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

Percentage Accurate: 99.5% → 99.8%

Time: 4.3s

Alternatives: 14

Speedup: 1.9×

• 21.3% 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, 1.9× 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 99.6%

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

3. Taylor expanded in z around 0

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

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

5. Applied rewrites 99.8%

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

Alternative 2: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-6, z, 4\right) \cdot y\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+191}:\\ \;\;\;\;\left(-x\right) \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-11}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+120}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (fma -6.0 z 4.0) y)))
   (if (<= z -4.2e+191)
     (* (- x) (* -6.0 z))
     (if (<= z -1.1e-11)
       t_0
       (if (<= z 5.4e-7)
         (fma -3.0 x (* 4.0 y))
         (if (<= z 9e+120) t_0 (* (* 6.0 x) z)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(-6.0, z, 4.0) * y;
	double tmp;
	if (z <= -4.2e+191) {
		tmp = -x * (-6.0 * z);
	} else if (z <= -1.1e-11) {
		tmp = t_0;
	} else if (z <= 5.4e-7) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else if (z <= 9e+120) {
		tmp = t_0;
	} else {
		tmp = (6.0 * x) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(-6.0, z, 4.0) * y)
	tmp = 0.0
	if (z <= -4.2e+191)
		tmp = Float64(Float64(-x) * Float64(-6.0 * z));
	elseif (z <= -1.1e-11)
		tmp = t_0;
	elseif (z <= 5.4e-7)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	elseif (z <= 9e+120)
		tmp = t_0;
	else
		tmp = Float64(Float64(6.0 * x) * z);
	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, -4.2e+191], N[((-x) * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-11], t$95$0, If[LessEqual[z, 5.4e-7], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+120], t$95$0, N[(N[(6.0 * x), $MachinePrecision] * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2000000000000001e191

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. 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 99.7

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

   5. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot -6} \]
   6. 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 99.8

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in x around inf

      \[\leadsto \left(-1 \cdot x\right) \cdot \left(\color{blue}{-6} \cdot z\right) \]
   9. 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 72.8

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

   10. Applied rewrites 72.8%

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

   if -4.2000000000000001e191 < z < -1.1000000000000001e-11 or 5.40000000000000018e-7 < z < 8.99999999999999953e120

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]
   4. 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 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto y \cdot \color{blue}{\left(4 + -6 \cdot z\right)} \]
   7. 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 58.2

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

   8. Applied rewrites 58.2%

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

   if -1.1000000000000001e-11 < z < 5.40000000000000018e-7

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
   4. 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 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 99.5

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

   8. Applied rewrites 99.5%

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

   if 8.99999999999999953e120 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 99.8

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 67.7

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

   11. Applied rewrites 67.7%

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

Alternative 3: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot x\right) \cdot z\\ t_1 := \mathsf{fma}\left(-6, z, 4\right) \cdot y\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+191}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 x) z)) (t_1 (* (fma -6.0 z 4.0) y)))
   (if (<= z -4.2e+191)
     t_0
     (if (<= z -1.1e-11)
       t_1
       (if (<= z 5.4e-7) (fma -3.0 x (* 4.0 y)) (if (<= z 9e+120) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * x) * z;
	double t_1 = fma(-6.0, z, 4.0) * y;
	double tmp;
	if (z <= -4.2e+191) {
		tmp = t_0;
	} else if (z <= -1.1e-11) {
		tmp = t_1;
	} else if (z <= 5.4e-7) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else if (z <= 9e+120) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * x) * z)
	t_1 = Float64(fma(-6.0, z, 4.0) * y)
	tmp = 0.0
	if (z <= -4.2e+191)
		tmp = t_0;
	elseif (z <= -1.1e-11)
		tmp = t_1;
	elseif (z <= 5.4e-7)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	elseif (z <= 9e+120)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * x), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(-6.0 * z + 4.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -4.2e+191], t$95$0, If[LessEqual[z, -1.1e-11], t$95$1, If[LessEqual[z, 5.4e-7], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+120], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000001e191 or 8.99999999999999953e120 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 99.8

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 68.3

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

   11. Applied rewrites 68.3%

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

   if -4.2000000000000001e191 < z < -1.1000000000000001e-11 or 5.40000000000000018e-7 < z < 8.99999999999999953e120

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]
   4. 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 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto y \cdot \color{blue}{\left(4 + -6 \cdot z\right)} \]
   7. 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 58.2

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

   8. Applied rewrites 58.2%

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

   if -1.1000000000000001e-11 < z < 5.40000000000000018e-7

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
   4. 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 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 99.5

