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

Percentage Accurate: 99.7% → 100.0%

Time: 5.0s

Alternatives: 10

Speedup: 1.5×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 100.0%

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

Alternative 2: 66.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} \cdot 4\\ t_1 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+161}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -100:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;t\_1 \leq 4000000:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x y) 4.0))
        (t_1 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y))))
   (if (<= t_1 -1e+161)
     t_0
     (if (<= t_1 -100.0) (* (/ z y) -4.0) (if (<= t_1 4000000.0) 4.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (x / y) * 4.0;
	double t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	double tmp;
	if (t_1 <= -1e+161) {
		tmp = t_0;
	} else if (t_1 <= -100.0) {
		tmp = (z / y) * -4.0;
	} else if (t_1 <= 4000000.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x / y) * 4.0d0
    t_1 = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
    if (t_1 <= (-1d+161)) then
        tmp = t_0
    else if (t_1 <= (-100.0d0)) then
        tmp = (z / y) * (-4.0d0)
    else if (t_1 <= 4000000.0d0) then
        tmp = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / y) * 4.0;
	double t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	double tmp;
	if (t_1 <= -1e+161) {
		tmp = t_0;
	} else if (t_1 <= -100.0) {
		tmp = (z / y) * -4.0;
	} else if (t_1 <= 4000000.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / y) * 4.0
	t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)
	tmp = 0
	if t_1 <= -1e+161:
		tmp = t_0
	elif t_1 <= -100.0:
		tmp = (z / y) * -4.0
	elif t_1 <= 4000000.0:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / y) * 4.0)
	t_1 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
	tmp = 0.0
	if (t_1 <= -1e+161)
		tmp = t_0;
	elseif (t_1 <= -100.0)
		tmp = Float64(Float64(z / y) * -4.0);
	elseif (t_1 <= 4000000.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / y) * 4.0;
	t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	tmp = 0.0;
	if (t_1 <= -1e+161)
		tmp = t_0;
	elseif (t_1 <= -100.0)
		tmp = (z / y) * -4.0;
	elseif (t_1 <= 4000000.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+161], t$95$0, If[LessEqual[t$95$1, -100.0], N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 4000000.0], 4.0, t$95$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 3/4 binary64))) z)) y)) < -1e161 or 4e6 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 59.5%

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

   if -1e161 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)) < -100

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 60.3%

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

   if -100 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)) < 4e6

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 96.0%

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

Alternative 3: 66.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} \cdot 4\\ t_1 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+161}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -100:\\ \;\;\;\;\frac{-4}{y} \cdot z\\ \mathbf{elif}\;t\_1 \leq 4000000:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x y) 4.0))
        (t_1 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y))))
   (if (<= t_1 -1e+161)
     t_0
     (if (<= t_1 -100.0) (* (/ -4.0 y) z) (if (<= t_1 4000000.0) 4.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (x / y) * 4.0;
	double t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	double tmp;
	if (t_1 <= -1e+161) {
		tmp = t_0;
	} else if (t_1 <= -100.0) {
		tmp = (-4.0 / y) * z;
	} else if (t_1 <= 4000000.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x / y) * 4.0d0
    t_1 = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
    if (t_1 <= (-1d+161)) then
        tmp = t_0
    else if (t_1 <= (-100.0d0)) then
        tmp = ((-4.0d0) / y) * z
    else if (t_1 <= 4000000.0d0) then
        tmp = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / y) * 4.0;
	double t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	double tmp;
	if (t_1 <= -1e+161) {
		tmp = t_0;
	} else if (t_1 <= -100.0) {
		tmp = (-4.0 / y) * z;
	} else if (t_1 <= 4000000.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / y) * 4.0
	t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)
	tmp = 0
	if t_1 <= -1e+161:
		tmp = t_0
	elif t_1 <= -100.0:
		tmp = (-4.0 / y) * z
	elif t_1 <= 4000000.0:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / y) * 4.0)
	t_1 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
	tmp = 0.0
	if (t_1 <= -1e+161)
		tmp = t_0;
	elseif (t_1 <= -100.0)
		tmp = Float64(Float64(-4.0 / y) * z);
	elseif (t_1 <= 4000000.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / y) * 4.0;
	t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	tmp = 0.0;
	if (t_1 <= -1e+161)
		tmp = t_0;
	elseif (t_1 <= -100.0)
		tmp = (-4.0 / y) * z;
	elseif (t_1 <= 4000000.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+161], t$95$0, If[LessEqual[t$95$1, -100.0], N[(N[(-4.0 / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 4000000.0], 4.0, t$95$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 3/4 binary64))) z)) y)) < -1e161 or 4e6 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 59.5%

