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

Percentage Accurate: 99.7% → 99.7%

Time: 9.7s

Alternatives: 8

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{6}{\frac{\frac{1}{y - x}}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ 6.0 (/ (/ 1.0 (- y x)) z))))

C

double code(double x, double y, double z) {
	return x + (6.0 / ((1.0 / (y - 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 = x + (6.0d0 / ((1.0d0 / (y - x)) / z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (6.0 / ((1.0 / (y - x)) / z));
}

Python

def code(x, y, z):
	return x + (6.0 / ((1.0 / (y - x)) / z))

Julia

function code(x, y, z)
	return Float64(x + Float64(6.0 / Float64(Float64(1.0 / Float64(y - x)) / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (6.0 / ((1.0 / (y - x)) / z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(6.0 / N[(N[(1.0 / N[(y - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. associate-*r* 99.8%

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

   2. *-commutative 99.8%

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

   3. flip-- 68.8%

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

   4. associate-*r/ 65.1%

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

3. Applied egg-rr 65.1%

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

   1. associate-/l* 68.7%

      \[\leadsto x + \color{blue}{\frac{6 \cdot z}{\frac{y + x}{y \cdot y - x \cdot x}}} \]

   2. associate-/l* 68.8%

      \[\leadsto x + \color{blue}{\frac{6}{\frac{\frac{y + x}{y \cdot y - x \cdot x}}{z}}} \]

   3. difference-of-squares 72.2%

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

   4. associate-/r* 99.8%

      \[\leadsto x + \frac{6}{\frac{\color{blue}{\frac{\frac{y + x}{y + x}}{y - x}}}{z}} \]

   5. *-inverses 99.8%

      \[\leadsto x + \frac{6}{\frac{\frac{\color{blue}{1}}{y - x}}{z}} \]

5. Simplified 99.8%

   \[\leadsto x + \color{blue}{\frac{6}{\frac{\frac{1}{y - x}}{z}}} \]

6. Final simplification 99.8%

   \[\leadsto x + \frac{6}{\frac{\frac{1}{y - x}}{z}} \]

Alternative 2: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-75} \lor \neg \left(y \leq 2.9 \cdot 10^{-95}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e-75) (not (<= y 2.9e-95)))
   (+ x (* 6.0 (* y z)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e-75) || !(y <= 2.9e-95)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	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 ((y <= (-2.9d-75)) .or. (.not. (y <= 2.9d-95))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e-75) || !(y <= 2.9e-95)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.9e-75) or not (y <= 2.9e-95):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.9e-75) || !(y <= 2.9e-95))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.9e-75) || ~((y <= 2.9e-95)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.9e-75], N[Not[LessEqual[y, 2.9e-95]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000002e-75 or 2.90000000000000002e-95 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 85.4%

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

      1. *-commutative 85.4%

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

   4. Simplified 85.4%

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

   if -2.9000000000000002e-75 < y < 2.90000000000000002e-95

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 94.6%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-75} \lor \neg \left(y \leq 2.9 \cdot 10^{-95}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-75} \lor \neg \left(y \leq 7.2 \cdot 10^{-95}\right):\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.55e-75) (not (<= y 7.2e-95)))
   (+ x (* z (* 6.0 y)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.55e-75) || !(y <= 7.2e-95)) {
		tmp = x + (z * (6.0 * y));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	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 ((y <= (-1.55d-75)) .or. (.not. (y <= 7.2d-95))) then
        tmp = x + (z * (6.0d0 * y))
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.55e-75) || !(y <= 7.2e-95)) {
		tmp = x + (z * (6.0 * y));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.55e-75) or not (y <= 7.2e-95):
		tmp = x + (z * (6.0 * y))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.55e-75) || !(y <= 7.2e-95))
		tmp = Float64(x + Float64(z * Float64(6.0 * y)));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.55e-75) || ~((y <= 7.2e-95)))
		tmp = x + (z * (6.0 * y));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.55e-75], N[Not[LessEqual[y, 7.2e-95]], $MachinePrecision]], N[(x + N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000003e-75 or 7.2e-95 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 85.5%

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

   if -1.55000000000000003e-75 < y < 7.2e-95

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 94.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-75} \lor \neg \left(y \leq 7.2 \cdot 10^{-95}\right):\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-96}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e-78)
   (+ x (* y (* 6.0 z)))
   (if (<= y 7.5e-96) (+ x (* -6.0 (* x z))) (+ x (* z (* 6.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e-78) {
		tmp = x + (y * (6.0 * z));
	} else if (y <= 7.5e-96) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (z * (6.0 * y));
	}
	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 (y <= (-3.4d-78)) then
        tmp = x + (y * (6.0d0 * z))
    else if (y <= 7.5d-96) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = x + (z * (6.0d0 * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e-78) {
		tmp = x + (y * (6.0 * z));
	} else if (y <= 7.5e-96) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (z * (6.0 * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e-78:
		tmp = x + (y * (6.0 * z))
	elif y <= 7.5e-96:
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = x + (z * (6.0 * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e-78)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	elseif (y <= 7.5e-96)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(x + Float64(z * Float64(6.0 * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e-78)
		tmp = x + (y * (6.0 * z));
	elseif (y <= 7.5e-96)
		tmp = x + (-6.0 * (x * z));
	else
		tmp = x + (z * (6.0 * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e-78], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-96], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.40000000000000012e-78

   1. Initial program 99.7%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. flip-- 64.6%

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

      4. associate-*r/ 62.0%

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

   3. Applied egg-rr 62.0%

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

      1. associate-/l* 64.5%

         \[\leadsto x + \color{blue}{\frac{6 \cdot z}{\frac{y + x}{y \cdot y - x \cdot x}}} \]

      2. associate-/l* 64.4%

         \[\leadsto x + \color{blue}{\frac{6}{\frac{\frac{y + x}{y \cdot y - x \cdot x}}{z}}} \]

      3. difference-of-squares 67.4%

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

      4. associate-/r* 99.8%

         \[\leadsto x + \frac{6}{\frac{\color{blue}{\frac{\frac{y + x}{y + x}}{y - x}}}{z}} \]

      5. *-inverses 99.8%

         \[\leadsto x + \frac{6}{\frac{\frac{\color{blue}{1}}{y - x}}{z}} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{\frac{6}{\frac{\frac{1}{y - x}}{z}}} \]

   6. Taylor expanded in y around inf 83.7%

      \[\leadsto x + \frac{6}{\color{blue}{\frac{1}{y \cdot z}}} \]
   7. Step-by-step derivation

      1. associate-/r* 83.8%

         \[\leadsto x + \frac{6}{\color{blue}{\frac{\frac{1}{y}}{z}}} \]

   8. Simplified 83.8%

      \[\leadsto x + \frac{6}{\color{blue}{\frac{\frac{1}{y}}{z}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 83.8%

         \[\leadsto x + \color{blue}{\frac{6}{\frac{1}{y}} \cdot z} \]

      2. associate-/r/ 83.8%

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

      3. metadata-eval 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-*r* 83.9%

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

      6. *-commutative 83.9%

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

   10. Applied egg-rr 83.9%

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

   if -3.40000000000000012e-78 < y < 7.5e-96

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 94.6%

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

   if 7.5e-96 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 87.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-96}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \end{array} \]

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in z around 0 99.8%

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

3. Final simplification 99.8%

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

Alternative 6: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 7: 61.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 67.5%

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

3. Final simplification 67.5%

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

Alternative 8: 36.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in z around 0 39.2%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 39.2%

   \[\leadsto x \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023280 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))