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

Percentage Accurate: 99.5% → 99.8%

Time: 2.9s

Alternatives: 14

Speedup: 1.3×

• 21.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, \mathsf{fma}\left(-6, z, 4\right), x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) (fma -6.0 z 4.0) x))

C

double code(double x, double y, double z) {
	return fma((y - x), fma(-6.0, z, 4.0), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), fma(-6.0, z, 4.0), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(-6.0 * z + 4.0), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

2. Taylor expanded in z around 0

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

   1. +-commutative N/A

      \[\leadsto \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right) + \color{blue}{x} \]

   2. associate-*r* N/A

      \[\leadsto \left(\left(-6 \cdot z\right) \cdot \left(y - x\right) + 4 \cdot \left(y - x\right)\right) + x \]

   3. distribute-rgt-out N/A

      \[\leadsto \left(y - x\right) \cdot \left(-6 \cdot z + 4\right) + x \]

   4. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6 \cdot z + 4}, x\right) \]

   5. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6 \cdot z} + 4, x\right) \]

   6. lower-fma.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 2: 97.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;\mathsf{fma}\left(-x, z, z \cdot y\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.56)
   (* (fma (- x) z (* z y)) -6.0)
   (if (<= z 0.5) (fma -3.0 x (* 4.0 y)) (* (* -6.0 (- y x)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.56) {
		tmp = fma(-x, z, (z * y)) * -6.0;
	} else if (z <= 0.5) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else {
		tmp = (-6.0 * (y - x)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.56)
		tmp = Float64(fma(Float64(-x), z, Float64(z * y)) * -6.0);
	elseif (z <= 0.5)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	else
		tmp = Float64(Float64(-6.0 * Float64(y - x)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.56], N[(N[((-x) * z + N[(z * y), $MachinePrecision]), $MachinePrecision] * -6.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], N[(N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.56000000000000005

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 97.7

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

   4. Applied rewrites 97.7%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot x\right) \cdot z + y \cdot z\right) \cdot -6 \]

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 95.5

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

   7. Applied rewrites 95.5%

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

   if -0.56000000000000005 < z < 0.5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

      2. lower-*.f64 97.8

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

   7. Applied rewrites 97.8%

      \[\leadsto \mathsf{fma}\left(-3, \color{blue}{x}, 4 \cdot y\right) \]

   if 0.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 97.7

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

   4. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-*.f64 97.7

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

   6. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 97.7

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

   8. Applied rewrites 97.7%

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

Alternative 3: 97.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.56)
   (* (* (- y x) z) -6.0)
   (if (<= z 0.5) (fma -3.0 x (* 4.0 y)) (* (* -6.0 (- y x)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.56) {
		tmp = ((y - x) * z) * -6.0;
	} else if (z <= 0.5) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else {
		tmp = (-6.0 * (y - x)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.56)
		tmp = Float64(Float64(Float64(y - x) * z) * -6.0);
	elseif (z <= 0.5)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	else
		tmp = Float64(Float64(-6.0 * Float64(y - x)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.56], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * -6.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], N[(N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.56000000000000005

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 97.7

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

   4. Applied rewrites 97.7%

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

   if -0.56000000000000005 < z < 0.5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

      2. lower-*.f64 97.8

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

   7. Applied rewrites 97.8%

      \[\leadsto \mathsf{fma}\left(-3, \color{blue}{x}, 4 \cdot y\right) \]

   if 0.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 97.7

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

   4. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-*.f64 97.7

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

   6. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 97.7

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

   8. Applied rewrites 97.7%

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

Alternative 4: 97.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* -6.0 (- y x)) z)))
   (if (<= z -0.56) t_0 (if (<= z 0.5) (fma -3.0 x (* 4.0 y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (-6.0 * (y - x)) * z;
	double tmp;
	if (z <= -0.56) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-6.0 * Float64(y - x)) * z)
	tmp = 0.0
	if (z <= -0.56)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -0.56], t$95$0, If[LessEqual[z, 0.5], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.56000000000000005 or 0.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 97.7

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

   4. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-*.f64 97.6

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

   6. Applied rewrites 97.6%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 97.7

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

   8. Applied rewrites 97.7%

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

   if -0.56000000000000005 < z < 0.5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

