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

Percentage Accurate: 99.5% → 99.8%

Time: 7.8s

Alternatives: 12

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (4.0 * (y - x)) + (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 = (4.0d0 * (y - x)) + (x + ((-6.0d0) * ((y - x) * z)))
end function

Java

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

Python

def code(x, y, z):
	return (4.0 * (y - x)) + (x + (-6.0 * ((y - x) * z)))

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * (y - x)) + (x + (-6.0 * ((y - x) * z)));
end

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around 0 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2650:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-237}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+147}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -2650.0)
     t_0
     (if (<= z -6.5e-237)
       (* 4.0 y)
       (if (<= z 0.5) (* x -3.0) (if (<= z 7.5e+147) (* -6.0 (* y z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -2650.0) {
		tmp = t_0;
	} else if (z <= -6.5e-237) {
		tmp = 4.0 * y;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 7.5e+147) {
		tmp = -6.0 * (y * z);
	} 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) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-2650.0d0)) then
        tmp = t_0
    else if (z <= (-6.5d-237)) then
        tmp = 4.0d0 * y
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 7.5d+147) then
        tmp = (-6.0d0) * (y * z)
    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 tmp;
	if (z <= -2650.0) {
		tmp = t_0;
	} else if (z <= -6.5e-237) {
		tmp = 4.0 * y;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 7.5e+147) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -2650.0:
		tmp = t_0
	elif z <= -6.5e-237:
		tmp = 4.0 * y
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 7.5e+147:
		tmp = -6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2650.0)
		tmp = t_0;
	elseif (z <= -6.5e-237)
		tmp = Float64(4.0 * y);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.5e+147)
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2650.0)
		tmp = t_0;
	elseif (z <= -6.5e-237)
		tmp = 4.0 * y;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 7.5e+147)
		tmp = -6.0 * (y * z);
	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]}, If[LessEqual[z, -2650.0], t$95$0, If[LessEqual[z, -6.5e-237], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.5e+147], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2650 or 7.50000000000000037e147 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 61.8%

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

   4. Taylor expanded in z around inf 61.7%

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

   if -2650 < z < -6.5000000000000001e-237

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 96.4%

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

   3. Taylor expanded in y around inf 57.4%

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

      1. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   if -6.5000000000000001e-237 < z < 0.5

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 98.4%

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

   3. Taylor expanded in y around 0 63.8%

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

      1. distribute-lft1-in 63.8%

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

      2. metadata-eval 63.8%

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

      3. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if 0.5 < z < 7.50000000000000037e147

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in y around inf 72.2%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. *-commutative 70.3%

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

   6. Simplified 70.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2650:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-237}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+147}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2800:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-234}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+150}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2800.0)
   (* x (* z 6.0))
   (if (<= z -7.4e-234)
     (* 4.0 y)
     (if (<= z 0.65)
       (* x -3.0)
       (if (<= z 2.2e+150) (* -6.0 (* y z)) (* 6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2800.0) {
		tmp = x * (z * 6.0);
	} else if (z <= -7.4e-234) {
		tmp = 4.0 * y;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else if (z <= 2.2e+150) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = 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 (z <= (-2800.0d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-7.4d-234)) then
        tmp = 4.0d0 * y
    else if (z <= 0.65d0) then
        tmp = x * (-3.0d0)
    else if (z <= 2.2d+150) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2800.0) {
		tmp = x * (z * 6.0);
	} else if (z <= -7.4e-234) {
		tmp = 4.0 * y;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else if (z <= 2.2e+150) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2800.0:
		tmp = x * (z * 6.0)
	elif z <= -7.4e-234:
		tmp = 4.0 * y
	elif z <= 0.65:
		tmp = x * -3.0
	elif z <= 2.2e+150:
		tmp = -6.0 * (y * z)
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2800.0)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -7.4e-234)
		tmp = Float64(4.0 * y);
	elseif (z <= 0.65)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.2e+150)
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2800.0)
		tmp = x * (z * 6.0);
	elseif (z <= -7.4e-234)
		tmp = 4.0 * y;
	elseif (z <= 0.65)
		tmp = x * -3.0;
	elseif (z <= 2.2e+150)
		tmp = -6.0 * (y * z);
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2800.0], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.4e-234], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 0.65], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.2e+150], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2800

