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

Percentage Accurate: 99.5% → 99.8%

Time: 15.4s

Alternatives: 13

Speedup: 1.9×

• 20.4% 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

real(8) function code(x, y, z)
    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

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in x around 0

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

5. Simplified 99.8%

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

Alternative 2: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ \mathbf{if}\;t\_0 \leq -1000000000000:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(x, -3, y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)))
   (if (<= t_0 -1000000000000.0)
     (* 6.0 (* z (- x y)))
     (if (<= t_0 1.0) (fma x -3.0 (* y 4.0)) (* z (* 6.0 (- x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double tmp;
	if (t_0 <= -1000000000000.0) {
		tmp = 6.0 * (z * (x - y));
	} else if (t_0 <= 1.0) {
		tmp = fma(x, -3.0, (y * 4.0));
	} else {
		tmp = z * (6.0 * (x - y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	tmp = 0.0
	if (t_0 <= -1000000000000.0)
		tmp = Float64(6.0 * Float64(z * Float64(x - y)));
	elseif (t_0 <= 1.0)
		tmp = fma(x, -3.0, Float64(y * 4.0));
	else
		tmp = Float64(z * Float64(6.0 * Float64(x - y)));
	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, -1000000000000.0], N[(6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[(x * -3.0 + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < -1e12

   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. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.6

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

   5. Simplified 99.6%

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

   if -1e12 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 1

   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

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. sub-neg N/A

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

      8. distribute-lft-in N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-lft-in N/A

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

      14. neg-mul-1 N/A

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

      15. associate-*r* N/A

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

      16. metadata-eval N/A

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

      17. metadata-eval N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-/.f64 N/A

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

      21. metadata-eval N/A

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

      22. metadata-eval N/A

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

      23. lower-*.f64 N/A

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

   4. Applied egg-rr 99.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-neg.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 99.9

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

      15. lift-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 99.9

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 96.7

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

   9. Simplified 96.7%

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

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

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 95.7

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

   5. Simplified 95.7%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 95.8

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

   7. Applied egg-rr 95.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2}{3} - z \leq -1000000000000:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;\frac{2}{3} - z \leq 1:\\ \;\;\;\;\mathsf{fma}\left(x, -3, y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ t_1 := 6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{if}\;t\_0 \leq -1000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(x, -3, y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)) (t_1 (* 6.0 (* z (- x y)))))
   (if (<= t_0 -1000000000000.0)
     t_1
     (if (<= t_0 1.0) (fma x -3.0 (* y 4.0)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double t_1 = 6.0 * (z * (x - y));
	double tmp;
	if (t_0 <= -1000000000000.0) {
		tmp = t_1;
	} else if (t_0 <= 1.0) {
		tmp = fma(x, -3.0, (y * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	t_1 = Float64(6.0 * Float64(z * Float64(x - y)))
	tmp = 0.0
	if (t_0 <= -1000000000000.0)
		tmp = t_1;
	elseif (t_0 <= 1.0)
		tmp = fma(x, -3.0, Float64(y * 4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1000000000000.0], t$95$1, If[LessEqual[t$95$0, 1.0], N[(x * -3.0 + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < -1e12 or 1 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z)

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 97.7

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

   5. Simplified 97.7%

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

   if -1e12 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 1

   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

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. sub-neg N/A

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

      8. distribute-lft-in N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-lft-in N/A

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

      14. neg-mul-1 N/A

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

      15. associate-*r* N/A

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

      16. metadata-eval N/A

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

      17. metadata-eval N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-/.f64 N/A

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

      21. metadata-eval N/A

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

      22. metadata-eval N/A

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

      23. lower-*.f64 N/A

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

   4. Applied egg-rr 99.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-neg.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 99.9

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

      15. lift-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 99.9

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 96.7

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

   9. Simplified 96.7%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2}{3} - z \leq -1000000000000:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;\frac{2}{3} - z \leq 1:\\ \;\;\;\;\mathsf{fma}\left(x, -3, y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \mathsf{fma}\left(6, z, -3\right)\\ \mathbf{if}\;z \leq -17:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (fma 6.0 z -3.0))))
   (if (<= z -17.0)
     t_0
     (if (<= z 6e-7)
       (fma 4.0 (- y x) x)
       (if (<= z 3.8e+72) t_0 (* -6.0 (* z y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * fma(6.0, z, -3.0);
	double tmp;
	if (z <= -17.0) {
		tmp = t_0;
	} else if (z <= 6e-7) {
		tmp = fma(4.0, (y - x), x);
	} else if (z <= 3.8e+72) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (z * y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * fma(6.0, z, -3.0))
	tmp = 0.0
	if (z <= -17.0)
		tmp = t_0;
	elseif (z <= 6e-7)
		tmp = fma(4.0, Float64(y - x), x);
	elseif (z <= 3.8e+72)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(z * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(6.0 * z + -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -17.0], t$95$0, If[LessEqual[z, 6e-7], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.8e+72], t$95$0, N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -17 or 5.9999999999999997e-7 < z < 3.80000000000000006e72

