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

Percentage Accurate: 99.5% → 99.7%

Time: 4.1s

Alternatives: 14

Speedup: 1.9×

• 20.9% 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: 99.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lift--.f64 N/A

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

   6. lift-/.f64 N/A

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

   7. *-commutative N/A

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

   8. flip-- N/A

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

   9. associate-*l/ N/A

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

   10. lower-/.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. lower--.f64 N/A

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

   13. metadata-eval N/A

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

   14. metadata-eval N/A

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

   15. metadata-eval N/A

       \[\leadsto x + \frac{\left(\color{blue}{\frac{4}{9}} - z \cdot z\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

   16. lower-*.f64 N/A

       \[\leadsto x + \frac{\left(\frac{4}{9} - \color{blue}{z \cdot z}\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

   17. *-commutative N/A

       \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

   18. lift-*.f64 N/A

       \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

   19. lift--.f64 N/A

       \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\color{blue}{\left(y - x\right)} \cdot 6\right)}{\frac{2}{3} + z} \]

   20. lower-+.f64 N/A

       \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{\frac{2}{3} + z}} \]

   21. metadata-eval 85.2

       \[\leadsto x + \frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{0.6666666666666666} + z} \]

4. Applied rewrites 85.2%

   \[\leadsto x + \color{blue}{\frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{0.6666666666666666 + z}} \]

5. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lift--.f64 99.8

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

7. Applied rewrites 99.8%

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

Alternative 2: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+66}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{elif}\;t\_0 \leq 0.66666666:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 4\right) \cdot y\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+55} \lor \neg \left(t\_0 \leq 10^{+210}\right):\\ \;\;\;\;\left(z \cdot 6\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)))
   (if (<= t_0 -5e+66)
     (* (* z x) 6.0)
     (if (<= t_0 0.66666666)
       (* (fma -6.0 z 4.0) y)
       (if (<= t_0 1.0)
         (fma -3.0 x (* 4.0 y))
         (if (or (<= t_0 2e+55) (not (<= t_0 1e+210)))
           (* (* z 6.0) x)
           (* (* y z) -6.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double tmp;
	if (t_0 <= -5e+66) {
		tmp = (z * x) * 6.0;
	} else if (t_0 <= 0.66666666) {
		tmp = fma(-6.0, z, 4.0) * y;
	} else if (t_0 <= 1.0) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else if ((t_0 <= 2e+55) || !(t_0 <= 1e+210)) {
		tmp = (z * 6.0) * x;
	} else {
		tmp = (y * z) * -6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	tmp = 0.0
	if (t_0 <= -5e+66)
		tmp = Float64(Float64(z * x) * 6.0);
	elseif (t_0 <= 0.66666666)
		tmp = Float64(fma(-6.0, z, 4.0) * y);
	elseif (t_0 <= 1.0)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	elseif ((t_0 <= 2e+55) || !(t_0 <= 1e+210))
		tmp = Float64(Float64(z * 6.0) * x);
	else
		tmp = Float64(Float64(y * z) * -6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+66], N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[t$95$0, 0.66666666], N[(N[(-6.0 * z + 4.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$0, 2e+55], N[Not[LessEqual[t$95$0, 1e+210]], $MachinePrecision]], N[(N[(z * 6.0), $MachinePrecision] * x), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < -4.99999999999999991e66

   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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 60.3

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 60.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z 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 60.3

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

   8. Applied rewrites 60.3%

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

   if -4.99999999999999991e66 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 0.66666665999999997

   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 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 99.5

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

   5. Applied rewrites 99.5%

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

   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 80.5

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

   8. Applied rewrites 80.5%

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

   if 0.66666665999999997 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 1

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 97.5

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

   5. Applied rewrites 97.5%

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

   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 97.6

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

   8. Applied rewrites 97.6%

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

   if 1 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 2.00000000000000002e55 or 9.99999999999999927e209 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) 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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 79.8

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.2

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

   8. Applied rewrites 74.2%

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

   if 2.00000000000000002e55 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 9.99999999999999927e209

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. flip-- N/A

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

      9. associate-*l/ N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

          \[\leadsto x + \frac{\left(\color{blue}{\frac{4}{9}} - z \cdot z\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

      16. lower-*.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - \color{blue}{z \cdot z}\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

      17. *-commutative N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

      18. lift-*.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\color{blue}{\left(y - x\right)} \cdot 6\right)}{\frac{2}{3} + z} \]

      20. lower-+.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{\frac{2}{3} + z}} \]

      21. metadata-eval 67.7

          \[\leadsto x + \frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{0.6666666666666666} + z} \]

