Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E

Percentage Accurate: 99.7% → 99.8%

Time: 6.2s

Alternatives: 14

Speedup: 1.1×

• 21.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (* z (- y x)) 6.0 x))

C

double code(double x, double y, double z) {
	return fma((z * (y - x)), 6.0, x);
}

Julia

function code(x, y, z)
	return fma(Float64(z * Float64(y - x)), 6.0, x)
end

Wolfram

code[x_, y_, z_] := N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] * 6.0 + x), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

   5. lift-*.f64 N/A

      \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

   6. associate-*r* N/A

      \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   8. lower-*.f64 99.8

      \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

4. Applied rewrites 99.8%

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

Alternative 2: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-6 \cdot z\right) \cdot x\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+137}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* -6.0 z) x)))
   (if (<= z -1.3e+137)
     t_0
     (if (<= z -4.8e-27)
       (* (* 6.0 z) y)
       (if (<= z 3.5e-42)
         (* 1.0 x)
         (if (<= z 2.5e+111) (* (* z y) 6.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (-6.0 * z) * x;
	double tmp;
	if (z <= -1.3e+137) {
		tmp = t_0;
	} else if (z <= -4.8e-27) {
		tmp = (6.0 * z) * y;
	} else if (z <= 3.5e-42) {
		tmp = 1.0 * x;
	} else if (z <= 2.5e+111) {
		tmp = (z * y) * 6.0;
	} 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) :: tmp
    t_0 = ((-6.0d0) * z) * x
    if (z <= (-1.3d+137)) then
        tmp = t_0
    else if (z <= (-4.8d-27)) then
        tmp = (6.0d0 * z) * y
    else if (z <= 3.5d-42) then
        tmp = 1.0d0 * x
    else if (z <= 2.5d+111) then
        tmp = (z * y) * 6.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-6.0 * z) * x;
	double tmp;
	if (z <= -1.3e+137) {
		tmp = t_0;
	} else if (z <= -4.8e-27) {
		tmp = (6.0 * z) * y;
	} else if (z <= 3.5e-42) {
		tmp = 1.0 * x;
	} else if (z <= 2.5e+111) {
		tmp = (z * y) * 6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-6.0 * z) * x
	tmp = 0
	if z <= -1.3e+137:
		tmp = t_0
	elif z <= -4.8e-27:
		tmp = (6.0 * z) * y
	elif z <= 3.5e-42:
		tmp = 1.0 * x
	elif z <= 2.5e+111:
		tmp = (z * y) * 6.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-6.0 * z) * x)
	tmp = 0.0
	if (z <= -1.3e+137)
		tmp = t_0;
	elseif (z <= -4.8e-27)
		tmp = Float64(Float64(6.0 * z) * y);
	elseif (z <= 3.5e-42)
		tmp = Float64(1.0 * x);
	elseif (z <= 2.5e+111)
		tmp = Float64(Float64(z * y) * 6.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-6.0 * z) * x;
	tmp = 0.0;
	if (z <= -1.3e+137)
		tmp = t_0;
	elseif (z <= -4.8e-27)
		tmp = (6.0 * z) * y;
	elseif (z <= 3.5e-42)
		tmp = 1.0 * x;
	elseif (z <= 2.5e+111)
		tmp = (z * y) * 6.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-6.0 * z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.3e+137], t$95$0, If[LessEqual[z, -4.8e-27], N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 3.5e-42], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 2.5e+111], N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e137 or 2.4999999999999998e111 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

      4. lower-fma.f64 60.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

   7. Applied rewrites 60.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \left(-6 \cdot z\right) \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 60.7%

       \[\leadsto \left(-6 \cdot z\right) \cdot x \]

   if -1.3e137 < z < -4.80000000000000004e-27

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 61.6

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 61.6%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
   6. Step-by-step derivation

