4.0 / y) * z
	elif (t_0 <= -50.0) or not (t_0 <= 10.0):
		tmp = (4.0 / y) * x
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
	tmp = 0.0
	if (t_0 <= -1e+92)
		tmp = Float64(Float64(-4.0 / y) * z);
	elseif ((t_0 <= -50.0) || !(t_0 <= 10.0))
		tmp = Float64(Float64(4.0 / y) * x);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	tmp = 0.0;
	if (t_0 <= -1e+92)
		tmp = (-4.0 / y) * z;
	elseif ((t_0 <= -50.0) || ~((t_0 <= 10.0)))
		tmp = (4.0 / y) * x;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+92], N[(N[(-4.0 / y), $MachinePrecision] * z), $MachinePrecision], If[Or[LessEqual[t$95$0, -50.0], N[Not[LessEqual[t$95$0, 10.0]], $MachinePrecision]], N[(N[(4.0 / y), $MachinePrecision] * x), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < -1e92

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot z}{y}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{-4}{y} \cdot z} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot 1}}{y} \cdot z \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{1}{y}\right)} \cdot z \]

      5. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \frac{1}{y}\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{1}{y}\right) \cdot z} \]

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{-4} \cdot \frac{1}{y}\right) \cdot z \]

      8. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot 1}{y}} \cdot z \]

      9. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{-4}}{y} \cdot z \]

      10. lower-/.f64 58.8

          \[\leadsto \color{blue}{\frac{-4}{y}} \cdot z \]

   5. Applied rewrites 58.8%

      \[\leadsto \color{blue}{\frac{-4}{y} \cdot z} \]

   if -1e92 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < -50 or 10 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

      3. lower-/.f64 56.7

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot 4 \]

   5. Applied rewrites 56.7%

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

   7. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot x} \]

   if -50 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < 10

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq -1 \cdot 10^{+92}:\\ \;\;\;\;\frac{-4}{y} \cdot z\\ \mathbf{elif}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq -50 \lor \neg \left(1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq 10\right):\\ \;\;\;\;\frac{4}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+24} \lor \neg \left(t\_0 \leq 10\right):\\ \;\;\;\;\frac{x - z}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y))))
   (if (or (<= t_0 -1e+24) (not (<= t_0 10.0)))
     (* (/ (- x z) y) 4.0)
     (fma (/ z y) -4.0 2.0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	double tmp;
	if ((t_0 <= -1e+24) || !(t_0 <= 10.0)) {
		tmp = ((x - z) / y) * 4.0;
	} else {
		tmp = fma((z / y), -4.0, 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
	tmp = 0.0
	if ((t_0 <= -1e+24) || !(t_0 <= 10.0))
		tmp = Float64(Float64(Float64(x - z) / y) * 4.0);
	else
		tmp = fma(Float64(z / y), -4.0, 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e+24], N[Not[LessEqual[t$95$0, 10.0]], $MachinePrecision]], N[(N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision] * 4.0), $MachinePrecision], N[(N[(z / y), $MachinePrecision] * -4.0 + 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < -9.9999999999999998e23 or 10 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x - z}{y} \cdot 4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x - z}{y} \cdot 4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x - z}{y}} \cdot 4 \]

      4. lower--.f64 99.7

         \[\leadsto \frac{\color{blue}{x - z}}{y} \cdot 4 \]

   5. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{x - z}{y} \cdot 4} \]

   if -9.9999999999999998e23 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < 10

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - z}{y}, 4, 2\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}} \]

