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

Percentage Accurate: 99.5% → 99.7%

Time: 8.8s

Alternatives: 7

Speedup: 1.2×

• 21.2% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. flip-- 89.4%

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

   2. associate-*r/ 85.8%

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

   3. metadata-eval 85.8%

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

   4. pow2 85.8%

      \[\leadsto x + \frac{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z} \]

6. Applied egg-rr 85.8%

   \[\leadsto x + \color{blue}{\frac{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}} \]
7. Step-by-step derivation

   1. *-commutative 85.8%

      \[\leadsto x + \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(\left(y - x\right) \cdot 6\right)}}{0.6666666666666666 + z} \]

   2. associate-/l* 89.0%

      \[\leadsto x + \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{\left(y - x\right) \cdot 6}}} \]

   3. *-commutative 89.0%

      \[\leadsto x + \frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{\color{blue}{6 \cdot \left(y - x\right)}}} \]

   4. associate-/r* 89.3%

      \[\leadsto x + \frac{0.4444444444444444 - {z}^{2}}{\color{blue}{\frac{\frac{0.6666666666666666 + z}{6}}{y - x}}} \]

8. Simplified 89.3%

   \[\leadsto x + \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{\frac{0.6666666666666666 + z}{6}}{y - x}}} \]

9. Taylor expanded in z around 0 99.7%

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

    1. +-commutative 99.7%

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

    2. fma-def 99.7%

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

11. Simplified 99.7%

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

12. Final simplification 99.7%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. +-commutative 99.3%

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

   2. associate-*l* 99.7%

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

   3. fma-def 99.7%

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

   4. sub-neg 99.7%

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

   5. distribute-rgt-in 99.7%

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

   6. metadata-eval 99.7%

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

   7. metadata-eval 99.7%

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

   8. distribute-lft-neg-out 99.7%

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

   9. distribute-rgt-neg-in 99.7%

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

   10. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Final simplification 99.7%

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

Alternative 3: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(6 \cdot \left(y - x\right)\right) \cdot \left(0.6666666666666666 - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* 6.0 (- y x)) (- 0.6666666666666666 z))))

C

double code(double x, double y, double z) {
	return x + ((6.0 * (y - x)) * (0.6666666666666666 - 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 + ((6.0d0 * (y - x)) * (0.6666666666666666d0 - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((6.0 * (y - x)) * (0.6666666666666666 - z));
}

Python

def code(x, y, z):
	return x + ((6.0 * (y - x)) * (0.6666666666666666 - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(6.0 * Float64(y - x)) * Float64(0.6666666666666666 - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((6.0 * (y - x)) * (0.6666666666666666 - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Final simplification 99.3%

   \[\leadsto x + \left(6 \cdot \left(y - x\right)\right) \cdot \left(0.6666666666666666 - z\right) \]
6. Add Preprocessing

Alternative 4: 50.9% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return 6.0 * (z * (x - y))

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = 6.0 * (z * (x - y));
end

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. flip-- 89.4%

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

   2. associate-*r/ 85.8%

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

   3. metadata-eval 85.8%

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

   4. pow2 85.8%

      \[\leadsto x + \frac{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z} \]

6. Applied egg-rr 85.8%

   \[\leadsto x + \color{blue}{\frac{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}} \]
7. Step-by-step derivation

   1. *-commutative 85.8%

      \[\leadsto x + \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(\left(y - x\right) \cdot 6\right)}}{0.6666666666666666 + z} \]

   2. associate-/l* 89.0%

      \[\leadsto x + \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{\left(y - x\right) \cdot 6}}} \]

   3. *-commutative 89.0%

      \[\leadsto x + \frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{\color{blue}{6 \cdot \left(y - x\right)}}} \]

   4. associate-/r* 89.3%

      \[\leadsto x + \frac{0.4444444444444444 - {z}^{2}}{\color{blue}{\frac{\frac{0.6666666666666666 + z}{6}}{y - x}}} \]

8. Simplified 89.3%

   \[\leadsto x + \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{\frac{0.6666666666666666 + z}{6}}{y - x}}} \]

9. Taylor expanded in z around 0 99.7%

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

    1. +-commutative 99.7%

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

    2. fma-def 99.7%

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

11. Simplified 99.7%

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

12. Taylor expanded in z around inf 49.5%

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

13. Final simplification 49.5%

    \[\leadsto 6 \cdot \left(z \cdot \left(x - y\right)\right) \]
14. Add Preprocessing

