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

Percentage Accurate: 99.6% → 99.7%

Time: 13.6s

Alternatives: 11

Speedup: 1.0×

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

Specification

Math

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

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: 99.6% 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

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

FPCore

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

C

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

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 + (z / ((1.0d0 / (y - x)) / 6.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. associate-*r* 99.4%

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

   2. *-commutative 99.4%

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

   3. flip-- 68.5%

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

   4. associate-*r/ 63.4%

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

3. Applied egg-rr 63.4%

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

   1. associate-/l* 68.4%

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

   2. *-commutative 68.4%

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

   3. associate-/l* 68.8%

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

   4. difference-of-squares 70.6%

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

   5. associate-/r* 99.8%

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

   6. *-inverses 99.8%

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

5. Simplified 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+156}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+235}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* z y))))
   (if (<= z -4.2e+156)
     t_0
     (if (<= z -7.3e+78)
       t_1
       (if (<= z -9.5e+35)
         t_0
         (if (<= z -1.5e-60)
           t_1
           (if (<= z 3.6e-50) x (if (<= z 2.4e+235) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -4.2e+156) {
		tmp = t_0;
	} else if (z <= -7.3e+78) {
		tmp = t_1;
	} else if (z <= -9.5e+35) {
		tmp = t_0;
	} else if (z <= -1.5e-60) {
		tmp = t_1;
	} else if (z <= 3.6e-50) {
		tmp = x;
	} else if (z <= 2.4e+235) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    t_1 = 6.0d0 * (z * y)
    if (z <= (-4.2d+156)) then
        tmp = t_0
    else if (z <= (-7.3d+78)) then
        tmp = t_1
    else if (z <= (-9.5d+35)) then
        tmp = t_0
    else if (z <= (-1.5d-60)) then
        tmp = t_1
    else if (z <= 3.6d-50) then
        tmp = x
    else if (z <= 2.4d+235) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -4.2e+156) {
		tmp = t_0;
	} else if (z <= -7.3e+78) {
		tmp = t_1;
	} else if (z <= -9.5e+35) {
		tmp = t_0;
	} else if (z <= -1.5e-60) {
		tmp = t_1;
	} else if (z <= 3.6e-50) {
		tmp = x;
	} else if (z <= 2.4e+235) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	t_1 = 6.0 * (z * y)
	tmp = 0
	if z <= -4.2e+156:
		tmp = t_0
	elif z <= -7.3e+78:
		tmp = t_1
	elif z <= -9.5e+35:
		tmp = t_0
	elif z <= -1.5e-60:
		tmp = t_1
	elif z <= 3.6e-50:
		tmp = x
	elif z <= 2.4e+235:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	t_1 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -4.2e+156)
		tmp = t_0;
	elseif (z <= -7.3e+78)
		tmp = t_1;
	elseif (z <= -9.5e+35)
		tmp = t_0;
	elseif (z <= -1.5e-60)
		tmp = t_1;
	elseif (z <= 3.6e-50)
		tmp = x;
	elseif (z <= 2.4e+235)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	t_1 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -4.2e+156)
		tmp = t_0;
	elseif (z <= -7.3e+78)
		tmp = t_1;
	elseif (z <= -9.5e+35)
		tmp = t_0;
	elseif (z <= -1.5e-60)
		tmp = t_1;
	elseif (z <= 3.6e-50)
		tmp = x;
	elseif (z <= 2.4e+235)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+156], t$95$0, If[LessEqual[z, -7.3e+78], t$95$1, If[LessEqual[z, -9.5e+35], t$95$0, If[LessEqual[z, -1.5e-60], t$95$1, If[LessEqual[z, 3.6e-50], x, If[LessEqual[z, 2.4e+235], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999963e156 or -7.3e78 < z < -9.50000000000000062e35 or 2.3999999999999999e235 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 73.7%

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

   if -4.19999999999999963e156 < z < -7.3e78 or -9.50000000000000062e35 < z < -1.50000000000000009e-60 or 3.59999999999999979e-50 < z < 2.3999999999999999e235

