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

Percentage Accurate: 99.5% → 99.8%

Time: 8.7s

Alternatives: 15

Speedup: 1.2×

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

Specification

Math

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

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

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

FPCore

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

C

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

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 + (((-6.0d0) * (z * (y - x))) + ((y - x) * 4.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in z around 0 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -1650:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-71}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -1650.0)
     t_0
     (if (<= z -1.2e-209)
       (* x (- (* z 6.0) 3.0))
       (if (<= z 1.8e-184)
         (* y 4.0)
         (if (<= z 7e-71)
           (* x -3.0)
           (if (<= z 5.6e+15) (* y (+ 4.0 (* -6.0 z))) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -1650.0) {
		tmp = t_0;
	} else if (z <= -1.2e-209) {
		tmp = x * ((z * 6.0) - 3.0);
	} else if (z <= 1.8e-184) {
		tmp = y * 4.0;
	} else if (z <= 7e-71) {
		tmp = x * -3.0;
	} else if (z <= 5.6e+15) {
		tmp = y * (4.0 + (-6.0 * 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) * (z * (y - x))
    if (z <= (-1650.0d0)) then
        tmp = t_0
    else if (z <= (-1.2d-209)) then
        tmp = x * ((z * 6.0d0) - 3.0d0)
    else if (z <= 1.8d-184) then
        tmp = y * 4.0d0
    else if (z <= 7d-71) then
        tmp = x * (-3.0d0)
    else if (z <= 5.6d+15) then
        tmp = y * (4.0d0 + ((-6.0d0) * 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 * (z * (y - x));
	double tmp;
	if (z <= -1650.0) {
		tmp = t_0;
	} else if (z <= -1.2e-209) {
		tmp = x * ((z * 6.0) - 3.0);
	} else if (z <= 1.8e-184) {
		tmp = y * 4.0;
	} else if (z <= 7e-71) {
		tmp = x * -3.0;
	} else if (z <= 5.6e+15) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -1650.0:
		tmp = t_0
	elif z <= -1.2e-209:
		tmp = x * ((z * 6.0) - 3.0)
	elif z <= 1.8e-184:
		tmp = y * 4.0
	elif z <= 7e-71:
		tmp = x * -3.0
	elif z <= 5.6e+15:
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -1650.0)
		tmp = t_0;
	elseif (z <= -1.2e-209)
		tmp = Float64(x * Float64(Float64(z * 6.0) - 3.0));
	elseif (z <= 1.8e-184)
		tmp = Float64(y * 4.0);
	elseif (z <= 7e-71)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.6e+15)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -1650.0)
		tmp = t_0;
	elseif (z <= -1.2e-209)
		tmp = x * ((z * 6.0) - 3.0);
	elseif (z <= 1.8e-184)
		tmp = y * 4.0;
	elseif (z <= 7e-71)
		tmp = x * -3.0;
	elseif (z <= 5.6e+15)
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1650.0], t$95$0, If[LessEqual[z, -1.2e-209], N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-184], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7e-71], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.6e+15], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1650 or 5.6e15 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.9%

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

   if -1650 < z < -1.2000000000000001e-209

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around inf 70.8%

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

   if -1.2000000000000001e-209 < z < 1.8000000000000001e-184

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if 1.8000000000000001e-184 < z < 6.9999999999999998e-71

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around inf 72.1%

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

      1. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   if 6.9999999999999998e-71 < z < 5.6e15

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in y around inf 73.1%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1650:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-71}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 3: 73.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.055:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-210}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.055)
     t_0
     (if (<= z -1.6e-210)
       (* x -3.0)
       (if (<= z 9.5e-182) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.055) {
		tmp = t_0;
	} else if (z <= -1.6e-210) {
		tmp = x * -3.0;
	} else if (z <= 9.5e-182) {
		tmp = y * 4.0;
	} 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) * (z * (y - x))
    if (z <= (-0.055d0)) then
        tmp = t_0
    else if (z <= (-1.6d-210)) then
        tmp = x * (-3.0d0)
    else if (z <= 9.5d-182) then
        tmp = y * 4.0d0
    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 * (z * (y - x));
	double tmp;
	if (z <= -0.055) {
		tmp = t_0;
	} else if (z <= -1.6e-210) {
		tmp = x * -3.0;
	} else if (z <= 9.5e-182) {
		tmp = y * 4.0;
	} 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 * (z * (y - x))
	tmp = 0
	if z <= -0.055:
		tmp = t_0
	elif z <= -1.6e-210:
		tmp = x * -3.0
	elif z <= 9.5e-182:
		tmp = y * 4.0
	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(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.055)
		tmp = t_0;
	elseif (z <= -1.6e-210)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.5e-182)
		tmp = Float64(y * 4.0);
	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 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.055)
		tmp = t_0;
	elseif (z <= -1.6e-210)
		tmp = x * -3.0;
	elseif (z <= 9.5e-182)
		tmp = y * 4.0;
	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[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.055], t$95$0, If[LessEqual[z, -1.6e-210], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.5e-182], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0550000000000000003 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. Step-by-step derivation

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.9%

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

   if -0.0550000000000000003 < z < -1.60000000000000014e-210 or 9.4999999999999994e-182 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 98.0%

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

   5. Taylor expanded in x around inf 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   if -1.60000000000000014e-210 < z < 9.4999999999999994e-182