      2. lower-*.f64 97.8

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

   7. Applied rewrites 97.8%

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

Alternative 5: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-6, z, 4\right) \cdot y\\ \mathbf{if}\;z \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\left(-x\right) \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-12}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.08:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+50}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (fma -6.0 z 4.0) y)))
   (if (<= z -1e+78)
     (* (- x) (* -6.0 z))
     (if (<= z -1.26e-12)
       t_0
       (if (<= z 0.08)
         (fma -3.0 x (* 4.0 y))
         (if (<= z 2.9e+50) t_0 (* (* z x) 6.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(-6.0, z, 4.0) * y;
	double tmp;
	if (z <= -1e+78) {
		tmp = -x * (-6.0 * z);
	} else if (z <= -1.26e-12) {
		tmp = t_0;
	} else if (z <= 0.08) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else if (z <= 2.9e+50) {
		tmp = t_0;
	} else {
		tmp = (z * x) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(-6.0, z, 4.0) * y)
	tmp = 0.0
	if (z <= -1e+78)
		tmp = Float64(Float64(-x) * Float64(-6.0 * z));
	elseif (z <= -1.26e-12)
		tmp = t_0;
	elseif (z <= 0.08)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	elseif (z <= 2.9e+50)
		tmp = t_0;
	else
		tmp = Float64(Float64(z * x) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-6.0 * z + 4.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -1e+78], N[((-x) * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.26e-12], t$95$0, If[LessEqual[z, 0.08], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+50], t$95$0, N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.00000000000000001e78

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-*.f64 99.7

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

   6. Applied rewrites 99.7%

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

   7. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 54.4

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

   9. Applied rewrites 54.4%

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

   if -1.00000000000000001e78 < z < -1.26000000000000008e-12 or 0.0800000000000000017 < z < 2.9e50

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right) + \color{blue}{x} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(-6 \cdot z\right) \cdot \left(y - x\right) + 4 \cdot \left(y - x\right)\right) + x \]

      3. distribute-rgt-out N/A

         \[\leadsto \left(y - x\right) \cdot \left(-6 \cdot z + 4\right) + x \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6 \cdot z + 4}, x\right) \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6 \cdot z} + 4, x\right) \]

      6. lower-fma.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      2. lower-*.f64 N/A

         \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      3. +-commutative N/A

         \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

      4. lift-fma.f64 48.9

         \[\leadsto \mathsf{fma}\left(-6, z, 4\right) \cdot y \]

   7. Applied rewrites 48.9%

      \[\leadsto \mathsf{fma}\left(-6, z, 4\right) \cdot \color{blue}{y} \]

   if -1.26000000000000008e-12 < z < 0.0800000000000000017

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 98.7

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

   4. Applied rewrites 98.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

      2. lower-*.f64 98.8

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

   7. Applied rewrites 98.8%

      \[\leadsto \mathsf{fma}\left(-3, \color{blue}{x}, 4 \cdot y\right) \]

   if 2.9e50 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 52.8

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

   7. Applied rewrites 52.8%

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

Alternative 6: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\left(-x\right) \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -25500000:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e+78)
   (* (- x) (* -6.0 z))
   (if (<= z -25500000.0)
     (* (* y z) -6.0)
     (if (<= z 0.66)
       (fma -3.0 x (* 4.0 y))
       (if (<= z 2.9e+50) (* y (* -6.0 z)) (* (* z x) 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+78) {
		tmp = -x * (-6.0 * z);
	} else if (z <= -25500000.0) {
		tmp = (y * z) * -6.0;
	} else if (z <= 0.66) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else if (z <= 2.9e+50) {
		tmp = y * (-6.0 * z);
	} else {
		tmp = (z * x) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e+78)
		tmp = Float64(Float64(-x) * Float64(-6.0 * z));
	elseif (z <= -25500000.0)
		tmp = Float64(Float64(y * z) * -6.0);
	elseif (z <= 0.66)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	elseif (z <= 2.9e+50)
		tmp = Float64(y * Float64(-6.0 * z));
	else
		tmp = Float64(Float64(z * x) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e+78], N[((-x) * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -25500000.0], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+50], N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.00000000000000001e78

