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

Percentage Accurate: 99.5% → 99.7%

Time: 10.8s

Alternatives: 10

Speedup: 1.9×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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: 99.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. distribute-rgt-in N/A

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

   5. +-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. associate-*r* N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-*.f64 N/A

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

   10. lower-neg.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. *-commutative N/A

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

   13. associate-*r* N/A

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

   14. lift-/.f64 N/A

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

   15. metadata-eval N/A

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

   16. metadata-eval N/A

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

   17. metadata-eval N/A

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

   18. metadata-eval N/A

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

   19. lift-/.f64 N/A

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

   20. lower-*.f64 N/A

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

   21. lift-/.f64 N/A

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

   22. metadata-eval N/A

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

   23. metadata-eval 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ \mathbf{if}\;t\_0 \leq 0.6666666666666:\\ \;\;\;\;\mathsf{fma}\left(6, z, -3\right) \cdot x\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)))
   (if (<= t_0 0.6666666666666)
     (* (fma 6.0 z -3.0) x)
     (if (<= t_0 4e+15) (fma (- y x) 4.0 x) (* (* y z) -6.0)))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double tmp;
	if (t_0 <= 0.6666666666666) {
		tmp = fma(6.0, z, -3.0) * x;
	} else if (t_0 <= 4e+15) {
		tmp = fma((y - x), 4.0, x);
	} else {
		tmp = (y * z) * -6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	tmp = 0.0
	if (t_0 <= 0.6666666666666)
		tmp = Float64(fma(6.0, z, -3.0) * x);
	elseif (t_0 <= 4e+15)
		tmp = fma(Float64(y - x), 4.0, x);
	else
		tmp = Float64(Float64(y * z) * -6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[t$95$0, 0.6666666666666], N[(N[(6.0 * z + -3.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$0, 4e+15], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 0.666666666666600016

   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 y around 0

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

      1. metadata-eval N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. sub-neg N/A

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

      6. *-lft-identity N/A

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

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

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

      8. neg-mul-1 N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. metadata-eval N/A

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

      12. distribute-rgt-in N/A

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

      13. +-commutative N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. neg-mul-1 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

   5. Applied rewrites 64.6%

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

   if 0.666666666666600016 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 4e15

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 98.1

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

   5. Applied rewrites 98.1%

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

   if 4e15 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z)

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 99.6

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(-6, z, 4\right), y - x, x\right)}}} \]

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.7

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

   7. Applied rewrites 99.7%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 63.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2}{3} - z \leq 0.6666666666666:\\ \;\;\;\;\mathsf{fma}\left(6, z, -3\right) \cdot x\\ \mathbf{elif}\;\frac{2}{3} - z \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.59:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.67:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.59)
   (* (* (- y x) z) -6.0)
   (if (<= z 0.67) (fma (- y x) 4.0 x) (* (* -6.0 (- y x)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.59) {
		tmp = ((y - x) * z) * -6.0;
	} else if (z <= 0.67) {
		tmp = fma((y - x), 4.0, x);
	} else {
		tmp = (-6.0 * (y - x)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.59)
		tmp = Float64(Float64(Float64(y - x) * z) * -6.0);
	elseif (z <= 0.67)
		tmp = fma(Float64(y - x), 4.0, x);
	else
		tmp = Float64(Float64(-6.0 * Float64(y - x)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.59], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * -6.0), $MachinePrecision], If[LessEqual[z, 0.67], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], N[(N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.589999999999999969

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.6

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

   5. Applied rewrites 99.6%

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

   if -0.589999999999999969 < z < 0.67000000000000004

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 97.3

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

   5. Applied rewrites 97.3%

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

   if 0.67000000000000004 < 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 99.7

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(-6, z, 4\right), y - x, x\right)}}} \]

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 98.8

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

   7. Applied rewrites 98.8%

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

   9. Applied rewrites 98.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.59:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.67:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(y - x\right) \cdot z\right) \cdot -6\\ \mathbf{if}\;z \leq -0.59:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.67:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* (- y x) z) -6.0)))
   (if (<= z -0.59) t_0 (if (<= z 0.67) (fma (- y x) 4.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y - x) * z) * -6.0;
	double tmp;
	if (z <= -0.59) {
		tmp = t_0;
	} else if (z <= 0.67) {
		tmp = fma((y - x), 4.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y - x) * z) * -6.0)
	tmp = 0.0
	if (z <= -0.59)
		tmp = t_0;
	elseif (z <= 0.67)
		tmp = fma(Float64(y - x), 4.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * -6.0), $MachinePrecision]}, If[LessEqual[z, -0.59], t$95$0, If[LessEqual[z, 0.67], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.589999999999999969 or 0.67000000000000004 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.2