   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. remove-double-neg N/A

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

      2. neg-mul-1 N/A

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

      3. distribute-lft-neg-in N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. distribute-neg-in N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-neg-in N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. metadata-eval N/A

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

      11. sub-neg N/A

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

      12. associate-*r* N/A

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

      13. mul-1-neg N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. lower-*.f64 N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. distribute-neg-in N/A

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

      19. distribute-lft-neg-in N/A

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

      20. metadata-eval N/A

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

      21. metadata-eval N/A

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

   5. Simplified 60.5%

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

   if -17 < z < 5.9999999999999997e-7

   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

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 97.6

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

   5. Simplified 97.6%

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

   if 3.80000000000000006e72 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.9

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 65.8

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

   8. Simplified 65.8%

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 65.8

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

   10. Applied egg-rr 65.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17:\\ \;\;\;\;x \cdot \mathsf{fma}\left(6, z, -3\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(6, z, -3\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(6 \cdot x\right)\\ \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* 6.0 x))))
   (if (<= z -46000000000.0)
     t_0
     (if (<= z 0.66)
       (fma 4.0 (- y x) x)
       (if (<= z 3.8e+72) t_0 (* -6.0 (* z y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * x);
	double tmp;
	if (z <= -46000000000.0) {
		tmp = t_0;
	} else if (z <= 0.66) {
		tmp = fma(4.0, (y - x), x);
	} else if (z <= 3.8e+72) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (z * y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * x))
	tmp = 0.0
	if (z <= -46000000000.0)
		tmp = t_0;
	elseif (z <= 0.66)
		tmp = fma(4.0, Float64(y - x), x);
	elseif (z <= 3.8e+72)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(z * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -46000000000.0], t$95$0, If[LessEqual[z, 0.66], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.8e+72], t$95$0, N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e10 or 0.660000000000000031 < z < 3.80000000000000006e72

   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. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.3

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

   5. Simplified 99.3%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 99.4

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

   7. Applied egg-rr 99.4%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 63.0

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

   10. Simplified 63.0%

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

   if -4.6e10 < z < 0.660000000000000031

   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

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 93.3

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

   5. Simplified 93.3%

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

   if 3.80000000000000006e72 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.9

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 65.8

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

   8. Simplified 65.8%

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 65.8

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

   10. Applied egg-rr 65.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;z \cdot \left(6 \cdot x\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(6 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(6 \cdot x\right)\\ \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* 6.0 x))))
   (if (<= z -46000000000.0)
     t_0
     (if (<= z 0.66)
       (fma 4.0 (- y x) x)
       (if (<= z 3.8e+72) t_0 (* y (* z -6.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * x);
	double tmp;
	if (z <= -46000000000.0) {
		tmp = t_0;
	} else if (z <= 0.66) {
		tmp = fma(4.0, (y - x), x);
	} else if (z <= 3.8e+72) {
		tmp = t_0;
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * x))
	tmp = 0.0
	if (z <= -46000000000.0)
		tmp = t_0;
	elseif (z <= 0.66)
		tmp = fma(4.0, Float64(y - x), x);
	elseif (z <= 3.8e+72)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(z * -6.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -46000000000.0], t$95$0, If[LessEqual[z, 0.66], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.8e+72], t$95$0, N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e10 or 0.660000000000000031 < z < 3.80000000000000006e72

   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. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.3

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

   5. Simplified 99.3%

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

      1. lift--.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 99.4

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

   7. Applied egg-rr 99.4%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 63.0

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

   10. Simplified 63.0%

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

   if -4.6e10 < z < 0.660000000000000031

   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

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 93.3

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

   5. Simplified 93.3%

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

   if 3.80000000000000006e72 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.9

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 65.8

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

   8. Simplified 65.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;z \cdot \left(6 \cdot x\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(6 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -46000000000.0)
   (* x (* 6.0 z))
   (if (<= z 0.66)
     (fma 4.0 (- y x) x)
     (if (<= z 3.8e+72) (* 6.0 (* z x)) (* y (* z -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -46000000000.0) {
		tmp = x * (6.0 * z);
	} else if (z <= 0.66) {
		tmp = fma(4.0, (y - x), x);
	} else if (z <= 3.8e+72) {
		tmp = 6.0 * (z * x);
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -46000000000.0)
		tmp = Float64(x * Float64(6.0 * z));
	elseif (z <= 0.66)
		tmp = fma(4.0, Float64(y - x), x);
	elseif (z <= 3.8e+72)
		tmp = Float64(6.0 * Float64(z * x));
	else
		tmp = Float64(y * Float64(z * -6.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -46000000000.0], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.66], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.8e+72], N[(6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.6e10

   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. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.5

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

   5. Simplified 99.5%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 60.2

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

   8. Simplified 60.2%

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

   if -4.6e10 < z < 0.660000000000000031

   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

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 93.3

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

   5. Simplified 93.3%

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

   if 0.660000000000000031 < z < 3.80000000000000006e72

   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 inf

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

      1. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 98.3

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

   5. Simplified 98.3%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 75.9

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

   8. Simplified 75.9%

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

   if 3.80000000000000006e72 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.9