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-*.f64 99.7

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

   6. Applied rewrites 99.7%

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

   7. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 54.4

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

   9. Applied rewrites 54.4%

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

   if -1.00000000000000001e78 < z < -2.55e7

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 96.5

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

   4. Applied rewrites 96.5%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 48.0%

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

   if -2.55e7 < z < 0.660000000000000031

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 96.8

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

   4. Applied rewrites 96.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

      2. lower-*.f64 96.9

         \[\leadsto \mathsf{fma}\left(-3, x, 4 \cdot y\right) \]

   7. Applied rewrites 96.9%

      \[\leadsto \mathsf{fma}\left(-3, \color{blue}{x}, 4 \cdot y\right) \]

   if 0.660000000000000031 < z < 2.9e50

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 86.6

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

   4. Applied rewrites 86.6%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 41.6

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

   9. Applied rewrites 41.6%

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

   if 2.9e50 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 52.8

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

   7. Applied rewrites 52.8%

      \[\leadsto \left(z \cdot x\right) \cdot \color{blue}{6} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 7: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+58}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{elif}\;t\_0 \leq -0.2:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;t\_0 \leq 50000000:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+78}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)))
   (if (<= t_0 -1e+58)
     (* (* z x) 6.0)
     (if (<= t_0 -0.2)
       (* y (* -6.0 z))
       (if (<= t_0 50000000.0)
         (fma 4.0 (- y x) x)
         (if (<= t_0 1e+78) (* (* y z) -6.0) (* (- x) (* -6.0 z))))))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double tmp;
	if (t_0 <= -1e+58) {
		tmp = (z * x) * 6.0;
	} else if (t_0 <= -0.2) {
		tmp = y * (-6.0 * z);
	} else if (t_0 <= 50000000.0) {
		tmp = fma(4.0, (y - x), x);
	} else if (t_0 <= 1e+78) {
		tmp = (y * z) * -6.0;
	} else {
		tmp = -x * (-6.0 * z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	tmp = 0.0
	if (t_0 <= -1e+58)
		tmp = Float64(Float64(z * x) * 6.0);
	elseif (t_0 <= -0.2)
		tmp = Float64(y * Float64(-6.0 * z));
	elseif (t_0 <= 50000000.0)
		tmp = fma(4.0, Float64(y - x), x);
	elseif (t_0 <= 1e+78)
		tmp = Float64(Float64(y * z) * -6.0);
	else
		tmp = Float64(Float64(-x) * Float64(-6.0 * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+58], N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[t$95$0, -0.2], N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 50000000.0], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$0, 1e+78], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision], N[((-x) * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < -9.99999999999999944e57

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 52.8

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

   7. Applied rewrites 52.8%

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

   if -9.99999999999999944e57 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < -0.20000000000000001

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 88.4

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

   4. Applied rewrites 88.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 42.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 42.9

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

   9. Applied rewrites 42.9%

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

   if -0.20000000000000001 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 5e7

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 96.8

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

   4. Applied rewrites 96.8%

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

   if 5e7 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 1.00000000000000001e78

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 96.6

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

   4. Applied rewrites 96.6%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 48.2%

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

   if 1.00000000000000001e78 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z)