   7. Applied rewrites 61.7%

      \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{y} \]

   if -4.80000000000000004e-27 < z < 3.5000000000000002e-42

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

      4. lower-fma.f64 76.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

   7. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 76.0%

       \[\leadsto 1 \cdot x \]

   if 3.5000000000000002e-42 < z < 2.4999999999999998e111

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 56.1

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 56.1%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+137}:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot -6\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+137}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) -6.0)))
   (if (<= z -1.3e+137)
     t_0
     (if (<= z -4.8e-27)
       (* (* 6.0 z) y)
       (if (<= z 3.5e-42)
         (* 1.0 x)
         (if (<= z 2.5e+111) (* (* z y) 6.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * x) * -6.0;
	double tmp;
	if (z <= -1.3e+137) {
		tmp = t_0;
	} else if (z <= -4.8e-27) {
		tmp = (6.0 * z) * y;
	} else if (z <= 3.5e-42) {
		tmp = 1.0 * x;
	} else if (z <= 2.5e+111) {
		tmp = (z * y) * 6.0;
	} 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) :: tmp
    t_0 = (z * x) * (-6.0d0)
    if (z <= (-1.3d+137)) then
        tmp = t_0
    else if (z <= (-4.8d-27)) then
        tmp = (6.0d0 * z) * y
    else if (z <= 3.5d-42) then
        tmp = 1.0d0 * x
    else if (z <= 2.5d+111) then
        tmp = (z * y) * 6.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * x) * -6.0;
	double tmp;
	if (z <= -1.3e+137) {
		tmp = t_0;
	} else if (z <= -4.8e-27) {
		tmp = (6.0 * z) * y;
	} else if (z <= 3.5e-42) {
		tmp = 1.0 * x;
	} else if (z <= 2.5e+111) {
		tmp = (z * y) * 6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * x) * -6.0
	tmp = 0
	if z <= -1.3e+137:
		tmp = t_0
	elif z <= -4.8e-27:
		tmp = (6.0 * z) * y
	elif z <= 3.5e-42:
		tmp = 1.0 * x
	elif z <= 2.5e+111:
		tmp = (z * y) * 6.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * x) * -6.0)
	tmp = 0.0
	if (z <= -1.3e+137)
		tmp = t_0;
	elseif (z <= -4.8e-27)
		tmp = Float64(Float64(6.0 * z) * y);
	elseif (z <= 3.5e-42)
		tmp = Float64(1.0 * x);
	elseif (z <= 2.5e+111)
		tmp = Float64(Float64(z * y) * 6.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * x) * -6.0;
	tmp = 0.0;
	if (z <= -1.3e+137)
		tmp = t_0;
	elseif (z <= -4.8e-27)
		tmp = (6.0 * z) * y;
	elseif (z <= 3.5e-42)
		tmp = 1.0 * x;
	elseif (z <= 2.5e+111)
		tmp = (z * y) * 6.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision]}, If[LessEqual[z, -1.3e+137], t$95$0, If[LessEqual[z, -4.8e-27], N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 3.5e-42], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 2.5e+111], N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e137 or 2.4999999999999998e111 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

      4. lower-fma.f64 60.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

   7. Applied rewrites 60.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

   8. Taylor expanded in z around inf

      \[\leadsto -6 \cdot \color{blue}{\left(x \cdot z\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 60.6%

       \[\leadsto \left(z \cdot x\right) \cdot \color{blue}{-6} \]

   if -1.3e137 < z < -4.80000000000000004e-27

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 61.6

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 61.6%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
   6. Step-by-step derivation

   7. Applied rewrites 61.7%

      \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{y} \]

   if -4.80000000000000004e-27 < z < 3.5000000000000002e-42

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

      4. lower-fma.f64 76.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

   7. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 76.0%

       \[\leadsto 1 \cdot x \]

   if 3.5000000000000002e-42 < z < 2.4999999999999998e111

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 56.1

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 56.1%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+137}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.16 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.16) (not (<= z 0.17)))
   (* (* (- y x) z) 6.0)
   (fma (* y z) 6.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.16) || !(z <= 0.17)) {
		tmp = ((y - x) * z) * 6.0;
	} else {
		tmp = fma((y * z), 6.0, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.16) || !(z <= 0.17))
		tmp = Float64(Float64(Float64(y - x) * z) * 6.0);
	else
		tmp = fma(Float64(y * z), 6.0, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.16], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * 6.0), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.160000000000000003 or 0.170000000000000012 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot z + x \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} + x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