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 88.6%

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

   4. Taylor expanded in y around inf 57.3%

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

      1. *-commutative 57.3%

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

   6. Simplified 57.3%

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

   if -1.50000000000000009e-60 < z < 3.59999999999999979e-50

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 77.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+156}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{+78}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+35}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-60}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+235}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* z y))))
   (if (<= z -3.3e+164)
     t_0
     (if (<= z -4.4e+79)
       t_1
       (if (<= z -4.8e+32)
         t_0
         (if (<= z -1.45e-60)
           (* z (* y 6.0))
           (if (<= z 3.2e-50) x (if (<= z 3.1e+230) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -3.3e+164) {
		tmp = t_0;
	} else if (z <= -4.4e+79) {
		tmp = t_1;
	} else if (z <= -4.8e+32) {
		tmp = t_0;
	} else if (z <= -1.45e-60) {
		tmp = z * (y * 6.0);
	} else if (z <= 3.2e-50) {
		tmp = x;
	} else if (z <= 3.1e+230) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    t_1 = 6.0d0 * (z * y)
    if (z <= (-3.3d+164)) then
        tmp = t_0
    else if (z <= (-4.4d+79)) then
        tmp = t_1
    else if (z <= (-4.8d+32)) then
        tmp = t_0
    else if (z <= (-1.45d-60)) then
        tmp = z * (y * 6.0d0)
    else if (z <= 3.2d-50) then
        tmp = x
    else if (z <= 3.1d+230) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (z * y);
	double tmp;
	if (z <= -3.3e+164) {
		tmp = t_0;
	} else if (z <= -4.4e+79) {
		tmp = t_1;
	} else if (z <= -4.8e+32) {
		tmp = t_0;
	} else if (z <= -1.45e-60) {
		tmp = z * (y * 6.0);
	} else if (z <= 3.2e-50) {
		tmp = x;
	} else if (z <= 3.1e+230) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	t_1 = 6.0 * (z * y)
	tmp = 0
	if z <= -3.3e+164:
		tmp = t_0
	elif z <= -4.4e+79:
		tmp = t_1
	elif z <= -4.8e+32:
		tmp = t_0
	elif z <= -1.45e-60:
		tmp = z * (y * 6.0)
	elif z <= 3.2e-50:
		tmp = x
	elif z <= 3.1e+230:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	t_1 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -3.3e+164)
		tmp = t_0;
	elseif (z <= -4.4e+79)
		tmp = t_1;
	elseif (z <= -4.8e+32)
		tmp = t_0;
	elseif (z <= -1.45e-60)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= 3.2e-50)
		tmp = x;
	elseif (z <= 3.1e+230)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	t_1 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -3.3e+164)
		tmp = t_0;
	elseif (z <= -4.4e+79)
		tmp = t_1;
	elseif (z <= -4.8e+32)
		tmp = t_0;
	elseif (z <= -1.45e-60)
		tmp = z * (y * 6.0);
	elseif (z <= 3.2e-50)
		tmp = x;
	elseif (z <= 3.1e+230)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+164], t$95$0, If[LessEqual[z, -4.4e+79], t$95$1, If[LessEqual[z, -4.8e+32], t$95$0, If[LessEqual[z, -1.45e-60], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-50], x, If[LessEqual[z, 3.1e+230], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.29999999999999995e164 or -4.3999999999999998e79 < z < -4.79999999999999983e32 or 3.09999999999999981e230 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 73.7%

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

   if -3.29999999999999995e164 < z < -4.3999999999999998e79 or 3.2e-50 < z < 3.09999999999999981e230

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 92.8%

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

   4. Taylor expanded in y around inf 56.4%

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

      1. *-commutative 56.4%

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

   6. Simplified 56.4%

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

   if -4.79999999999999983e32 < z < -1.45e-60

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 99.3%

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

   3. Taylor expanded in z around inf 73.9%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. associate-*r* 60.5%

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

      2. *-commutative 60.5%

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

   6. Simplified 60.5%

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

   if -1.45e-60 < z < 3.2e-50

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 77.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+164}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+79}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+32}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+230}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-82} \lor \neg \left(z \leq 5.2 \cdot 10^{-50}\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e-82) (not (<= z 5.2e-50))) (* 6.0 (* z (- y x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e-82) || !(z <= 5.2e-50)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = 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 ((z <= (-2.8d-82)) .or. (.not. (z <= 5.2d-50))) then
        tmp = 6.0d0 * (z * (y - x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e-82) || !(z <= 5.2e-50)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e-82) or not (z <= 5.2e-50):
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e-82) || !(z <= 5.2e-50))
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.8e-82) || ~((z <= 5.2e-50)))
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e-82], N[Not[LessEqual[z, 5.2e-50]], $MachinePrecision]], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000024e-82 or 5.2000000000000003e-50 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 91.5%