   4. Applied rewrites 67.7%

      \[\leadsto x + \color{blue}{\frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{0.6666666666666666 + z}} \]

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 99.8

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in z around inf

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

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

   10. Applied rewrites 99.7%

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

   11. Taylor expanded in x around 0

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

       1. lower-*.f64 65.8

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

   13. Applied rewrites 65.8%

       \[\leadsto \left(y \cdot z\right) \cdot -6 \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2}{3} - z \leq -5 \cdot 10^{+66}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{elif}\;\frac{2}{3} - z \leq 0.66666666:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 4\right) \cdot y\\ \mathbf{elif}\;\frac{2}{3} - z \leq 1:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{elif}\;\frac{2}{3} - z \leq 2 \cdot 10^{+55} \lor \neg \left(\frac{2}{3} - z \leq 10^{+210}\right):\\ \;\;\;\;\left(z \cdot 6\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ \mathbf{if}\;t\_0 \leq -2:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+55} \lor \neg \left(t\_0 \leq 10^{+210}\right):\\ \;\;\;\;\left(z \cdot 6\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)))
   (if (<= t_0 -2.0)
     (* (* z x) 6.0)
     (if (<= t_0 1.0)
       (fma -3.0 x (* 4.0 y))
       (if (or (<= t_0 2e+55) (not (<= t_0 1e+210)))
         (* (* z 6.0) x)
         (* (* y z) -6.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double tmp;
	if (t_0 <= -2.0) {
		tmp = (z * x) * 6.0;
	} else if (t_0 <= 1.0) {
		tmp = fma(-3.0, x, (4.0 * y));
	} else if ((t_0 <= 2e+55) || !(t_0 <= 1e+210)) {
		tmp = (z * 6.0) * x;
	} else {
		tmp = (y * z) * -6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	tmp = 0.0
	if (t_0 <= -2.0)
		tmp = Float64(Float64(z * x) * 6.0);
	elseif (t_0 <= 1.0)
		tmp = fma(-3.0, x, Float64(4.0 * y));
	elseif ((t_0 <= 2e+55) || !(t_0 <= 1e+210))
		tmp = Float64(Float64(z * 6.0) * x);
	else
		tmp = Float64(Float64(y * z) * -6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[t$95$0, -2.0], N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$0, 2e+55], N[Not[LessEqual[t$95$0, 1e+210]], $MachinePrecision]], N[(N[(z * 6.0), $MachinePrecision] * x), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 56.6

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z 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 56.7

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

   8. Applied rewrites 56.7%

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

   if -2 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 1

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 95.9

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

   5. Applied rewrites 95.9%

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

   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 95.9

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

   8. Applied rewrites 95.9%

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

   if 1 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 2.00000000000000002e55 or 9.99999999999999927e209 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) 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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 79.8

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.2

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

   8. Applied rewrites 74.2%

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

   if 2.00000000000000002e55 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 9.99999999999999927e209

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. flip-- N/A

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

      9. associate-*l/ N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

          \[\leadsto x + \frac{\left(\color{blue}{\frac{4}{9}} - z \cdot z\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

      16. lower-*.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - \color{blue}{z \cdot z}\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

      17. *-commutative N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

      18. lift-*.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\color{blue}{\left(y - x\right)} \cdot 6\right)}{\frac{2}{3} + z} \]

      20. lower-+.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{\frac{2}{3} + z}} \]

      21. metadata-eval 67.7

          \[\leadsto x + \frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{0.6666666666666666} + z} \]

   4. Applied rewrites 67.7%

      \[\leadsto x + \color{blue}{\frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{0.6666666666666666 + z}} \]