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-*.f64 99.7

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

   6. Applied rewrites 99.7%

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

   7. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 54.4

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

   9. Applied rewrites 54.4%

      \[\leadsto \left(-x\right) \cdot \left(\color{blue}{-6} \cdot z\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 8: 51.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\left(-x\right) \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -0.6:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e+78)
   (* (- x) (* -6.0 z))
   (if (<= z -0.6)
     (* (* y z) -6.0)
     (if (<= z 0.66)
       (* 4.0 y)
       (if (<= z 2.9e+50) (* y (* -6.0 z)) (* (* z x) 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+78) {
		tmp = -x * (-6.0 * z);
	} else if (z <= -0.6) {
		tmp = (y * z) * -6.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if (z <= 2.9e+50) {
		tmp = y * (-6.0 * z);
	} else {
		tmp = (z * x) * 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 <= (-1d+78)) then
        tmp = -x * ((-6.0d0) * z)
    else if (z <= (-0.6d0)) then
        tmp = (y * z) * (-6.0d0)
    else if (z <= 0.66d0) then
        tmp = 4.0d0 * y
    else if (z <= 2.9d+50) then
        tmp = y * ((-6.0d0) * z)
    else
        tmp = (z * x) * 6.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+78) {
		tmp = -x * (-6.0 * z);
	} else if (z <= -0.6) {
		tmp = (y * z) * -6.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if (z <= 2.9e+50) {
		tmp = y * (-6.0 * z);
	} else {
		tmp = (z * x) * 6.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e+78:
		tmp = -x * (-6.0 * z)
	elif z <= -0.6:
		tmp = (y * z) * -6.0
	elif z <= 0.66:
		tmp = 4.0 * y
	elif z <= 2.9e+50:
		tmp = y * (-6.0 * z)
	else:
		tmp = (z * x) * 6.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e+78)
		tmp = Float64(Float64(-x) * Float64(-6.0 * z));
	elseif (z <= -0.6)
		tmp = Float64(Float64(y * z) * -6.0);
	elseif (z <= 0.66)
		tmp = Float64(4.0 * y);
	elseif (z <= 2.9e+50)
		tmp = Float64(y * Float64(-6.0 * z));
	else
		tmp = Float64(Float64(z * x) * 6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1e+78)
		tmp = -x * (-6.0 * z);
	elseif (z <= -0.6)
		tmp = (y * z) * -6.0;
	elseif (z <= 0.66)
		tmp = 4.0 * y;
	elseif (z <= 2.9e+50)
		tmp = y * (-6.0 * z);
	else
		tmp = (z * x) * 6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e+78], N[((-x) * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.6], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 2.9e+50], N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.00000000000000001e78

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-*.f64 99.7

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

   6. Applied rewrites 99.7%

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

   7. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 54.4

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

   9. Applied rewrites 54.4%

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

   if -1.00000000000000001e78 < z < -0.599999999999999978

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 91.0

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

   4. Applied rewrites 91.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.4%

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

   if -0.599999999999999978 < z < 0.660000000000000031

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 50.4

         \[\leadsto 4 \cdot y \]

   7. Applied rewrites 50.4%

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

   if 0.660000000000000031 < z < 2.9e50

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 86.6

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

   4. Applied rewrites 86.6%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 41.6

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

   9. Applied rewrites 41.6%

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

   if 2.9e50 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 52.8

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

   7. Applied rewrites 52.8%

      \[\leadsto \left(z \cdot x\right) \cdot \color{blue}{6} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 51.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot 6\\ \mathbf{if}\;z \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.6:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) 6.0)))
   (if (<= z -1e+78)
     t_0
     (if (<= z -0.6)
       (* (* y z) -6.0)
       (if (<= z 0.66) (* 4.0 y) (if (<= z 2.9e+50) (* y (* -6.0 z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * x) * 6.0;
	double tmp;
	if (z <= -1e+78) {
		tmp = t_0;
	} else if (z <= -0.6) {
		tmp = (y * z) * -6.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if (z <= 2.9e+50) {
		tmp = y * (-6.0 * z);
	} 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 <= (-1d+78)) then
        tmp = t_0
    else if (z <= (-0.6d0)) then
        tmp = (y * z) * (-6.0d0)
    else if (z <= 0.66d0) then
        tmp = 4.0d0 * y
    else if (z <= 2.9d+50) then
        tmp = y * ((-6.0d0) * z)
    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 <= -1e+78) {
		tmp = t_0;
	} else if (z <= -0.6) {
		tmp = (y * z) * -6.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if (z <= 2.9e+50) {
		tmp = y * (-6.0 * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * x) * 6.0
	tmp = 0
	if z <= -1e+78:
		tmp = t_0
	elif z <= -0.6:
		tmp = (y * z) * -6.0
	elif z <= 0.66:
		tmp = 4.0 * y
	elif z <= 2.9e+50:
		tmp = y * (-6.0 * z)
	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 <= -1e+78)
		tmp = t_0;
	elseif (z <= -0.6)
		tmp = Float64(Float64(y * z) * -6.0);
	elseif (z <= 0.66)
		tmp = Float64(4.0 * y);
	elseif (z <= 2.9e+50)
		tmp = Float64(y * Float64(-6.0 * z));
	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 <= -1e+78)
		tmp = t_0;
	elseif (z <= -0.6)
		tmp = (y * z) * -6.0;
	elseif (z <= 0.66)
		tmp = 4.0 * y;
	elseif (z <= 2.9e+50)
		tmp = y * (-6.0 * z);
	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, -1e+78], t$95$0, If[LessEqual[z, -0.6], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 2.9e+50], N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.00000000000000001e78 or 2.9e50 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 53.5