      8. lower-*.f64 99.8

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      5. lower--.f64 98.7

         \[\leadsto \left(\color{blue}{\left(y - x\right)} \cdot z\right) \cdot 6 \]

   7. Applied rewrites 98.7%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} \]

   if -0.160000000000000003 < z < 0.170000000000000012

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 98.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z}, 6, x\right) \]

   7. Applied rewrites 98.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z}, 6, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.16 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.15 \lor \neg \left(z \leq 1760\right):\\ \;\;\;\;\left(6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.15) (not (<= z 1760.0)))
   (* (* 6.0 (- y x)) z)
   (fma (* y z) 6.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.15) || !(z <= 1760.0)) {
		tmp = (6.0 * (y - x)) * z;
	} else {
		tmp = fma((y * z), 6.0, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.15) || !(z <= 1760.0))
		tmp = Float64(Float64(6.0 * Float64(y - x)) * z);
	else
		tmp = fma(Float64(y * z), 6.0, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.15], N[Not[LessEqual[z, 1760.0]], $MachinePrecision]], N[(N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.149999999999999994 or 1760 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.8

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(6 \cdot \left(y - x\right) + \frac{x}{z}\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(y - x\right) + \frac{x}{z}\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(y - x\right) + \frac{x}{z}\right) \cdot z} \]

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 99.7

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

   7. Applied rewrites 99.7%

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

   8. Taylor expanded in z around inf

      \[\leadsto \left(6 \cdot \left(y - x\right)\right) \cdot z \]
   9. Step-by-step derivation

   10. Applied rewrites 98.6%

       \[\leadsto \left(6 \cdot \left(y - x\right)\right) \cdot z \]

   if -0.149999999999999994 < z < 1760

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 98.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z}, 6, x\right) \]

   7. Applied rewrites 98.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z}, 6, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.15 \lor \neg \left(z \leq 1760\right):\\ \;\;\;\;\left(6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-9}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x - -6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.8e-9)
   (* (- y x) (* 6.0 z))
   (if (<= z 0.17) (- x (* -6.0 (* z y))) (* (* (- y x) z) 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e-9) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.17) {
		tmp = x - (-6.0 * (z * y));
	} else {
		tmp = ((y - x) * z) * 6.0;
	}
	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) :: tmp
    if (z <= (-3.8d-9)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 0.17d0) then
        tmp = x - ((-6.0d0) * (z * y))
    else
        tmp = ((y - x) * z) * 6.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e-9) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.17) {
		tmp = x - (-6.0 * (z * y));
	} else {
		tmp = ((y - x) * z) * 6.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.8e-9:
		tmp = (y - x) * (6.0 * z)
	elif z <= 0.17:
		tmp = x - (-6.0 * (z * y))
	else:
		tmp = ((y - x) * z) * 6.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.8e-9)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 0.17)
		tmp = Float64(x - Float64(-6.0 * Float64(z * y)));
	else
		tmp = Float64(Float64(Float64(y - x) * z) * 6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.8e-9)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 0.17)
		tmp = x - (-6.0 * (z * y));
	else
		tmp = ((y - x) * z) * 6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.8e-9], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], N[(x - N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * 6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000011e-9

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot z + x \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} + x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

      8. lower-*.f64 99.8

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      5. lower--.f64 97.9

         \[\leadsto \left(\color{blue}{\left(y - x\right)} \cdot z\right) \cdot 6 \]

   7. Applied rewrites 97.9%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} \]
   8. Step-by-step derivation

   9. Applied rewrites 98.1%

      \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(6 \cdot z\right)} \]

   if -3.80000000000000011e-9 < z < 0.170000000000000012

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 98.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z}, 6, x\right) \]