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 99.8

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in z around inf

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

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

   10. Applied rewrites 99.7%

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

   11. Taylor expanded in x around 0

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

       1. lower-*.f64 65.8

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

   13. Applied rewrites 65.8%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2}{3} - z \leq -2:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{elif}\;\frac{2}{3} - z \leq 1:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{elif}\;\frac{2}{3} - z \leq 2 \cdot 10^{+55} \lor \neg \left(\frac{2}{3} - z \leq 10^{+210}\right):\\ \;\;\;\;\left(z \cdot 6\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot 6\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+62}:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq -3.7 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) 6.0)))
   (if (<= z -2.9e+211)
     t_0
     (if (<= z -1.9e+62)
       (* (* -6.0 z) y)
       (if (or (<= z -3.7) (not (<= z 0.52))) t_0 (fma 4.0 (- y x) x))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * x) * 6.0;
	double tmp;
	if (z <= -2.9e+211) {
		tmp = t_0;
	} else if (z <= -1.9e+62) {
		tmp = (-6.0 * z) * y;
	} else if ((z <= -3.7) || !(z <= 0.52)) {
		tmp = t_0;
	} else {
		tmp = fma(4.0, (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * x) * 6.0)
	tmp = 0.0
	if (z <= -2.9e+211)
		tmp = t_0;
	elseif (z <= -1.9e+62)
		tmp = Float64(Float64(-6.0 * z) * y);
	elseif ((z <= -3.7) || !(z <= 0.52))
		tmp = t_0;
	else
		tmp = fma(4.0, Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision]}, If[LessEqual[z, -2.9e+211], t$95$0, If[LessEqual[z, -1.9e+62], N[(N[(-6.0 * z), $MachinePrecision] * y), $MachinePrecision], If[Or[LessEqual[z, -3.7], N[Not[LessEqual[z, 0.52]], $MachinePrecision]], t$95$0, N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e211 or -1.89999999999999992e62 < z < -3.7000000000000002 or 0.52000000000000002 < 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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 64.7

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 64.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z 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 62.8

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

   8. Applied rewrites 62.8%

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

   if -2.9e211 < z < -1.89999999999999992e62

   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 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 65.7

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

   8. Applied rewrites 65.7%

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

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 65.8

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

   11. Applied rewrites 65.8%

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

   if -3.7000000000000002 < z < 0.52000000000000002

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 95.9

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

   5. Applied rewrites 95.9%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+211}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+62}:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq -3.7 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot 6\right) \cdot x\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+62}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq -3.7:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z 6.0) x)))
   (if (<= z -2.9e+211)
     t_0
     (if (<= z -1.9e+62)
       (* (* y z) -6.0)
       (if (<= z -3.7)
         t_0
         (if (<= z 0.52) (fma 4.0 (- y x) x) (* (* z x) 6.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * 6.0) * x;
	double tmp;
	if (z <= -2.9e+211) {
		tmp = t_0;
	} else if (z <= -1.9e+62) {
		tmp = (y * z) * -6.0;
	} else if (z <= -3.7) {
		tmp = t_0;
	} else if (z <= 0.52) {
		tmp = fma(4.0, (y - x), x);
	} else {
		tmp = (z * x) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * 6.0) * x)
	tmp = 0.0
	if (z <= -2.9e+211)
		tmp = t_0;
	elseif (z <= -1.9e+62)
		tmp = Float64(Float64(y * z) * -6.0);
	elseif (z <= -3.7)
		tmp = t_0;
	elseif (z <= 0.52)
		tmp = fma(4.0, Float64(y - x), x);
	else
		tmp = Float64(Float64(z * x) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * 6.0), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -2.9e+211], t$95$0, If[LessEqual[z, -1.9e+62], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision], If[LessEqual[z, -3.7], t$95$0, If[LessEqual[z, 0.52], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9e211 or -1.89999999999999992e62 < z < -3.7000000000000002

   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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 79.8

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.2

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

   8. Applied rewrites 74.2%

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

   if -2.9e211 < z < -1.89999999999999992e62

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. flip-- N/A

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

      9. associate-*l/ N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

          \[\leadsto x + \frac{\left(\color{blue}{\frac{4}{9}} - z \cdot z\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

      16. lower-*.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - \color{blue}{z \cdot z}\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

      17. *-commutative N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

      18. lift-*.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\color{blue}{\left(y - x\right)} \cdot 6\right)}{\frac{2}{3} + z} \]

      20. lower-+.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{\frac{2}{3} + z}} \]

      21. metadata-eval 67.7

          \[\leadsto x + \frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{0.6666666666666666} + z} \]

   4. Applied rewrites 67.7%

      \[\leadsto x + \color{blue}{\frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{0.6666666666666666 + z}} \]

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 99.8

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in z around inf

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

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

   10. Applied rewrites 99.7%

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

   11. Taylor expanded in x around 0

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

       1. lower-*.f64 65.8

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

   13. Applied rewrites 65.8%

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

   if -3.7000000000000002 < z < 0.52000000000000002

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 95.9

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

   5. Applied rewrites 95.9%

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

   if 0.52000000000000002 < 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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 56.6

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z 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 56.7