   8. Applied rewrites 98.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 98.7%

       \[\leadsto \mathsf{fma}\left(\frac{z}{y}, \color{blue}{-4}, 2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq -1 \cdot 10^{+24} \lor \neg \left(1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq 10\right):\\ \;\;\;\;\frac{x - z}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -50 \lor \neg \left(t\_0 \leq 5 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{-4}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y))))
   (if (or (<= t_0 -50.0) (not (<= t_0 5e+35))) (* (/ -4.0 y) z) 2.0)))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	double tmp;
	if ((t_0 <= -50.0) || !(t_0 <= 5e+35)) {
		tmp = (-4.0 / y) * z;
	} else {
		tmp = 2.0;
	}
	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 = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
    if ((t_0 <= (-50.0d0)) .or. (.not. (t_0 <= 5d+35))) then
        tmp = ((-4.0d0) / y) * z
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	double tmp;
	if ((t_0 <= -50.0) || !(t_0 <= 5e+35)) {
		tmp = (-4.0 / y) * z;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)
	tmp = 0
	if (t_0 <= -50.0) or not (t_0 <= 5e+35):
		tmp = (-4.0 / y) * z
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
	tmp = 0.0
	if ((t_0 <= -50.0) || !(t_0 <= 5e+35))
		tmp = Float64(Float64(-4.0 / y) * z);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
	tmp = 0.0;
	if ((t_0 <= -50.0) || ~((t_0 <= 5e+35)))
		tmp = (-4.0 / y) * z;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -50.0], N[Not[LessEqual[t$95$0, 5e+35]], $MachinePrecision]], N[(N[(-4.0 / y), $MachinePrecision] * z), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < -50 or 5.00000000000000021e35 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot z}{y}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{-4}{y} \cdot z} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot 1}}{y} \cdot z \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{1}{y}\right)} \cdot z \]

      5. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \frac{1}{y}\right) \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{1}{y}\right) \cdot z} \]

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{-4} \cdot \frac{1}{y}\right) \cdot z \]

      8. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-4 \cdot 1}{y}} \cdot z \]

      9. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{-4}}{y} \cdot z \]

      10. lower-/.f64 52.7

          \[\leadsto \color{blue}{\frac{-4}{y}} \cdot z \]

   5. Applied rewrites 52.7%

      \[\leadsto \color{blue}{\frac{-4}{y} \cdot z} \]

   if -50 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 1/4 binary64))) z)) y)) < 5.00000000000000021e35

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2} \]
   4. Step-by-step derivation

   5. Applied rewrites 93.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq -50 \lor \neg \left(1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \leq 5 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{-4}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+79} \lor \neg \left(x \leq 9.5 \cdot 10^{-22}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, 4, 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.6e+79) (not (<= x 9.5e-22)))
   (fma (/ x y) 4.0 2.0)
   (fma (/ z y) -4.0 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.6e+79) || !(x <= 9.5e-22)) {
		tmp = fma((x / y), 4.0, 2.0);
	} else {
		tmp = fma((z / y), -4.0, 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.6e+79) || !(x <= 9.5e-22))
		tmp = fma(Float64(x / y), 4.0, 2.0);
	else
		tmp = fma(Float64(z / y), -4.0, 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.6e+79], N[Not[LessEqual[x, 9.5e-22]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * 4.0 + 2.0), $MachinePrecision], N[(N[(z / y), $MachinePrecision] * -4.0 + 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.59999999999999942e79 or 9.4999999999999994e-22 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{4 \cdot \frac{x + \frac{1}{4} \cdot y}{y} + 1} \]

      2. div-add N/A

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{y} + \frac{\frac{1}{4} \cdot y}{y}\right)} + 1 \]

      3. distribute-lft-in N/A

         \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y}{y}\right)} + 1 \]

      4. associate-/l* N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + 4 \cdot \color{blue}{\left(\frac{1}{4} \cdot \frac{y}{y}\right)}\right) + 1 \]

      5. *-inverses N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + 4 \cdot \left(\frac{1}{4} \cdot \color{blue}{1}\right)\right) + 1 \]

      6. metadata-eval N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + 4 \cdot \color{blue}{\frac{1}{4}}\right) + 1 \]

      7. metadata-eval N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + \color{blue}{1}\right) + 1 \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{4 \cdot \frac{x}{y} + \left(1 + 1\right)} \]

      9. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{4 \cdot x}{y}} + \left(1 + 1\right) \]

      10. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{4}{y} \cdot x} + \left(1 + 1\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{4 \cdot 1}}{y} \cdot x + \left(1 + 1\right) \]