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

   5. Applied rewrites 99.2%

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

   if -0.589999999999999969 < z < 0.67000000000000004

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 97.3

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

   5. Applied rewrites 97.3%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.59:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.67:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+15}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.67:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.2e+15)
   (* (* y z) -6.0)
   (if (<= z 0.67) (fma (- y x) 4.0 x) (* (* z x) 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.2e+15) {
		tmp = (y * z) * -6.0;
	} else if (z <= 0.67) {
		tmp = fma((y - x), 4.0, x);
	} else {
		tmp = (z * x) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.2e+15)
		tmp = Float64(Float64(y * z) * -6.0);
	elseif (z <= 0.67)
		tmp = fma(Float64(y - x), 4.0, x);
	else
		tmp = Float64(Float64(z * x) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.2e+15], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision], If[LessEqual[z, 0.67], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e15

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 99.6

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(-6, z, 4\right), y - x, x\right)}}} \]

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.7

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

   7. Applied rewrites 99.7%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 63.0%

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

   if -2.2e15 < z < 0.67000000000000004

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 96.6

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

   5. Applied rewrites 96.6%

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

   if 0.67000000000000004 < 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 99.7

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(-6, z, 4\right), y - x, x\right)}}} \]

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 98.8

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

   7. Applied rewrites 98.8%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 64.5%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+15}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{elif}\;z \leq 0.67:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot 6\\ \mathbf{if}\;z \leq -5.8:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.67:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) 6.0)))
   (if (<= z -5.8) t_0 (if (<= z 0.67) (fma (- y x) 4.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z * x) * 6.0;
	double tmp;
	if (z <= -5.8) {
		tmp = t_0;
	} else if (z <= 0.67) {
		tmp = fma((y - x), 4.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * x) * 6.0)
	tmp = 0.0
	if (z <= -5.8)
		tmp = t_0;
	elseif (z <= 0.67)
		tmp = fma(Float64(y - x), 4.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * 6.0), $MachinePrecision]}, If[LessEqual[z, -5.8], t$95$0, If[LessEqual[z, 0.67], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999982 or 0.67000000000000004 < z

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 99.6

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(-6, z, 4\right), y - x, x\right)}}} \]

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.2

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

   7. Applied rewrites 99.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 54.2%

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

   if -5.79999999999999982 < z < 0.67000000000000004

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 97.3

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

   5. Applied rewrites 97.3%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \mathbf{elif}\;z \leq 0.67:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+63}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-65}:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.2e+63) (* -3.0 x) (if (<= x 3.5e-65) (* 4.0 y) (* -3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e+63) {
		tmp = -3.0 * x;
	} else if (x <= 3.5e-65) {
		tmp = 4.0 * y;
	} else {
		tmp = -3.0 * x;
	}
	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 <= (-6.2d+63)) then
        tmp = (-3.0d0) * x
    else if (x <= 3.5d-65) then
        tmp = 4.0d0 * y
    else
        tmp = (-3.0d0) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e+63) {
		tmp = -3.0 * x;
	} else if (x <= 3.5e-65) {
		tmp = 4.0 * y;
	} else {
		tmp = -3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.2e+63:
		tmp = -3.0 * x
	elif x <= 3.5e-65:
		tmp = 4.0 * y
	else:
		tmp = -3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.2e+63)
		tmp = Float64(-3.0 * x);
	elseif (x <= 3.5e-65)
		tmp = Float64(4.0 * y);
	else
		tmp = Float64(-3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.2e+63)
		tmp = -3.0 * x;
	elseif (x <= 3.5e-65)
		tmp = 4.0 * y;
	else
		tmp = -3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.2e+63], N[(-3.0 * x), $MachinePrecision], If[LessEqual[x, 3.5e-65], N[(4.0 * y), $MachinePrecision], N[(-3.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000001e63 or 3.50000000000000005e-65 < x

   1. Initial program 99.0%

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

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 45.7

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

   5. Applied rewrites 45.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 37.6%

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

   if -6.2000000000000001e63 < x < 3.50000000000000005e-65

   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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 55.7

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

   5. Applied rewrites 55.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.9%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+63}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-65}:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.8% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lift--.f64 N/A

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

   9. sub-neg N/A

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

   10. +-commutative N/A

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

   11. distribute-lft-in N/A

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

   12. neg-mul-1 N/A

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

   13. associate-*r* N/A

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

   14. metadata-eval N/A

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

   15. metadata-eval N/A

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

   16. lower-fma.f64 N/A

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

   17. metadata-eval N/A

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

   18. lift-/.f64 N/A

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

   19. metadata-eval N/A

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

   20. metadata-eval 99.8

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

4. Applied rewrites 99.8%

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

Alternative 9: 50.4% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 50.3

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

5. Applied rewrites 50.3%

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

Alternative 10: 26.2% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 50.3

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

5. Applied rewrites 50.3%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 25.5%

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

Reproduce

herbie shell --seed 2024235 
(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))))