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

   if -1e161 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)) < -100

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 60.1%

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

   if -100 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)) < 4e6

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 96.0%

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

Alternative 4: 66.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{4}{y}\\ t_1 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+218}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -100:\\ \;\;\;\;\frac{-4}{y} \cdot z\\ \mathbf{elif}\;t\_1 \leq 4000000:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ 4.0 y)))
        (t_1 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y))))
   (if (<= t_1 -5e+218)
     t_0
     (if (<= t_1 -100.0) (* (/ -4.0 y) z) (if (<= t_1 4000000.0) 4.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.0 / y);
	double t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	double tmp;
	if (t_1 <= -5e+218) {
		tmp = t_0;
	} else if (t_1 <= -100.0) {
		tmp = (-4.0 / y) * z;
	} else if (t_1 <= 4000000.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (4.0d0 / y)
    t_1 = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
    if (t_1 <= (-5d+218)) then
        tmp = t_0
    else if (t_1 <= (-100.0d0)) then
        tmp = ((-4.0d0) / y) * z
    else if (t_1 <= 4000000.0d0) then
        tmp = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (4.0 / y);
	double t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	double tmp;
	if (t_1 <= -5e+218) {
		tmp = t_0;
	} else if (t_1 <= -100.0) {
		tmp = (-4.0 / y) * z;
	} else if (t_1 <= 4000000.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.0 / y)
	t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)
	tmp = 0
	if t_1 <= -5e+218:
		tmp = t_0
	elif t_1 <= -100.0:
		tmp = (-4.0 / y) * z
	elif t_1 <= 4000000.0:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.0 / y))
	t_1 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
	tmp = 0.0
	if (t_1 <= -5e+218)
		tmp = t_0;
	elseif (t_1 <= -100.0)
		tmp = Float64(Float64(-4.0 / y) * z);
	elseif (t_1 <= 4000000.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.0 / y);
	t_1 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	tmp = 0.0;
	if (t_1 <= -5e+218)
		tmp = t_0;
	elseif (t_1 <= -100.0)
		tmp = (-4.0 / y) * z;
	elseif (t_1 <= 4000000.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+218], t$95$0, If[LessEqual[t$95$1, -100.0], N[(N[(-4.0 / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 4000000.0], 4.0, t$95$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 3/4 binary64))) z)) y)) < -4.99999999999999983e218 or 4e6 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 60.0%

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

   7. Applied rewrites 59.8%

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

   if -4.99999999999999983e218 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)) < -100

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 58.8%

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

   if -100 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)) < 4e6

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 96.0%

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

Alternative 5: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -20000 \lor \neg \left(t\_0 \leq 50000000000\right):\\ \;\;\;\;\frac{x - z}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, 4, 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y))))
   (if (or (<= t_0 -20000.0) (not (<= t_0 50000000000.0)))
     (* (/ (- x z) y) 4.0)
     (fma (/ x y) 4.0 4.0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	double tmp;
	if ((t_0 <= -20000.0) || !(t_0 <= 50000000000.0)) {
		tmp = ((x - z) / y) * 4.0;
	} else {
		tmp = fma((x / y), 4.0, 4.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
	tmp = 0.0
	if ((t_0 <= -20000.0) || !(t_0 <= 50000000000.0))
		tmp = Float64(Float64(Float64(x - z) / y) * 4.0);
	else
		tmp = fma(Float64(x / y), 4.0, 4.0);
	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 * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -20000.0], N[Not[LessEqual[t$95$0, 50000000000.0]], $MachinePrecision]], N[(N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision] * 4.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * 4.0 + 4.0), $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 3/4 binary64))) z)) y)) < -2e4 or 5e10 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 99.6%

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

   if -2e4 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)) < 5e10

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 98.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \leq -20000 \lor \neg \left(1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \leq 50000000000\right):\\ \;\;\;\;\frac{x - z}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, 4, 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -100 \lor \neg \left(t\_0 \leq 4000000\right):\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y))))
   (if (or (<= t_0 -100.0) (not (<= t_0 4000000.0))) (* x (/ 4.0 y)) 4.0)))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	double tmp;
	if ((t_0 <= -100.0) || !(t_0 <= 4000000.0)) {
		tmp = x * (4.0 / y);
	} else {
		tmp = 4.0;
	}
	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 * 0.75d0)) - z)) / y)
    if ((t_0 <= (-100.0d0)) .or. (.not. (t_0 <= 4000000.0d0))) then
        tmp = x * (4.0d0 / y)
    else
        tmp = 4.0d0
    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 * 0.75)) - z)) / y);
	double tmp;
	if ((t_0 <= -100.0) || !(t_0 <= 4000000.0)) {
		tmp = x * (4.0 / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)
	tmp = 0
	if (t_0 <= -100.0) or not (t_0 <= 4000000.0):
		tmp = x * (4.0 / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
	tmp = 0.0
	if ((t_0 <= -100.0) || !(t_0 <= 4000000.0))
		tmp = Float64(x * Float64(4.0 / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
	tmp = 0.0;
	if ((t_0 <= -100.0) || ~((t_0 <= 4000000.0)))
		tmp = x * (4.0 / y);
	else
		tmp = 4.0;
	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 * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -100.0], N[Not[LessEqual[t$95$0, 4000000.0]], $MachinePrecision]], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 4.0]]