   7. Applied rewrites 98.9%

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

      1. lift-fma.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6 + x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{x + \left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot z\right)} \]

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

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(6\right)\right) \cdot \left(y \cdot z\right)} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(6\right)\right) \cdot \left(y \cdot z\right)} \]

      6. metadata-eval N/A

         \[\leadsto x - \color{blue}{-6} \cdot \left(y \cdot z\right) \]

      7. lower-*.f64 98.9

         \[\leadsto x - \color{blue}{-6 \cdot \left(y \cdot z\right)} \]

   9. Applied rewrites 98.9%

      \[\leadsto \color{blue}{x - -6 \cdot \left(z \cdot y\right)} \]

   if 0.170000000000000012 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot z + x \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} + x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

      8. lower-*.f64 99.8

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      5. lower--.f64 99.6

         \[\leadsto \left(\color{blue}{\left(y - x\right)} \cdot z\right) \cdot 6 \]

   7. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 98.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-9}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.8e-9)
   (* (- y x) (* 6.0 z))
   (if (<= z 0.17) (fma (* y z) 6.0 x) (* (* (- y x) z) 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e-9) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.17) {
		tmp = fma((y * z), 6.0, x);
	} else {
		tmp = ((y - x) * z) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.8e-9)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 0.17)
		tmp = fma(Float64(y * z), 6.0, x);
	else
		tmp = Float64(Float64(Float64(y - x) * z) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.8e-9], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * 6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000011e-9

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot z + x \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} + x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

      8. lower-*.f64 99.8

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      5. lower--.f64 97.9

         \[\leadsto \left(\color{blue}{\left(y - x\right)} \cdot z\right) \cdot 6 \]

   7. Applied rewrites 97.9%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} \]
   8. Step-by-step derivation

   9. Applied rewrites 98.1%

      \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(6 \cdot z\right)} \]

   if -3.80000000000000011e-9 < z < 0.170000000000000012

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 98.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z}, 6, x\right) \]

   7. Applied rewrites 98.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z}, 6, x\right) \]

   if 0.170000000000000012 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot z + x \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} + x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

      8. lower-*.f64 99.8

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot 6}, x\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot 6 \]

      5. lower--.f64 99.6

         \[\leadsto \left(\color{blue}{\left(y - x\right)} \cdot z\right) \cdot 6 \]

   7. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-93} \lor \neg \left(x \leq 10^{-76}\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e-93) (not (<= x 1e-76)))
   (* (fma -6.0 z 1.0) x)
   (* (* z y) 6.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-93) || !(x <= 1e-76)) {
		tmp = fma(-6.0, z, 1.0) * x;
	} else {
		tmp = (z * y) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e-93) || !(x <= 1e-76))
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	else
		tmp = Float64(Float64(z * y) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e-93], N[Not[LessEqual[x, 1e-76]], $MachinePrecision]], N[(N[(-6.0 * z + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1499999999999999e-93 or 9.99999999999999927e-77 < x

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

      4. lower-fma.f64 79.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

   if -1.1499999999999999e-93 < x < 9.99999999999999927e-77

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 81.5

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 81.5%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-93} \lor \neg \left(x \leq 10^{-76}\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6 \cdot x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.2e+31)
   (* (fma -6.0 z 1.0) x)
   (if (<= x 4.8e+95) (fma (* y z) 6.0 x) (fma (* -6.0 x) z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e+31) {
		tmp = fma(-6.0, z, 1.0) * x;
	} else if (x <= 4.8e+95) {
		tmp = fma((y * z), 6.0, x);
	} else {
		tmp = fma((-6.0 * x), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2e+31)
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	elseif (x <= 4.8e+95)
		tmp = fma(Float64(y * z), 6.0, x);
	else
		tmp = fma(Float64(-6.0 * x), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2e+31], N[(N[(-6.0 * z + 1.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 4.8e+95], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision], N[(N[(-6.0 * x), $MachinePrecision] * z + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.19999999999999991e31