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

   8. Applied rewrites 99.5%

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

Alternative 4: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+191}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2100000:\\ \;\;\;\;\left(-6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+120}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 x) z)))
   (if (<= z -4.2e+191)
     t_0
     (if (<= z -2100000.0)
       (* (* -6.0 y) z)
       (if (<= z 0.68)
         (fma -3.0 x (* 4.0 y))
         (if (<= z 9e+120) (* (* y z) -6.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * x) * z;
	double tmp;
	if (z <= -4.2e+191) {
		tmp = t_0;
	} else if (z <= -2100000.0) {
		tmp = (-6.0 * y) * z;
	} else if (z <= 0.68) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else if (z <= 9e+120) {
		tmp = (y * z) * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * x) * z)
	tmp = 0.0
	if (z <= -4.2e+191)
		tmp = t_0;
	elseif (z <= -2100000.0)
		tmp = Float64(Float64(-6.0 * y) * z);
	elseif (z <= 0.68)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	elseif (z <= 9e+120)
		tmp = Float64(Float64(y * z) * -6.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.2e+191], t$95$0, If[LessEqual[z, -2100000.0], N[(N[(-6.0 * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 0.68], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+120], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2000000000000001e191 or 8.99999999999999953e120 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 99.8

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 68.3

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

   11. Applied rewrites 68.3%

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

   if -4.2000000000000001e191 < z < -2.1e6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 99.9

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

   8. Applied rewrites 99.9%

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

   9. Taylor expanded in x around 0

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

       1. lower-*.f64 61.3

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

   11. Applied rewrites 61.3%

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

   if -2.1e6 < z < 0.680000000000000049

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
   4. 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 97.2

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 97.3

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

   8. Applied rewrites 97.3%

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

   if 0.680000000000000049 < z < 8.99999999999999953e120

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. 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 94.1

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.4%

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

Alternative 5: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+191}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2100000:\\ \;\;\;\;\left(-6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+120}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 x) z)))
   (if (<= z -4.2e+191)
     t_0
     (if (<= z -2100000.0)
       (* (* -6.0 y) z)
       (if (<= z 0.68)
         (fma 4.0 (- y x) x)
         (if (<= z 9e+120) (* (* y z) -6.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * x) * z;
	double tmp;
	if (z <= -4.2e+191) {
		tmp = t_0;
	} else if (z <= -2100000.0) {
		tmp = (-6.0 * y) * z;
	} else if (z <= 0.68) {
		tmp = fma(4.0, (y - x), x);
	} else if (z <= 9e+120) {
		tmp = (y * z) * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * x) * z)
	tmp = 0.0
	if (z <= -4.2e+191)
		tmp = t_0;
	elseif (z <= -2100000.0)
		tmp = Float64(Float64(-6.0 * y) * z);
	elseif (z <= 0.68)
		tmp = fma(4.0, Float64(y - x), x);
	elseif (z <= 9e+120)
		tmp = Float64(Float64(y * z) * -6.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.2e+191], t$95$0, If[LessEqual[z, -2100000.0], N[(N[(-6.0 * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 0.68], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 9e+120], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2000000000000001e191 or 8.99999999999999953e120 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 99.8

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 68.3

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

   11. Applied rewrites 68.3%

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

   if -4.2000000000000001e191 < z < -2.1e6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 99.9

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

   8. Applied rewrites 99.9%

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

   9. Taylor expanded in x around 0

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

       1. lower-*.f64 61.3

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

   11. Applied rewrites 61.3%

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

   if -2.1e6 < z < 0.680000000000000049

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
   4. 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 97.2

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

   5. Applied rewrites 97.2%

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

   if 0.680000000000000049 < z < 8.99999999999999953e120

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. 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 94.1

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.4%

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

Alternative 6: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot x\right) \cdot z\\ t_1 := \left(-6 \cdot y\right) \cdot z\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+191}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 x) z)) (t_1 (* (* -6.0 y) z)))
   (if (<= z -4.2e+191)
     t_0
     (if (<= z -2100000.0)
       t_1
       (if (<= z 0.68) (fma 4.0 (- y x) x) (if (<= z 9e+120) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * x) * z;
	double t_1 = (-6.0 * y) * z;
	double tmp;
	if (z <= -4.2e+191) {
		tmp = t_0;
	} else if (z <= -2100000.0) {
		tmp = t_1;
	} else if (z <= 0.68) {
		tmp = fma(4.0, (y - x), x);
	} else if (z <= 9e+120) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * x) * z)
	t_1 = Float64(Float64(-6.0 * y) * z)
	tmp = 0.0
	if (z <= -4.2e+191)
		tmp = t_0;
	elseif (z <= -2100000.0)
		tmp = t_1;
	elseif (z <= 0.68)
		tmp = fma(4.0, Float64(y - x), x);
	elseif (z <= 9e+120)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * x), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(-6.0 * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.2e+191], t$95$0, If[LessEqual[z, -2100000.0], t$95$1, If[LessEqual[z, 0.68], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 9e+120], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000001e191 or 8.99999999999999953e120 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 99.8