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

   7. Applied rewrites 53.5%

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

   if -1.00000000000000001e78 < z < -0.599999999999999978

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 91.0

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

   4. Applied rewrites 91.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.4%

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

   if -0.599999999999999978 < z < 0.660000000000000031

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 50.4

         \[\leadsto 4 \cdot y \]

   7. Applied rewrites 50.4%

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

   if 0.660000000000000031 < z < 2.9e50

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 86.6

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

   4. Applied rewrites 86.6%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 41.6

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

   9. Applied rewrites 41.6%

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

Alternative 10: 51.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot 6\\ t_1 := y \cdot \left(-6 \cdot z\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.6:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) 6.0)) (t_1 (* y (* -6.0 z))))
   (if (<= z -1e+78)
     t_0
     (if (<= z -0.6)
       t_1
       (if (<= z 0.66) (* 4.0 y) (if (<= z 2.9e+50) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * x) * 6.0;
	double t_1 = y * (-6.0 * z);
	double tmp;
	if (z <= -1e+78) {
		tmp = t_0;
	} else if (z <= -0.6) {
		tmp = t_1;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if (z <= 2.9e+50) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (z * x) * 6.0d0
    t_1 = y * ((-6.0d0) * z)
    if (z <= (-1d+78)) then
        tmp = t_0
    else if (z <= (-0.6d0)) then
        tmp = t_1
    else if (z <= 0.66d0) then
        tmp = 4.0d0 * y
    else if (z <= 2.9d+50) then
        tmp = t_1
    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 t_1 = y * (-6.0 * z);
	double tmp;
	if (z <= -1e+78) {
		tmp = t_0;
	} else if (z <= -0.6) {
		tmp = t_1;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if (z <= 2.9e+50) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * x) * 6.0
	t_1 = y * (-6.0 * z)
	tmp = 0
	if z <= -1e+78:
		tmp = t_0
	elif z <= -0.6:
		tmp = t_1
	elif z <= 0.66:
		tmp = 4.0 * y
	elif z <= 2.9e+50:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * x) * 6.0)
	t_1 = Float64(y * Float64(-6.0 * z))
	tmp = 0.0
	if (z <= -1e+78)
		tmp = t_0;
	elseif (z <= -0.6)
		tmp = t_1;
	elseif (z <= 0.66)
		tmp = Float64(4.0 * y);
	elseif (z <= 2.9e+50)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * x) * 6.0;
	t_1 = y * (-6.0 * z);
	tmp = 0.0;
	if (z <= -1e+78)
		tmp = t_0;
	elseif (z <= -0.6)
		tmp = t_1;
	elseif (z <= 0.66)
		tmp = 4.0 * y;
	elseif (z <= 2.9e+50)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+78], t$95$0, If[LessEqual[z, -0.6], t$95$1, If[LessEqual[z, 0.66], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 2.9e+50], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000001e78 or 2.9e50 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 53.5

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

   7. Applied rewrites 53.5%

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

   if -1.00000000000000001e78 < z < -0.599999999999999978 or 0.660000000000000031 < z < 2.9e50

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 89.3

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

   4. Applied rewrites 89.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 43.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 43.8

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

   9. Applied rewrites 43.8%

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

   if -0.599999999999999978 < z < 0.660000000000000031

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 50.4

         \[\leadsto 4 \cdot y \]

   7. Applied rewrites 50.4%

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

Alternative 11: 51.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot 6\\ \mathbf{if}\;z \leq -0.145:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) 6.0)))
   (if (<= z -0.145) t_0 (if (<= z 0.5) (* 4.0 y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z * x) * 6.0;
	double tmp;
	if (z <= -0.145) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * x) * 6.0d0
    if (z <= (-0.145d0)) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = 4.0d0 * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * x) * 6.0;
	double tmp;
	if (z <= -0.145) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * x) * 6.0
	tmp = 0
	if z <= -0.145:
		tmp = t_0
	elif z <= 0.5:
		tmp = 4.0 * y
	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 <= -0.145)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(4.0 * y);
	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 <= -0.145)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = 4.0 * y;
	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, -0.145], t$95$0, If[LessEqual[z, 0.5], N[(4.0 * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.14499999999999999 or 0.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 97.7