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

   8. Applied rewrites 56.7%

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

Alternative 6: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot 6\right) \cdot x\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+62}:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq -3.7:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z 6.0) x)))
   (if (<= z -2.9e+211)
     t_0
     (if (<= z -1.9e+62)
       (* (* -6.0 z) y)
       (if (<= z -3.7)
         t_0
         (if (<= z 0.52) (fma 4.0 (- y x) x) (* (* z x) 6.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * 6.0) * x;
	double tmp;
	if (z <= -2.9e+211) {
		tmp = t_0;
	} else if (z <= -1.9e+62) {
		tmp = (-6.0 * z) * y;
	} else if (z <= -3.7) {
		tmp = t_0;
	} else if (z <= 0.52) {
		tmp = fma(4.0, (y - x), x);
	} else {
		tmp = (z * x) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * 6.0) * x)
	tmp = 0.0
	if (z <= -2.9e+211)
		tmp = t_0;
	elseif (z <= -1.9e+62)
		tmp = Float64(Float64(-6.0 * z) * y);
	elseif (z <= -3.7)
		tmp = t_0;
	elseif (z <= 0.52)
		tmp = fma(4.0, Float64(y - x), x);
	else
		tmp = Float64(Float64(z * x) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * 6.0), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -2.9e+211], t$95$0, If[LessEqual[z, -1.9e+62], N[(N[(-6.0 * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, -3.7], t$95$0, If[LessEqual[z, 0.52], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9e211 or -1.89999999999999992e62 < z < -3.7000000000000002

   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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 79.8

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.2

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

   8. Applied rewrites 74.2%

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

   if -2.9e211 < z < -1.89999999999999992e62

   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 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 65.7

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

   8. Applied rewrites 65.7%

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

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 65.8

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

   11. Applied rewrites 65.8%

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

   if -3.7000000000000002 < z < 0.52000000000000002

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 95.9

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

   5. Applied rewrites 95.9%

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

   if 0.52000000000000002 < 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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 56.6

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z 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 56.7

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

   8. Applied rewrites 56.7%

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

Alternative 7: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56 \lor \neg \left(z \leq 0.53\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.56) (not (<= z 0.53)))
   (* (* (- y x) z) -6.0)
   (fma -3.0 x (* 4.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.56) || !(z <= 0.53)) {
		tmp = ((y - x) * z) * -6.0;
	} else {
		tmp = fma(-3.0, x, (4.0 * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.56) || !(z <= 0.53))
		tmp = Float64(Float64(Float64(y - x) * z) * -6.0);
	else
		tmp = fma(-3.0, x, Float64(4.0 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.56], N[Not[LessEqual[z, 0.53]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * -6.0), $MachinePrecision], N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.56000000000000005 or 0.53000000000000003 < 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 97.5

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

   5. Applied rewrites 97.5%

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

   if -0.56000000000000005 < z < 0.53000000000000003

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 95.9

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

   5. Applied rewrites 95.9%

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

   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 95.9

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

   8. Applied rewrites 95.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56 \lor \neg \left(z \leq 0.53\right):\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-81} \lor \neg \left(x \leq 2.7 \cdot 10^{-30}\right):\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(-6, z, 3\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 4\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e-81) (not (<= x 2.7e-30)))
   (* (- x) (fma -6.0 z 3.0))
   (* (fma -6.0 z 4.0) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-81) || !(x <= 2.7e-30)) {
		tmp = -x * fma(-6.0, z, 3.0);
	} else {
		tmp = fma(-6.0, z, 4.0) * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e-81) || !(x <= 2.7e-30))
		tmp = Float64(Float64(-x) * fma(-6.0, z, 3.0));
	else
		tmp = Float64(fma(-6.0, z, 4.0) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e-81], N[Not[LessEqual[x, 2.7e-30]], $MachinePrecision]], N[((-x) * N[(-6.0 * z + 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(-6.0 * z + 4.0), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000026e-81 or 2.69999999999999987e-30 < 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

      \[\leadsto \color{blue}{x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]
   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 82.4

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

   8. Applied rewrites 82.4%

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

   if -5.50000000000000026e-81 < x < 2.69999999999999987e-30

   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

      \[\leadsto \color{blue}{x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]
   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 83.2

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

   8. Applied rewrites 83.2%

      \[\leadsto \mathsf{fma}\left(-6, z, 4\right) \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-81} \lor \neg \left(x \leq 2.7 \cdot 10^{-30}\right):\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(-6, z, 3\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, z, 4\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;\left(y - x\right) \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.53:\\ \;\;\;\;\mathsf{fma}\left(-3, x, 4 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.56)
   (* (- y x) (* -6.0 z))
   (if (<= z 0.53) (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 <= -0.56) {
		tmp = (y - x) * (-6.0 * z);
	} else if (z <= 0.53) {
		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 <= -0.56)
		tmp = Float64(Float64(y - x) * Float64(-6.0 * z));
	elseif (z <= 0.53)
		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, -0.56], N[(N[(y - x), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.53], 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 < -0.56000000000000005