Alternative 5: 51.3% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 53.3%

   \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
6. Step-by-step derivation

   1. sub-neg 53.3%

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

   2. distribute-rgt-in 53.3%

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

   3. metadata-eval 53.3%

      \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

   4. metadata-eval 53.3%

      \[\leadsto x \cdot \left(1 + \left(\color{blue}{\left(-4\right)} + \left(-z\right) \cdot -6\right)\right) \]

   5. distribute-lft-neg-in 53.3%

      \[\leadsto x \cdot \left(1 + \left(\left(-4\right) + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

   6. associate-+r+ 53.3%

      \[\leadsto x \cdot \color{blue}{\left(\left(1 + \left(-4\right)\right) + \left(-z \cdot -6\right)\right)} \]

   7. metadata-eval 53.3%

      \[\leadsto x \cdot \left(\left(1 + \color{blue}{-4}\right) + \left(-z \cdot -6\right)\right) \]

   8. metadata-eval 53.3%

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

   9. distribute-rgt-neg-in 53.3%

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

   10. metadata-eval 53.3%

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

7. Simplified 53.3%

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

8. Final simplification 53.3%

   \[\leadsto x \cdot \left(-3 + 6 \cdot z\right) \]
9. Add Preprocessing

Alternative 6: 27.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ 6 \cdot \left(x \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 6.0 (* x z)))

C

double code(double x, double y, double z) {
	return 6.0 * (x * 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 = 6.0d0 * (x * z)
end function

Java

public static double code(double x, double y, double z) {
	return 6.0 * (x * z);
}

Python

def code(x, y, z):
	return 6.0 * (x * z)

Julia

function code(x, y, z)
	return Float64(6.0 * Float64(x * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 6.0 * (x * z);
end

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 53.3%

   \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
6. Step-by-step derivation

   1. sub-neg 53.3%

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

   2. distribute-rgt-in 53.3%

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

   3. metadata-eval 53.3%

      \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

   4. metadata-eval 53.3%

      \[\leadsto x \cdot \left(1 + \left(\color{blue}{\left(-4\right)} + \left(-z\right) \cdot -6\right)\right) \]

   5. distribute-lft-neg-in 53.3%

      \[\leadsto x \cdot \left(1 + \left(\left(-4\right) + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

   6. associate-+r+ 53.3%

      \[\leadsto x \cdot \color{blue}{\left(\left(1 + \left(-4\right)\right) + \left(-z \cdot -6\right)\right)} \]

   7. metadata-eval 53.3%

      \[\leadsto x \cdot \left(\left(1 + \color{blue}{-4}\right) + \left(-z \cdot -6\right)\right) \]

   8. metadata-eval 53.3%

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

   9. distribute-rgt-neg-in 53.3%

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

   10. metadata-eval 53.3%

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

7. Simplified 53.3%

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

8. Taylor expanded in z around inf 28.1%

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

   1. *-commutative 28.1%

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

10. Simplified 28.1%

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

11. Final simplification 28.1%

    \[\leadsto 6 \cdot \left(x \cdot z\right) \]
12. Add Preprocessing

Alternative 7: 25.6% accurate, 4.3× 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 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 53.3%

   \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
6. Step-by-step derivation

   1. sub-neg 53.3%

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

   2. distribute-rgt-in 53.3%

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

   3. metadata-eval 53.3%

      \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

   4. metadata-eval 53.3%

      \[\leadsto x \cdot \left(1 + \left(\color{blue}{\left(-4\right)} + \left(-z\right) \cdot -6\right)\right) \]

   5. distribute-lft-neg-in 53.3%

      \[\leadsto x \cdot \left(1 + \left(\left(-4\right) + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

   6. associate-+r+ 53.3%

      \[\leadsto x \cdot \color{blue}{\left(\left(1 + \left(-4\right)\right) + \left(-z \cdot -6\right)\right)} \]

   7. metadata-eval 53.3%

      \[\leadsto x \cdot \left(\left(1 + \color{blue}{-4}\right) + \left(-z \cdot -6\right)\right) \]

   8. metadata-eval 53.3%

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

   9. distribute-rgt-neg-in 53.3%

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

   10. metadata-eval 53.3%

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

7. Simplified 53.3%

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

8. Taylor expanded in z around 0 27.6%

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

   1. *-commutative 27.6%

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

10. Simplified 27.6%

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

11. Final simplification 27.6%

    \[\leadsto x \cdot -3 \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024033 
(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))))