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

   if -2.80000000000000024e-82 < z < 5.2000000000000003e-50

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 78.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-82} \lor \neg \left(z \leq 5.2 \cdot 10^{-50}\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.2e-79)
   (* z (* (- y x) 6.0))
   (if (<= z 5.4e-53) x (* 6.0 (* z (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.2e-79) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 5.4e-53) {
		tmp = x;
	} else {
		tmp = 6.0 * (z * (y - 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 (z <= (-4.2d-79)) then
        tmp = z * ((y - x) * 6.0d0)
    else if (z <= 5.4d-53) then
        tmp = x
    else
        tmp = 6.0d0 * (z * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.2e-79) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 5.4e-53) {
		tmp = x;
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.2e-79:
		tmp = z * ((y - x) * 6.0)
	elif z <= 5.4e-53:
		tmp = x
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.2e-79)
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	elseif (z <= 5.4e-53)
		tmp = x;
	else
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.2e-79)
		tmp = z * ((y - x) * 6.0);
	elseif (z <= 5.4e-53)
		tmp = x;
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.2e-79], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-53], x, N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1999999999999999e-79

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 90.9%

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

   4. Taylor expanded in y around 0 89.7%

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

      1. +-commutative 89.7%

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

      2. *-commutative 89.7%

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

      3. metadata-eval 89.7%

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

      4. associate-*r* 89.7%

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

      5. associate-*r* 89.7%

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

      6. neg-mul-1 89.7%

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

      7. *-commutative 89.7%

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

      8. distribute-lft-in 89.7%

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

      9. distribute-lft-out 90.9%

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

      10. sub-neg 90.9%

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

      11. *-commutative 90.9%

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

      12. associate-*l* 91.0%

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

   6. Simplified 91.0%

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

   if -4.1999999999999999e-79 < z < 5.3999999999999998e-53

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 78.2%

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

   if 5.3999999999999998e-53 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 92.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 6: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-52}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e-82)
   (* z (* (- y x) 6.0))
   (if (<= z 9.6e-52) (+ x (* -6.0 (* x z))) (* 6.0 (* z (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e-82) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 9.6e-52) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = 6.0 * (z * (y - 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 (z <= (-1d-82)) then
        tmp = z * ((y - x) * 6.0d0)
    else if (z <= 9.6d-52) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = 6.0d0 * (z * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e-82) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 9.6e-52) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e-82:
		tmp = z * ((y - x) * 6.0)
	elif z <= 9.6e-52:
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e-82)
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	elseif (z <= 9.6e-52)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1e-82)
		tmp = z * ((y - x) * 6.0);
	elseif (z <= 9.6e-52)
		tmp = x + (-6.0 * (x * z));
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e-82], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-52], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e-82