      12. associate-*r/ N/A

          \[\leadsto \color{blue}{\left(4 \cdot \frac{1}{y}\right)} \cdot x + \left(1 + 1\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(4 \cdot \frac{1}{y}\right) \cdot x + \color{blue}{2} \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(4 \cdot \frac{1}{y}, x, 2\right)} \]

      15. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4 \cdot 1}{y}}, x, 2\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{4}}{y}, x, 2\right) \]

      17. lower-/.f64 88.1

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4}{y}}, x, 2\right) \]

   5. Applied rewrites 88.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 88.3%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{4}, 2\right) \]

   if -9.59999999999999942e79 < x < 9.4999999999999994e-22

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - z}{y}, 4, 2\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}} \]

   8. Applied rewrites 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 90.5%

       \[\leadsto \mathsf{fma}\left(\frac{z}{y}, \color{blue}{-4}, 2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+79} \lor \neg \left(x \leq 9.5 \cdot 10^{-22}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, 4, 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+79} \lor \neg \left(x \leq 9.5 \cdot 10^{-22}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, 4, 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.6e+79) (not (<= x 9.5e-22)))
   (fma (/ x y) 4.0 2.0)
   (fma (/ -4.0 y) z 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.6e+79) || !(x <= 9.5e-22)) {
		tmp = fma((x / y), 4.0, 2.0);
	} else {
		tmp = fma((-4.0 / y), z, 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.6e+79) || !(x <= 9.5e-22))
		tmp = fma(Float64(x / y), 4.0, 2.0);
	else
		tmp = fma(Float64(-4.0 / y), z, 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.6e+79], N[Not[LessEqual[x, 9.5e-22]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * 4.0 + 2.0), $MachinePrecision], N[(N[(-4.0 / y), $MachinePrecision] * z + 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.59999999999999942e79 or 9.4999999999999994e-22 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{4 \cdot \frac{x + \frac{1}{4} \cdot y}{y} + 1} \]

      2. div-add N/A

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{y} + \frac{\frac{1}{4} \cdot y}{y}\right)} + 1 \]

      3. distribute-lft-in N/A

         \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y}{y}\right)} + 1 \]

      4. associate-/l* N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + 4 \cdot \color{blue}{\left(\frac{1}{4} \cdot \frac{y}{y}\right)}\right) + 1 \]

      5. *-inverses N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + 4 \cdot \left(\frac{1}{4} \cdot \color{blue}{1}\right)\right) + 1 \]

      6. metadata-eval N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + 4 \cdot \color{blue}{\frac{1}{4}}\right) + 1 \]

      7. metadata-eval N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + \color{blue}{1}\right) + 1 \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{4 \cdot \frac{x}{y} + \left(1 + 1\right)} \]

      9. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{4 \cdot x}{y}} + \left(1 + 1\right) \]

      10. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{4}{y} \cdot x} + \left(1 + 1\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{4 \cdot 1}}{y} \cdot x + \left(1 + 1\right) \]

      12. associate-*r/ N/A

          \[\leadsto \color{blue}{\left(4 \cdot \frac{1}{y}\right)} \cdot x + \left(1 + 1\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(4 \cdot \frac{1}{y}\right) \cdot x + \color{blue}{2} \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(4 \cdot \frac{1}{y}, x, 2\right)} \]

      15. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4 \cdot 1}{y}}, x, 2\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{4}}{y}, x, 2\right) \]

      17. lower-/.f64 88.1

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4}{y}}, x, 2\right) \]

   5. Applied rewrites 88.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 88.3%

      \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \color{blue}{4}, 2\right) \]

   if -9.59999999999999942e79 < x < 9.4999999999999994e-22

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - z}{y}, 4, 2\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}} \]