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 57.7%

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

   4. Taylor expanded in z around inf 57.7%

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

      1. *-commutative 57.7%

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

   6. Simplified 57.7%

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

   if -2800 < z < -7.40000000000000025e-234

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 96.4%

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

   3. Taylor expanded in y around inf 57.4%

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

      1. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   if -7.40000000000000025e-234 < z < 0.650000000000000022

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 98.4%

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

   3. Taylor expanded in y around 0 63.8%

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

      1. distribute-lft1-in 63.8%

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

      2. metadata-eval 63.8%

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

      3. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if 0.650000000000000022 < z < 2.19999999999999999e150

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in y around inf 72.2%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. *-commutative 70.3%

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

   6. Simplified 70.3%

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

   if 2.19999999999999999e150 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in x around inf 70.9%

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

   4. Taylor expanded in z around inf 70.9%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-234}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+150}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.00038:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-237}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.00038)
     t_0
     (if (<= z -1e-237) (* 4.0 y) (if (<= z 0.5) (* x -3.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.00038) {
		tmp = t_0;
	} else if (z <= -1e-237) {
		tmp = 4.0 * y;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.00038d0)) then
        tmp = t_0
    else if (z <= (-1d-237)) then
        tmp = 4.0d0 * y
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    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 * ((y - x) * z);
	double tmp;
	if (z <= -0.00038) {
		tmp = t_0;
	} else if (z <= -1e-237) {
		tmp = 4.0 * y;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.00038:
		tmp = t_0
	elif z <= -1e-237:
		tmp = 4.0 * y
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.00038)
		tmp = t_0;
	elseif (z <= -1e-237)
		tmp = Float64(4.0 * y);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.00038)
		tmp = t_0;
	elseif (z <= -1e-237)
		tmp = 4.0 * y;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00038], t$95$0, If[LessEqual[z, -1e-237], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e-4 or 0.5 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 97.6%

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

   if -3.8000000000000002e-4 < z < -9.9999999999999999e-238

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 97.8%

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

   3. Taylor expanded in y around inf 58.1%

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

      1. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   if -9.9999999999999999e-238 < z < 0.5

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 98.4%

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

   3. Taylor expanded in y around 0 63.8%

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

      1. distribute-lft1-in 63.8%

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

      2. metadata-eval 63.8%

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

      3. *-commutative 63.8%

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

   5. Simplified 63.8%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00038:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-237}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 5: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -13.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -13.5)
     t_0
     (if (<= z -4.3e-237)
       (* y (+ 4.0 (* -6.0 z)))
       (if (<= z 0.5) (* x -3.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -13.5) {
		tmp = t_0;
	} else if (z <= -4.3e-237) {
		tmp = y * (4.0 + (-6.0 * z));
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-13.5d0)) then
        tmp = t_0
    else if (z <= (-4.3d-237)) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    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 * ((y - x) * z);
	double tmp;
	if (z <= -13.5) {
		tmp = t_0;
	} else if (z <= -4.3e-237) {
		tmp = y * (4.0 + (-6.0 * z));
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -13.5:
		tmp = t_0
	elif z <= -4.3e-237:
		tmp = y * (4.0 + (-6.0 * z))
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -13.5)
		tmp = t_0;
	elseif (z <= -4.3e-237)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -13.5)
		tmp = t_0;
	elseif (z <= -4.3e-237)
		tmp = y * (4.0 + (-6.0 * z));
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -13.5], t$95$0, If[LessEqual[z, -4.3e-237], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -13.5 or 0.5 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 97.6%