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 90.9%

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

   4. Taylor expanded in y around 0 89.7%

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

      1. +-commutative 89.7%

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

      2. *-commutative 89.7%

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

      3. metadata-eval 89.7%

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

      4. associate-*r* 89.7%

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

      5. associate-*r* 89.7%

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

      6. neg-mul-1 89.7%

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

      7. *-commutative 89.7%

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

      8. distribute-lft-in 89.7%

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

      9. distribute-lft-out 90.9%

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

      10. sub-neg 90.9%

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

      11. *-commutative 90.9%

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

      12. associate-*l* 91.0%

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

   6. Simplified 91.0%

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

   if -1e-82 < z < 9.6000000000000007e-52

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 78.2%

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

   if 9.6000000000000007e-52 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 92.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-52}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 7: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.00024:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17)
   (* z (* (- y x) 6.0))
   (if (<= z 0.00024) (+ x (* 6.0 (* z y))) (* 6.0 (* z (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 0.00024) {
		tmp = x + (6.0 * (z * y));
	} else {
		tmp = 6.0 * (z * (y - 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 (z <= (-0.17d0)) then
        tmp = z * ((y - x) * 6.0d0)
    else if (z <= 0.00024d0) then
        tmp = x + (6.0d0 * (z * y))
    else
        tmp = 6.0d0 * (z * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 0.00024) {
		tmp = x + (6.0 * (z * y));
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = z * ((y - x) * 6.0)
	elif z <= 0.00024:
		tmp = x + (6.0 * (z * y))
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	elseif (z <= 0.00024)
		tmp = Float64(x + Float64(6.0 * Float64(z * y)));
	else
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.17)
		tmp = z * ((y - x) * 6.0);
	elseif (z <= 0.00024)
		tmp = x + (6.0 * (z * y));
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00024], N[(x + N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 97.0%

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

   4. Taylor expanded in y around 0 95.4%

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

      1. +-commutative 95.4%

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

      2. *-commutative 95.4%

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

      3. metadata-eval 95.4%

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

      4. associate-*r* 95.4%

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

      5. associate-*r* 95.4%

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

      6. neg-mul-1 95.4%

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

      7. *-commutative 95.4%

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

      8. distribute-lft-in 95.4%

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

      9. distribute-lft-out 97.0%

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

      10. sub-neg 97.0%

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

      11. *-commutative 97.0%

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

      12. associate-*l* 97.0%

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

   6. Simplified 97.0%

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

   if -0.170000000000000012 < z < 2.40000000000000006e-4

   1. Initial program 99.3%

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

   2. Taylor expanded in y around inf 98.1%

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

      1. *-commutative 98.1%

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

   4. Simplified 98.1%

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

   if 2.40000000000000006e-4 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 98.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.00024:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 8: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.16)
   (* z (* (- y x) 6.0))
   (if (<= z 7.5) (+ x (* z (* y 6.0))) (* 6.0 (* z (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.16) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 7.5) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = 6.0 * (z * (y - 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 (z <= (-0.16d0)) then
        tmp = z * ((y - x) * 6.0d0)
    else if (z <= 7.5d0) then
        tmp = x + (z * (y * 6.0d0))
    else
        tmp = 6.0d0 * (z * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.16) {
		tmp = z * ((y - x) * 6.0);
	} else if (z <= 7.5) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.16:
		tmp = z * ((y - x) * 6.0)
	elif z <= 7.5:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.16)
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	elseif (z <= 7.5)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	else
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.16)
		tmp = z * ((y - x) * 6.0);
	elseif (z <= 7.5)
		tmp = x + (z * (y * 6.0));
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.16], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.160000000000000003

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 97.0%

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

   4. Taylor expanded in y around 0 95.4%

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

      1. +-commutative 95.4%

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

      2. *-commutative 95.4%

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

      3. metadata-eval 95.4%

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

      4. associate-*r* 95.4%

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

      5. associate-*r* 95.4%

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

      6. neg-mul-1 95.4%

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

      7. *-commutative 95.4%

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

      8. distribute-lft-in 95.4%

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

      9. distribute-lft-out 97.0%

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

      10. sub-neg 97.0%

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

      11. *-commutative 97.0%

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

      12. associate-*l* 97.0%

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

   6. Simplified 97.0%

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

   if -0.160000000000000003 < z < 7.5

   1. Initial program 99.3%

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

   2. Taylor expanded in y around inf 98.2%

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

   if 7.5 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 98.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 9: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.165))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.165)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = 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 ((z <= (-0.165d0)) .or. (.not. (z <= 0.165d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.165)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 0.165):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.165))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 0.165)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 0.165]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 0.165000000000000008 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 97.8%

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

   4. Taylor expanded in y around 0 55.9%

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

   if -0.165000000000000008 < z < 0.165000000000000008

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 66.9%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around 0 99.7%

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

3. Final simplification 99.7%

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

Alternative 11: 36.0% 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 99.5%

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

2. Taylor expanded in z around 0 35.7%

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

3. Final simplification 35.7%

   \[\leadsto x \]

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 2023275 
(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)))