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 68.3

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

   11. Applied rewrites 68.3%

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

   if -4.2000000000000001e191 < z < -2.1e6 or 0.680000000000000049 < z < 8.99999999999999953e120

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 97.5

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

   8. Applied rewrites 97.5%

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

   9. Taylor expanded in x around 0

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

       1. lower-*.f64 58.6

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

   11. Applied rewrites 58.6%

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

   if -2.1e6 < z < 0.680000000000000049

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
   4. 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 97.2

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

   5. Applied rewrites 97.2%

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

Alternative 7: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot 6\\ t_1 := \left(-6 \cdot y\right) \cdot z\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+191}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) 6.0)) (t_1 (* (* -6.0 y) z)))
   (if (<= z -4.2e+191)
     t_0
     (if (<= z -2100000.0)
       t_1
       (if (<= z 0.68) (fma 4.0 (- y x) x) (if (<= z 9e+120) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * x) * 6.0;
	double t_1 = (-6.0 * y) * z;
	double tmp;
	if (z <= -4.2e+191) {
		tmp = t_0;
	} else if (z <= -2100000.0) {
		tmp = t_1;
	} else if (z <= 0.68) {
		tmp = fma(4.0, (y - x), x);
	} else if (z <= 9e+120) {
		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(Float64(-6.0 * y) * z)
	tmp = 0.0
	if (z <= -4.2e+191)
		tmp = t_0;
	elseif (z <= -2100000.0)
		tmp = t_1;
	elseif (z <= 0.68)
		tmp = fma(4.0, Float64(y - x), x);
	elseif (z <= 9e+120)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(-6.0 * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.2e+191], t$95$0, If[LessEqual[z, -2100000.0], t$95$1, If[LessEqual[z, 0.68], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 9e+120], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000001e191 or 8.99999999999999953e120 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. 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 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto 6 \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. 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 68.1

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

   8. Applied rewrites 68.1%

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

   if -4.2000000000000001e191 < z < -2.1e6 or 0.680000000000000049 < z < 8.99999999999999953e120

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 97.5

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

   8. Applied rewrites 97.5%

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

   9. Taylor expanded in x around 0

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

       1. lower-*.f64 58.6

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

   11. Applied rewrites 58.6%

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

   if -2.1e6 < z < 0.680000000000000049

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
   4. 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 97.2

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

   5. Applied rewrites 97.2%

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

Alternative 8: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.52 \lor \neg \left(z \leq 0.68\right):\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.52) (not (<= z 0.68)))
   (* (* -6.0 (- y x)) z)
   (fma -3.0 x (* 4.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.52) || !(z <= 0.68)) {
		tmp = (-6.0 * (y - x)) * z;
	} else {
		tmp = fma(-3.0, x, (4.0 * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.52) || !(z <= 0.68))
		tmp = Float64(Float64(-6.0 * Float64(y - x)) * z);
	else
		tmp = fma(-3.0, x, Float64(4.0 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.52], N[Not[LessEqual[z, 0.68]], $MachinePrecision]], N[(N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.52000000000000002 or 0.680000000000000049 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 97.8

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

   8. Applied rewrites 97.8%

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

   if -0.52000000000000002 < z < 0.680000000000000049

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto -3 \cdot x + \color{blue}{4 \cdot y} \]
   7. 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

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

   8. Applied rewrites 98.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.52 \lor \neg \left(z \leq 0.68\right):\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -106000000 \lor \neg \left(y \leq 2.5 \cdot 10^{-41}\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 4\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(-6, z, 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -106000000.0) (not (<= y 2.5e-41)))
   (* (fma -6.0 z 4.0) y)
   (* (- x) (fma -6.0 z 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -106000000.0) || !(y <= 2.5e-41)) {
		tmp = fma(-6.0, z, 4.0) * y;
	} else {
		tmp = -x * fma(-6.0, z, 3.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -106000000.0) || !(y <= 2.5e-41))
		tmp = Float64(fma(-6.0, z, 4.0) * y);
	else
		tmp = Float64(Float64(-x) * fma(-6.0, z, 3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -106000000.0], N[Not[LessEqual[y, 2.5e-41]], $MachinePrecision]], N[(N[(-6.0 * z + 4.0), $MachinePrecision] * y), $MachinePrecision], N[((-x) * N[(-6.0 * z + 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e8 or 2.4999999999999998e-41 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]
   4. 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 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto y \cdot \color{blue}{\left(4 + -6 \cdot z\right)} \]
   7. 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 78.1