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

   if -13.5 < z < -4.29999999999999982e-237

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in y around inf 59.8%

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

   if -4.29999999999999982e-237 < z < 0.5

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 98.4%

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

   3. Taylor expanded in y around 0 63.8%

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

      1. distribute-lft1-in 63.8%

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

      2. metadata-eval 63.8%

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

      3. *-commutative 63.8%

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

   5. Simplified 63.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13.5:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 6: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -480:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{elif}\;z \leq 130000:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -480.0)
     t_0
     (if (<= z -4.7e-237)
       (* y (+ 4.0 (* -6.0 z)))
       (if (<= z 130000.0) (* x (- (* z 6.0) 3.0)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -480.0) {
		tmp = t_0;
	} else if (z <= -4.7e-237) {
		tmp = y * (4.0 + (-6.0 * z));
	} else if (z <= 130000.0) {
		tmp = x * ((z * 6.0) - 3.0);
	} 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) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-480.0d0)) then
        tmp = t_0
    else if (z <= (-4.7d-237)) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else if (z <= 130000.0d0) then
        tmp = x * ((z * 6.0d0) - 3.0d0)
    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 * ((y - x) * z);
	double tmp;
	if (z <= -480.0) {
		tmp = t_0;
	} else if (z <= -4.7e-237) {
		tmp = y * (4.0 + (-6.0 * z));
	} else if (z <= 130000.0) {
		tmp = x * ((z * 6.0) - 3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -480.0:
		tmp = t_0
	elif z <= -4.7e-237:
		tmp = y * (4.0 + (-6.0 * z))
	elif z <= 130000.0:
		tmp = x * ((z * 6.0) - 3.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -480.0)
		tmp = t_0;
	elseif (z <= -4.7e-237)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	elseif (z <= 130000.0)
		tmp = Float64(x * Float64(Float64(z * 6.0) - 3.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -480.0)
		tmp = t_0;
	elseif (z <= -4.7e-237)
		tmp = y * (4.0 + (-6.0 * z));
	elseif (z <= 130000.0)
		tmp = x * ((z * 6.0) - 3.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -480.0], t$95$0, If[LessEqual[z, -4.7e-237], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 130000.0], N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -480 or 1.3e5 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 98.2%

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

   if -480 < z < -4.6999999999999998e-237

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in y around inf 59.8%

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

   if -4.6999999999999998e-237 < z < 1.3e5

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 65.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{elif}\;z \leq 130000:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 50.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-236}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.68)
     t_0
     (if (<= z -1.05e-236) (* 4.0 y) (if (<= z 0.6) (* x -3.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.68) {
		tmp = t_0;
	} else if (z <= -1.05e-236) {
		tmp = 4.0 * y;
	} else if (z <= 0.6) {
		tmp = x * -3.0;
	} 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) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.68d0)) then
        tmp = t_0
    else if (z <= (-1.05d-236)) then
        tmp = 4.0d0 * y
    else if (z <= 0.6d0) then
        tmp = x * (-3.0d0)
    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 * (y * z);
	double tmp;
	if (z <= -0.68) {
		tmp = t_0;
	} else if (z <= -1.05e-236) {
		tmp = 4.0 * y;
	} else if (z <= 0.6) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.68:
		tmp = t_0
	elif z <= -1.05e-236:
		tmp = 4.0 * y
	elif z <= 0.6:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.68)
		tmp = t_0;
	elseif (z <= -1.05e-236)
		tmp = Float64(4.0 * y);
	elseif (z <= 0.6)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.68)
		tmp = t_0;
	elseif (z <= -1.05e-236)
		tmp = 4.0 * y;
	elseif (z <= 0.6)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.68], t$95$0, If[LessEqual[z, -1.05e-236], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 0.6], N[(x * -3.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.680000000000000049 or 0.599999999999999978 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in y around inf 53.4%