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 3/4 binary64))) z)) y)) < -100 or 4e6 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y))

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 53.9%

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

   7. Applied rewrites 53.8%

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

   if -100 < (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)) < 4e6

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 96.0%

      \[\leadsto \color{blue}{4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \leq -100 \lor \neg \left(1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \leq 4000000\right):\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+61} \lor \neg \left(x \leq 2.4 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, 4, 4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.75e+61) (not (<= x 2.4e+30)))
   (fma (/ x y) 4.0 4.0)
   (fma (/ z y) -4.0 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.75e+61) || !(x <= 2.4e+30)) {
		tmp = fma((x / y), 4.0, 4.0);
	} else {
		tmp = fma((z / y), -4.0, 4.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.75e+61) || !(x <= 2.4e+30))
		tmp = fma(Float64(x / y), 4.0, 4.0);
	else
		tmp = fma(Float64(z / y), -4.0, 4.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.75e+61], N[Not[LessEqual[x, 2.4e+30]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * 4.0 + 4.0), $MachinePrecision], N[(N[(z / y), $MachinePrecision] * -4.0 + 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75000000000000009e61 or 2.3999999999999999e30 < x

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 89.0%

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

   if -1.75000000000000009e61 < x < 2.3999999999999999e30

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 91.4%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+61} \lor \neg \left(x \leq 2.4 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, 4, 4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+61} \lor \neg \left(x \leq 2.4 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.75e+61) (not (<= x 2.4e+30)))
   (fma (/ 4.0 y) x 4.0)
   (fma (/ z y) -4.0 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.75e+61) || !(x <= 2.4e+30)) {
		tmp = fma((4.0 / y), x, 4.0);
	} else {
		tmp = fma((z / y), -4.0, 4.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.75e+61) || !(x <= 2.4e+30))
		tmp = fma(Float64(4.0 / y), x, 4.0);
	else
		tmp = fma(Float64(z / y), -4.0, 4.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.75e+61], N[Not[LessEqual[x, 2.4e+30]], $MachinePrecision]], N[(N[(4.0 / y), $MachinePrecision] * x + 4.0), $MachinePrecision], N[(N[(z / y), $MachinePrecision] * -4.0 + 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75000000000000009e61 or 2.3999999999999999e30 < x

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{x + \frac{3}{4} \cdot y}{y}} \]
   4. Step-by-step derivation

   5. Applied rewrites 88.7%

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

   if -1.75000000000000009e61 < x < 2.3999999999999999e30

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 91.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+61} \lor \neg \left(x \leq 2.4 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+61} \lor \neg \left(x \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.2e+61) (not (<= x 3.4e+50)))
   (* (/ x y) 4.0)
   (fma (/ z y) -4.0 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e+61) || !(x <= 3.4e+50)) {
		tmp = (x / y) * 4.0;
	} else {
		tmp = fma((z / y), -4.0, 4.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.2e+61) || !(x <= 3.4e+50))
		tmp = Float64(Float64(x / y) * 4.0);
	else
		tmp = fma(Float64(z / y), -4.0, 4.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.2e+61], N[Not[LessEqual[x, 3.4e+50]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * 4.0), $MachinePrecision], N[(N[(z / y), $MachinePrecision] * -4.0 + 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.20000000000000021e61 or 3.3999999999999998e50 < x

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 76.3%

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

   if -7.20000000000000021e61 < x < 3.3999999999999998e50

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 89.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+61} \lor \neg \left(x \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{y} \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -4, 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 33.9% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 4.0)

C

double code(double x, double y, double z) {
	return 4.0;
}

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 = 4.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 4.0;
}

Python

def code(x, y, z):
	return 4.0

Julia

function code(x, y, z)
	return 4.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0;
end

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

5. Applied rewrites 29.9%

   \[\leadsto \color{blue}{4} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025019 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))