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

   8. Applied rewrites 78.1%

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

   if -1.06e8 < y < 2.4999999999999998e-41

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]
   4. 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 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(3 + -6 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(3 + \color{blue}{-6 \cdot z}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot \left(3 + \color{blue}{-6} \cdot z\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) \cdot \left(3 + \color{blue}{-6 \cdot z}\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(3 + \color{blue}{-6} \cdot z\right) \]

      5. +-commutative N/A

         \[\leadsto \left(-x\right) \cdot \left(-6 \cdot z + 3\right) \]

      6. lower-fma.f64 85.0

         \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(-6, z, 3\right) \]

   8. Applied rewrites 85.0%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -106000000 \lor \neg \left(y \leq 2.5 \cdot 10^{-41}\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 4\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(-6, z, 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.52)
   (* (* -6.0 (- y x)) z)
   (if (<= z 0.68) (fma -3.0 x (* 4.0 y)) (* (* (- y x) z) -6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.52) {
		tmp = (-6.0 * (y - x)) * z;
	} else if (z <= 0.68) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else {
		tmp = ((y - x) * z) * -6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.52)
		tmp = Float64(Float64(-6.0 * Float64(y - x)) * z);
	elseif (z <= 0.68)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	else
		tmp = Float64(Float64(Float64(y - x) * z) * -6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.52], N[(N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 0.68], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.52000000000000002

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r/ N/A

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

      7. div-add N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 98.5

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

   8. Applied rewrites 98.5%

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

   if -0.52000000000000002 < z < 0.680000000000000049

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto -3 \cdot x + \color{blue}{4 \cdot y} \]
   7. 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

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

   8. Applied rewrites 98.8%

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

   if 0.680000000000000049 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. 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 97.0

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

   5. Applied rewrites 97.0%

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

Alternative 11: 75.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \lor \neg \left(z \leq 0.68\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.2) (not (<= z 0.68))) (* (* z x) 6.0) (fma 4.0 (- y x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.2) || !(z <= 0.68)) {
		tmp = (z * x) * 6.0;
	} else {
		tmp = fma(4.0, (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.2) || !(z <= 0.68))
		tmp = Float64(Float64(z * x) * 6.0);
	else
		tmp = fma(4.0, Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.2], N[Not[LessEqual[z, 0.68]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.1999999999999993 or 0.680000000000000049 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto 6 \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. 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 53.0

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

   8. Applied rewrites 53.0%

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

   if -9.1999999999999993 < z < 0.680000000000000049

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

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

   5. Applied rewrites 98.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \lor \neg \left(z \leq 0.68\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+122} \lor \neg \left(x \leq 1.65 \cdot 10^{+17}\right):\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;4 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e+122) (not (<= x 1.65e+17))) (* -3.0 x) (* 4.0 y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+122) || !(x <= 1.65e+17)) {
		tmp = -3.0 * x;
	} else {
		tmp = 4.0 * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.05d+122)) .or. (.not. (x <= 1.65d+17))) then
        tmp = (-3.0d0) * x
    else
        tmp = 4.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+122) || !(x <= 1.65e+17)) {
		tmp = -3.0 * x;
	} else {
		tmp = 4.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e+122) or not (x <= 1.65e+17):
		tmp = -3.0 * x
	else:
		tmp = 4.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e+122) || !(x <= 1.65e+17))
		tmp = Float64(-3.0 * x);
	else
		tmp = Float64(4.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.05e+122) || ~((x <= 1.65e+17)))
		tmp = -3.0 * x;
	else
		tmp = 4.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e+122], N[Not[LessEqual[x, 1.65e+17]], $MachinePrecision]], N[(-3.0 * x), $MachinePrecision], N[(4.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05000000000000008e122 or 1.65e17 < x

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
   4. 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 47.4

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

   5. Applied rewrites 47.4%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 41.1

         \[\leadsto -3 \cdot x \]

   8. Applied rewrites 41.1%

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

   if -1.05000000000000008e122 < x < 1.65e17

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
   4. 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 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 35.8

         \[\leadsto 4 \cdot y \]

   8. Applied rewrites 35.8%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+122} \lor \neg \left(x \leq 1.65 \cdot 10^{+17}\right):\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;4 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.3% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
4. 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 47.1

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

5. Applied rewrites 47.1%

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

Alternative 14: 26.5% accurate, 5.2× 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 99.6%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
4. 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 47.1

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

5. Applied rewrites 47.1%

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

6. Taylor expanded in x around inf

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

   1. lower-*.f64 25.3

      \[\leadsto -3 \cdot x \]

8. Applied rewrites 25.3%

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

Reproduce

herbie shell --seed 2025085 
(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))))