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 65.8

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

   8. Simplified 65.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \mathsf{fma}\left(z, -6, 4\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(6, z, -3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (fma z -6.0 4.0))))
   (if (<= y -1.45e-38) t_0 (if (<= y 4.5e+41) (* x (fma 6.0 z -3.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * fma(z, -6.0, 4.0);
	double tmp;
	if (y <= -1.45e-38) {
		tmp = t_0;
	} else if (y <= 4.5e+41) {
		tmp = x * fma(6.0, z, -3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(y * fma(z, -6.0, 4.0))
	tmp = 0.0
	if (y <= -1.45e-38)
		tmp = t_0;
	elseif (y <= 4.5e+41)
		tmp = Float64(x * fma(6.0, z, -3.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * -6.0 + 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e-38], t$95$0, If[LessEqual[y, 4.5e+41], N[(x * N[(6.0 * z + -3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999997e-38 or 4.5000000000000001e41 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-lft-in N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. metadata-eval N/A

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

      13. lower-fma.f64 82.0

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

   5. Simplified 82.0%

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

   if -1.44999999999999997e-38 < y < 4.5000000000000001e41

   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. remove-double-neg N/A

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

      2. neg-mul-1 N/A

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

      3. distribute-lft-neg-in N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. distribute-neg-in N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-neg-in N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. metadata-eval N/A

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

      11. sub-neg N/A

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

      12. associate-*r* N/A

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

      13. mul-1-neg N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. lower-*.f64 N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. distribute-neg-in N/A

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

      19. distribute-lft-neg-in N/A

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

      20. metadata-eval N/A

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

      21. metadata-eval N/A

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

   5. Simplified 80.0%

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

Alternative 9: 74.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -46000000000.0)
   (* x (* 6.0 z))
   (if (<= z 0.66) (fma 4.0 (- y x) x) (* 6.0 (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -46000000000.0) {
		tmp = x * (6.0 * z);
	} else if (z <= 0.66) {
		tmp = fma(4.0, (y - x), x);
	} else {
		tmp = 6.0 * (z * x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -46000000000.0)
		tmp = Float64(x * Float64(6.0 * z));
	elseif (z <= 0.66)
		tmp = fma(4.0, Float64(y - x), x);
	else
		tmp = Float64(6.0 * Float64(z * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -46000000000.0], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.66], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e10

   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. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.5

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

   5. Simplified 99.5%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 60.2

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

   8. Simplified 60.2%

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

   if -4.6e10 < z < 0.660000000000000031

   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

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 93.3

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

   5. Simplified 93.3%

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

   if 0.660000000000000031 < 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. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.6

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 50.3

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

   8. Simplified 50.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot x\right)\\ \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z x))))
   (if (<= z -46000000000.0) t_0 (if (<= z 0.66) (fma 4.0 (- y x) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * x);
	double tmp;
	if (z <= -46000000000.0) {
		tmp = t_0;
	} else if (z <= 0.66) {
		tmp = fma(4.0, (y - x), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * x))
	tmp = 0.0
	if (z <= -46000000000.0)
		tmp = t_0;
	elseif (z <= 0.66)
		tmp = fma(4.0, Float64(y - x), x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -46000000000.0], t$95$0, If[LessEqual[z, 0.66], N[(4.0 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e10 or 0.660000000000000031 < 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. metadata-eval N/A

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

      2. distribute-lft-neg-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. neg-mul-1 N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 99.6

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 55.0

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

   8. Simplified 55.0%

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

   if -4.6e10 < z < 0.660000000000000031

   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

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 93.3

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

   5. Simplified 93.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -46000000000:\\ \;\;\;\;6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;\mathsf{fma}\left(4, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 255000000000:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e-26)
   (* x -3.0)
   (if (<= x 255000000000.0) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e-26) {
		tmp = x * -3.0;
	} else if (x <= 255000000000.0) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.6d-26)) then
        tmp = x * (-3.0d0)
    else if (x <= 255000000000.0d0) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e-26) {
		tmp = x * -3.0;
	} else if (x <= 255000000000.0) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e-26:
		tmp = x * -3.0
	elif x <= 255000000000.0:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e-26)
		tmp = Float64(x * -3.0);
	elseif (x <= 255000000000.0)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.6e-26)
		tmp = x * -3.0;
	elseif (x <= 255000000000.0)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e-26], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 255000000000.0], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.60000000000000018e-26 or 2.55e11 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 48.3

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

   5. Simplified 48.3%

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

   6. Taylor expanded in y around 0

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 38.1

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

   8. Simplified 38.1%

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

   if -4.60000000000000018e-26 < x < 2.55e11

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 46.4

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

   5. Simplified 46.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 40.5

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

   8. Simplified 40.5%

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

Alternative 12: 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 99.6%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. lower--.f64 47.3

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

5. Simplified 47.3%

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

Alternative 13: 27.1% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (-3.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. lower--.f64 47.3

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

5. Simplified 47.3%

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

6. Taylor expanded in y around 0

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

   1. distribute-rgt1-in N/A

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

   2. metadata-eval N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 22.9

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

8. Simplified 22.9%

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

Reproduce

herbie shell --seed 2024212 
(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))))