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

   4. Taylor expanded in z around inf 52.8%

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

      1. *-commutative 52.8%

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

   6. Simplified 52.8%

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

   if -0.680000000000000049 < z < -1.04999999999999989e-236

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 97.8%

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

   3. Taylor expanded in y around inf 58.1%

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

      1. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   if -1.04999999999999989e-236 < z < 0.599999999999999978

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 98.4%

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

   3. Taylor expanded in y around 0 63.8%

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

      1. distribute-lft1-in 63.8%

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

      2. metadata-eval 63.8%

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

      3. *-commutative 63.8%

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

   5. Simplified 63.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-236}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + 4 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.55) (not (<= z 0.65)))
   (* -6.0 (* (- y x) z))
   (+ (* x -3.0) (* 4.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.55) || !(z <= 0.65)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = (x * -3.0) + (4.0 * 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 ((z <= (-0.55d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    else
        tmp = (x * (-3.0d0)) + (4.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.55) || !(z <= 0.65)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = (x * -3.0) + (4.0 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.55) or not (z <= 0.65):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = (x * -3.0) + (4.0 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.55) || !(z <= 0.65))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(Float64(x * -3.0) + Float64(4.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.55) || ~((z <= 0.65)))
		tmp = -6.0 * ((y - x) * z);
	else
		tmp = (x * -3.0) + (4.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.55], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(4.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.55000000000000004 or 0.650000000000000022 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 97.6%

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

   if -0.55000000000000004 < z < 0.650000000000000022

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 98.1%

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

   3. Taylor expanded in x around 0 98.1%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + 4 \cdot y\\ \end{array} \]

Alternative 9: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around 0 99.5%

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

   1. neg-mul-1 99.5%

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

   2. +-commutative 99.5%

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

   3. sub-neg 99.5%

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

4. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 10: 99.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. associate-*l* 99.8%

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

   2. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 11: 38.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+58}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-82}:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.06e+58) (* x -3.0) (if (<= x 4.6e-82) (* 4.0 y) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.06e+58) {
		tmp = x * -3.0;
	} else if (x <= 4.6e-82) {
		tmp = 4.0 * y;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.06d+58)) then
        tmp = x * (-3.0d0)
    else if (x <= 4.6d-82) then
        tmp = 4.0d0 * y
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.06e+58) {
		tmp = x * -3.0;
	} else if (x <= 4.6e-82) {
		tmp = 4.0 * y;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.06e+58:
		tmp = x * -3.0
	elif x <= 4.6e-82:
		tmp = 4.0 * y
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.06e+58)
		tmp = Float64(x * -3.0);
	elseif (x <= 4.6e-82)
		tmp = Float64(4.0 * y);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.06e+58)
		tmp = x * -3.0;
	elseif (x <= 4.6e-82)
		tmp = 4.0 * y;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.06e+58], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 4.6e-82], N[(4.0 * y), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05999999999999997e58 or 4.59999999999999994e-82 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 54.2%

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

   3. Taylor expanded in y around 0 42.5%

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

      1. distribute-lft1-in 42.5%

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

      2. metadata-eval 42.5%

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

      3. *-commutative 42.5%

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

   5. Simplified 42.5%

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

   if -1.05999999999999997e58 < x < 4.59999999999999994e-82

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 56.9%

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

   3. Taylor expanded in y around inf 43.4%

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

      1. *-commutative 43.4%

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

   5. Simplified 43.4%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+58}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-82}:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 12: 26.0% 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 99.5%

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

2. Taylor expanded in z around 0 55.4%

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

3. Taylor expanded in y around 0 30.8%

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

   1. distribute-lft1-in 30.8%

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

   2. metadata-eval 30.8%

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

   3. *-commutative 30.8%

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

5. Simplified 30.8%

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

6. Final simplification 30.8%

   \[\leadsto x \cdot -3 \]

Reproduce

herbie shell --seed 2023240 
(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))))