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. flip-- N/A

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

      9. associate-*l/ N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

          \[\leadsto x + \frac{\left(\color{blue}{\frac{4}{9}} - z \cdot z\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

      16. lower-*.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - \color{blue}{z \cdot z}\right) \cdot \left(6 \cdot \left(y - x\right)\right)}{\frac{2}{3} + z} \]

      17. *-commutative N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

      18. lift-*.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}}{\frac{2}{3} + z} \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\color{blue}{\left(y - x\right)} \cdot 6\right)}{\frac{2}{3} + z} \]

      20. lower-+.f64 N/A

          \[\leadsto x + \frac{\left(\frac{4}{9} - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{\frac{2}{3} + z}} \]

      21. metadata-eval 76.8

          \[\leadsto x + \frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{\color{blue}{0.6666666666666666} + z} \]

   4. Applied rewrites 76.8%

      \[\leadsto x + \color{blue}{\frac{\left(0.4444444444444444 - z \cdot z\right) \cdot \left(\left(y - x\right) \cdot 6\right)}{0.6666666666666666 + z}} \]

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 99.7

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

   7. Applied rewrites 99.7%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 96.4

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

   10. Applied rewrites 96.4%

       \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot -6} \]
   11. 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 96.4

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

   12. Applied rewrites 96.4%

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

   if -0.56000000000000005 < z < 0.53000000000000003

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 95.9

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

   5. Applied rewrites 95.9%

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

   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 95.9

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

   8. Applied rewrites 95.9%

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

   if 0.53000000000000003 < 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 98.6

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

   5. Applied rewrites 98.6%

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

Alternative 10: 74.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.7) (not (<= z 0.52))) (* (* z x) 6.0) (fma 4.0 (- y x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7) || !(z <= 0.52)) {
		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 <= -3.7) || !(z <= 0.52))
		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, -3.7], N[Not[LessEqual[z, 0.52]], $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 < -3.7000000000000002 or 0.52000000000000002 < 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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 57.9

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 57.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z 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 56.4

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

   8. Applied rewrites 56.4%

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

   if -3.7000000000000002 < z < 0.52000000000000002

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 95.9

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

   5. Applied rewrites 95.9%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-98} \lor \neg \left(x \leq 2950000000\right):\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;4 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.9e-98) (not (<= x 2950000000.0))) (* -3.0 x) (* 4.0 y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.9e-98) || !(x <= 2950000000.0)) {
		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 <= (-2.9d-98)) .or. (.not. (x <= 2950000000.0d0))) 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 <= -2.9e-98) || !(x <= 2950000000.0)) {
		tmp = -3.0 * x;
	} else {
		tmp = 4.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.9e-98) or not (x <= 2950000000.0):
		tmp = -3.0 * x
	else:
		tmp = 4.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.9e-98) || !(x <= 2950000000.0))
		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 <= -2.9e-98) || ~((x <= 2950000000.0)))
		tmp = -3.0 * x;
	else
		tmp = 4.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.9e-98], N[Not[LessEqual[x, 2950000000.0]], $MachinePrecision]], N[(-3.0 * x), $MachinePrecision], N[(4.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e-98 or 2.95e9 < 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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{x} \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \frac{2}{3} - z, 1\right) \cdot x \]

      7. metadata-eval 83.2

         \[\leadsto \mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x \]

   5. Applied rewrites 83.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, 0.6666666666666666 - z, 1\right) \cdot x} \]

   6. Taylor expanded in z around 0

      \[\leadsto -3 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 36.4%

      \[\leadsto -3 \cdot x \]

   if -2.9e-98 < x < 2.95e9

   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 49.2

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

   5. Applied rewrites 49.2%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 40.3

         \[\leadsto 4 \cdot y \]

   8. Applied rewrites 40.3%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-98} \lor \neg \left(x \leq 2950000000\right):\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;4 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.7% 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 99.5%

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

3. Taylor expanded in z around 0

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

Alternative 13: 51.4% 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 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 46.5

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

5. Applied rewrites 46.5%

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

Alternative 14: 26.5% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 4.0d0 * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 46.5

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

5. Applied rewrites 46.5%

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

6. Taylor expanded in x around 0

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

   1. lower-*.f64 22.2

      \[\leadsto 4 \cdot y \]

8. Applied rewrites 22.2%

   \[\leadsto 4 \cdot \color{blue}{y} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025057 
(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))))