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

   4. Applied rewrites 97.7%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 52.2

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

   7. Applied rewrites 52.2%

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

   if -0.14499999999999999 < z < 0.5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 50.4

         \[\leadsto 4 \cdot y \]

   7. Applied rewrites 50.4%

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

Alternative 12: 37.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(4, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.1e-23) (* -3.0 x) (if (<= x 3.6e-31) (fma 4.0 y x) (* -3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.1e-23) {
		tmp = -3.0 * x;
	} else if (x <= 3.6e-31) {
		tmp = fma(4.0, y, x);
	} else {
		tmp = -3.0 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.1e-23)
		tmp = Float64(-3.0 * x);
	elseif (x <= 3.6e-31)
		tmp = fma(4.0, y, x);
	else
		tmp = Float64(-3.0 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.1e-23], N[(-3.0 * x), $MachinePrecision], If[LessEqual[x, 3.6e-31], N[(4.0 * y + x), $MachinePrecision], N[(-3.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e-23 or 3.60000000000000004e-31 < x

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 49.8

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

   4. Applied rewrites 49.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto -3 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 35.9

         \[\leadsto -3 \cdot x \]

   7. Applied rewrites 35.9%

      \[\leadsto -3 \cdot \color{blue}{x} \]

   if -1.1e-23 < x < 3.60000000000000004e-31

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 50.5

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

   4. Applied rewrites 50.5%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 39.2%

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

Alternative 13: 37.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.62 \cdot 10^{-59}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-31}:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.62e-59) (* -3.0 x) (if (<= x 3.6e-31) (* 4.0 y) (* -3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.62e-59) {
		tmp = -3.0 * x;
	} else if (x <= 3.6e-31) {
		tmp = 4.0 * y;
	} else {
		tmp = -3.0 * 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 (x <= (-1.62d-59)) then
        tmp = (-3.0d0) * x
    else if (x <= 3.6d-31) then
        tmp = 4.0d0 * y
    else
        tmp = (-3.0d0) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.62e-59) {
		tmp = -3.0 * x;
	} else if (x <= 3.6e-31) {
		tmp = 4.0 * y;
	} else {
		tmp = -3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.62e-59:
		tmp = -3.0 * x
	elif x <= 3.6e-31:
		tmp = 4.0 * y
	else:
		tmp = -3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.62e-59)
		tmp = Float64(-3.0 * x);
	elseif (x <= 3.6e-31)
		tmp = Float64(4.0 * y);
	else
		tmp = Float64(-3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.62e-59)
		tmp = -3.0 * x;
	elseif (x <= 3.6e-31)
		tmp = 4.0 * y;
	else
		tmp = -3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.62e-59], N[(-3.0 * x), $MachinePrecision], If[LessEqual[x, 3.6e-31], N[(4.0 * y), $MachinePrecision], N[(-3.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.61999999999999989e-59 or 3.60000000000000004e-31 < x

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 49.7

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

   4. Applied rewrites 49.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto -3 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 35.3

         \[\leadsto -3 \cdot x \]

   7. Applied rewrites 35.3%

      \[\leadsto -3 \cdot \color{blue}{x} \]

   if -1.61999999999999989e-59 < x < 3.60000000000000004e-31

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 50.6

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

   4. Applied rewrites 50.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 40.2

         \[\leadsto 4 \cdot y \]

   7. Applied rewrites 40.2%

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

Alternative 14: 25.5% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ -3 \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* -3.0 x))

C

double code(double x, double y, double z) {
	return -3.0 * 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 = (-3.0d0) * x
end function

Java

public static double code(double x, double y, double z) {
	return -3.0 * x;
}

Python

def code(x, y, z):
	return -3.0 * x

Julia

function code(x, y, z)
	return Float64(-3.0 * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -3.0 * x;
end

Wolfram

code[x_, y_, z_] := N[(-3.0 * x), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

2. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. lift--.f64 50.1

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

4. Applied rewrites 50.1%

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

5. Taylor expanded in x around inf

   \[\leadsto -3 \cdot \color{blue}{x} \]
6. Step-by-step derivation

   1. lower-*.f64 25.5

      \[\leadsto -3 \cdot x \]

7. Applied rewrites 25.5%

   \[\leadsto -3 \cdot \color{blue}{x} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025114 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))