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

      4. lower-fma.f64 91.3

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

   5. Applied rewrites 91.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

   if -1.19999999999999991e31 < x < 4.8000000000000001e95

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 90.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z}, 6, x\right) \]

   7. Applied rewrites 90.7%

      \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot z}, 6, x\right) \]

   if 4.8000000000000001e95 < x

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. lower-fma.f64 99.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, z, x\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y - x\right) \cdot 6}, z, x\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{6 \cdot \left(y - x\right)}, z, x\right) \]

      7. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{6 \cdot \left(y - x\right)}, z, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(y - x\right), z, x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{-6 \cdot x}, z, x\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 93.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{-6 \cdot x}, z, x\right) \]

   7. Applied rewrites 93.7%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-6 \cdot x}, z, x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6 \cdot x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-27} \lor \neg \left(z \leq 3.5 \cdot 10^{-42}\right):\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-27) (not (<= z 3.5e-42))) (* (* 6.0 y) z) (* 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-27) || !(z <= 3.5e-42)) {
		tmp = (6.0 * y) * z;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.8d-27)) .or. (.not. (z <= 3.5d-42))) then
        tmp = (6.0d0 * y) * z
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-27) || !(z <= 3.5e-42)) {
		tmp = (6.0 * y) * z;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-27) or not (z <= 3.5e-42):
		tmp = (6.0 * y) * z
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-27) || !(z <= 3.5e-42))
		tmp = Float64(Float64(6.0 * y) * z);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e-27) || ~((z <= 3.5e-42)))
		tmp = (6.0 * y) * z;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-27], N[Not[LessEqual[z, 3.5e-42]], $MachinePrecision]], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000004e-27 or 3.5000000000000002e-42 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 51.3

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 51.3%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
   6. Step-by-step derivation

   7. Applied rewrites 51.2%

      \[\leadsto \left(6 \cdot y\right) \cdot \color{blue}{z} \]

   if -4.80000000000000004e-27 < z < 3.5000000000000002e-42

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

      4. lower-fma.f64 76.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

   7. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 76.0%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-27} \lor \neg \left(z \leq 3.5 \cdot 10^{-42}\right):\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.8e-27)
   (* (* 6.0 z) y)
   (if (<= z 3.5e-42) (* 1.0 x) (* (* z y) 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e-27) {
		tmp = (6.0 * z) * y;
	} else if (z <= 3.5e-42) {
		tmp = 1.0 * x;
	} else {
		tmp = (z * y) * 6.0;
	}
	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) :: tmp
    if (z <= (-4.8d-27)) then
        tmp = (6.0d0 * z) * y
    else if (z <= 3.5d-42) then
        tmp = 1.0d0 * x
    else
        tmp = (z * y) * 6.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e-27) {
		tmp = (6.0 * z) * y;
	} else if (z <= 3.5e-42) {
		tmp = 1.0 * x;
	} else {
		tmp = (z * y) * 6.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.8e-27:
		tmp = (6.0 * z) * y
	elif z <= 3.5e-42:
		tmp = 1.0 * x
	else:
		tmp = (z * y) * 6.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.8e-27)
		tmp = Float64(Float64(6.0 * z) * y);
	elseif (z <= 3.5e-42)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(z * y) * 6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.8e-27)
		tmp = (6.0 * z) * y;
	elseif (z <= 3.5e-42)
		tmp = 1.0 * x;
	else
		tmp = (z * y) * 6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.8e-27], N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 3.5e-42], N[(1.0 * x), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000004e-27

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 53.2

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
   6. Step-by-step derivation

   7. Applied rewrites 53.2%

      \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{y} \]

   if -4.80000000000000004e-27 < z < 3.5000000000000002e-42

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

      4. lower-fma.f64 76.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

   7. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 76.0%

       \[\leadsto 1 \cdot x \]

   if 3.5000000000000002e-42 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 49.3