   8. Applied rewrites 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+79} \lor \neg \left(x \leq 9.5 \cdot 10^{-22}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, 4, 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+79} \lor \neg \left(x \leq 5.7 \cdot 10^{-21}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.6e+79) (not (<= x 5.7e-21)))
   (fma (/ 4.0 y) x 2.0)
   (fma (/ -4.0 y) z 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.6e+79) || !(x <= 5.7e-21)) {
		tmp = fma((4.0 / y), x, 2.0);
	} else {
		tmp = fma((-4.0 / y), z, 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.6e+79) || !(x <= 5.7e-21))
		tmp = fma(Float64(4.0 / y), x, 2.0);
	else
		tmp = fma(Float64(-4.0 / y), z, 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.6e+79], N[Not[LessEqual[x, 5.7e-21]], $MachinePrecision]], N[(N[(4.0 / y), $MachinePrecision] * x + 2.0), $MachinePrecision], N[(N[(-4.0 / y), $MachinePrecision] * z + 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.59999999999999942e79 or 5.6999999999999996e-21 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{4 \cdot \frac{x + \frac{1}{4} \cdot y}{y} + 1} \]

      2. div-add N/A

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{y} + \frac{\frac{1}{4} \cdot y}{y}\right)} + 1 \]

      3. distribute-lft-in N/A

         \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y}{y}\right)} + 1 \]

      4. associate-/l* N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + 4 \cdot \color{blue}{\left(\frac{1}{4} \cdot \frac{y}{y}\right)}\right) + 1 \]

      5. *-inverses N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + 4 \cdot \left(\frac{1}{4} \cdot \color{blue}{1}\right)\right) + 1 \]

      6. metadata-eval N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + 4 \cdot \color{blue}{\frac{1}{4}}\right) + 1 \]

      7. metadata-eval N/A

         \[\leadsto \left(4 \cdot \frac{x}{y} + \color{blue}{1}\right) + 1 \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{4 \cdot \frac{x}{y} + \left(1 + 1\right)} \]

      9. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{4 \cdot x}{y}} + \left(1 + 1\right) \]

      10. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{4}{y} \cdot x} + \left(1 + 1\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{4 \cdot 1}}{y} \cdot x + \left(1 + 1\right) \]

      12. associate-*r/ N/A

          \[\leadsto \color{blue}{\left(4 \cdot \frac{1}{y}\right)} \cdot x + \left(1 + 1\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(4 \cdot \frac{1}{y}\right) \cdot x + \color{blue}{2} \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(4 \cdot \frac{1}{y}, x, 2\right)} \]

      15. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4 \cdot 1}{y}}, x, 2\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{4}}{y}, x, 2\right) \]

      17. lower-/.f64 88.1

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4}{y}}, x, 2\right) \]

   5. Applied rewrites 88.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 2\right)} \]

   if -9.59999999999999942e79 < x < 5.6999999999999996e-21

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - z}{y}, 4, 2\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}} \]

   8. Applied rewrites 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+79} \lor \neg \left(x \leq 5.7 \cdot 10^{-21}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+134} \lor \neg \left(x \leq 1.28 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{x}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.5e+134) (not (<= x 1.28e+120)))
   (* (/ x y) 4.0)
   (fma (/ -4.0 y) z 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.5e+134) || !(x <= 1.28e+120)) {
		tmp = (x / y) * 4.0;
	} else {
		tmp = fma((-4.0 / y), z, 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.5e+134) || !(x <= 1.28e+120))
		tmp = Float64(Float64(x / y) * 4.0);
	else
		tmp = fma(Float64(-4.0 / y), z, 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.5e+134], N[Not[LessEqual[x, 1.28e+120]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * 4.0), $MachinePrecision], N[(N[(-4.0 / y), $MachinePrecision] * z + 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4999999999999997e134 or 1.27999999999999996e120 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

      3. lower-/.f64 82.4

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot 4 \]

   5. Applied rewrites 82.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot 4} \]

   if -4.4999999999999997e134 < x < 1.27999999999999996e120

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - z}{y}, 4, 2\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}} \]

   8. Applied rewrites 84.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+134} \lor \neg \left(x \leq 1.28 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{x}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-4}{y}, z, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.7% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 2.0)

C

double code(double x, double y, double z) {
	return 2.0;
}

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 = 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 2.0;
}

Python

def code(x, y, z):
	return 2.0

Julia

function code(x, y, z)
	return 2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0;
end

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{2} \]
4. Step-by-step derivation

5. Applied rewrites 38.3%

   \[\leadsto \color{blue}{2} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025015 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))