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.8e-27)
   (* (* 6.0 z) y)
   (if (<= z 3.5e-42) (* 1.0 x) (* (* 6.0 y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e-27) {
		tmp = (6.0 * z) * y;
	} else if (z <= 3.5e-42) {
		tmp = 1.0 * x;
	} else {
		tmp = (6.0 * y) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.8d-27)) then
        tmp = (6.0d0 * z) * y
    else if (z <= 3.5d-42) then
        tmp = 1.0d0 * x
    else
        tmp = (6.0d0 * y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e-27) {
		tmp = (6.0 * z) * y;
	} else if (z <= 3.5e-42) {
		tmp = 1.0 * x;
	} else {
		tmp = (6.0 * y) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.8e-27:
		tmp = (6.0 * z) * y
	elif z <= 3.5e-42:
		tmp = 1.0 * x
	else:
		tmp = (6.0 * y) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.8e-27)
		tmp = Float64(Float64(6.0 * z) * y);
	elseif (z <= 3.5e-42)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(6.0 * y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.8e-27)
		tmp = (6.0 * z) * y;
	elseif (z <= 3.5e-42)
		tmp = 1.0 * x;
	else
		tmp = (6.0 * y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.8e-27], N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 3.5e-42], N[(1.0 * x), $MachinePrecision], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000004e-27

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 53.2

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
   6. Step-by-step derivation

   7. Applied rewrites 53.2%

      \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{y} \]

   if -4.80000000000000004e-27 < z < 3.5000000000000002e-42

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

      8. lower-*.f64 99.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

      4. lower-fma.f64 76.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

   7. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 76.0%

       \[\leadsto 1 \cdot x \]

   if 3.5000000000000002e-42 < z

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 49.3

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot 6} \]
   6. Step-by-step derivation

   7. Applied rewrites 49.2%

      \[\leadsto \left(6 \cdot y\right) \cdot \color{blue}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(6 \cdot \left(y - x\right), z, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (* 6.0 (- y x)) z x))

C

double code(double x, double y, double z) {
	return fma((6.0 * (y - x)), z, x);
}

Julia

function code(x, y, z)
	return fma(Float64(6.0 * Float64(y - x)), z, x)
end

Wolfram

code[x_, y_, z_] := N[(N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

   4. lower-fma.f64 99.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, z, x\right)} \]

   5. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y - x\right) \cdot 6}, z, x\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{6 \cdot \left(y - x\right)}, z, x\right) \]

   7. lower-*.f64 99.7

      \[\leadsto \mathsf{fma}\left(\color{blue}{6 \cdot \left(y - x\right)}, z, x\right) \]

4. Applied rewrites 99.7%

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

Alternative 14: 36.7% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot z} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z} + x \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

   5. lift-*.f64 N/A

      \[\leadsto z \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

   6. associate-*r* N/A

      \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6} + x \]

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

   8. lower-*.f64 99.8

      \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(y - x\right)}, 6, x\right) \]

4. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(1 + -6 \cdot z\right) \cdot x} \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\left(-6 \cdot z + 1\right)} \cdot x \]

   4. lower-fma.f64 62.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right)} \cdot x \]

7. Applied rewrites 62.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z, 1\right) \cdot x} \]

8. Taylor expanded in z around 0

   \[\leadsto 1 \cdot x \]
9. Step-by-step derivation

10. Applied rewrites 35.6%

    \[\leadsto 1 \cdot x \]

11. Final simplification 35.6%

    \[\leadsto 1 \cdot x \]
12. Add Preprocessing

Developer Target 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(6 \cdot z\right) \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))

C

double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - 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 = x - ((6.0d0 * z) * (x - y))
end function

Java

public static double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Python

def code(x, y, z):
	return x - ((6.0 * z) * (x - y))

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(6.0 * z) * Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((6.0 * z) * (x - y));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2025016 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (* 6 z) (- x y))))

  (+ x (* (* (- y x) 6.0) z)))