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.055:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-210}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 4: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6 - 3\right)\\ t_1 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -670:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-206}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6200:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- (* z 6.0) 3.0))) (t_1 (* -6.0 (* z (- y x)))))
   (if (<= z -670.0)
     t_1
     (if (<= z -2.6e-206)
       t_0
       (if (<= z 1.25e-182) (* y 4.0) (if (<= z 6200.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((z * 6.0) - 3.0);
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -670.0) {
		tmp = t_1;
	} else if (z <= -2.6e-206) {
		tmp = t_0;
	} else if (z <= 1.25e-182) {
		tmp = y * 4.0;
	} else if (z <= 6200.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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 = x * ((z * 6.0d0) - 3.0d0)
    t_1 = (-6.0d0) * (z * (y - x))
    if (z <= (-670.0d0)) then
        tmp = t_1
    else if (z <= (-2.6d-206)) then
        tmp = t_0
    else if (z <= 1.25d-182) then
        tmp = y * 4.0d0
    else if (z <= 6200.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * ((z * 6.0) - 3.0);
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -670.0) {
		tmp = t_1;
	} else if (z <= -2.6e-206) {
		tmp = t_0;
	} else if (z <= 1.25e-182) {
		tmp = y * 4.0;
	} else if (z <= 6200.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((z * 6.0) - 3.0)
	t_1 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -670.0:
		tmp = t_1
	elif z <= -2.6e-206:
		tmp = t_0
	elif z <= 1.25e-182:
		tmp = y * 4.0
	elif z <= 6200.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(z * 6.0) - 3.0))
	t_1 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -670.0)
		tmp = t_1;
	elseif (z <= -2.6e-206)
		tmp = t_0;
	elseif (z <= 1.25e-182)
		tmp = Float64(y * 4.0);
	elseif (z <= 6200.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((z * 6.0) - 3.0);
	t_1 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -670.0)
		tmp = t_1;
	elseif (z <= -2.6e-206)
		tmp = t_0;
	elseif (z <= 1.25e-182)
		tmp = y * 4.0;
	elseif (z <= 6200.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -670.0], t$95$1, If[LessEqual[z, -2.6e-206], t$95$0, If[LessEqual[z, 1.25e-182], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6200.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -670 or 6200 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.9%

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

   if -670 < z < -2.6e-206 or 1.25000000000000006e-182 < z < 6200

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around inf 65.6%

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

   if -2.6e-206 < z < 1.25000000000000006e-182

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -670:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6200:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 5: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1850:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-207}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -1850.0)
     t_0
     (if (<= z -3.5e-207)
       (* x -3.0)
       (if (<= z 3.8e-184) (* y 4.0) (if (<= z 6.2e-33) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -1850.0) {
		tmp = t_0;
	} else if (z <= -3.5e-207) {
		tmp = x * -3.0;
	} else if (z <= 3.8e-184) {
		tmp = y * 4.0;
	} else if (z <= 6.2e-33) {
		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 * (x * z)
    if (z <= (-1850.0d0)) then
        tmp = t_0
    else if (z <= (-3.5d-207)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.8d-184) then
        tmp = y * 4.0d0
    else if (z <= 6.2d-33) 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 * (x * z);
	double tmp;
	if (z <= -1850.0) {
		tmp = t_0;
	} else if (z <= -3.5e-207) {
		tmp = x * -3.0;
	} else if (z <= 3.8e-184) {
		tmp = y * 4.0;
	} else if (z <= 6.2e-33) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -1850.0:
		tmp = t_0
	elif z <= -3.5e-207:
		tmp = x * -3.0
	elif z <= 3.8e-184:
		tmp = y * 4.0
	elif z <= 6.2e-33:
		tmp = x * -3.0
	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 <= -1850.0)
		tmp = t_0;
	elseif (z <= -3.5e-207)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.8e-184)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.2e-33)
		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 * (x * z);
	tmp = 0.0;
	if (z <= -1850.0)
		tmp = t_0;
	elseif (z <= -3.5e-207)
		tmp = x * -3.0;
	elseif (z <= 3.8e-184)
		tmp = y * 4.0;
	elseif (z <= 6.2e-33)
		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[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1850.0], t$95$0, If[LessEqual[z, -3.5e-207], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.8e-184], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.2e-33], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1850 or 6.19999999999999994e-33 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around inf 51.6%

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

   6. Taylor expanded in z around inf 51.8%

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

   if -1850 < z < -3.5000000000000002e-207 or 3.80000000000000017e-184 < z < 6.19999999999999994e-33

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 97.9%

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

   5. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

   7. Simplified 68.3%

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

   if -3.5000000000000002e-207 < z < 3.80000000000000017e-184

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-207}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-208}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-185}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1850.0)
   (* x (* z 6.0))
   (if (<= z -1.6e-208)
     (* x -3.0)
     (if (<= z 2.6e-185)
       (* y 4.0)
       (if (<= z 6.2e-33) (* x -3.0) (* 6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1850.0) {
		tmp = x * (z * 6.0);
	} else if (z <= -1.6e-208) {
		tmp = x * -3.0;
	} else if (z <= 2.6e-185) {
		tmp = y * 4.0;
	} else if (z <= 6.2e-33) {
		tmp = x * -3.0;
	} 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 <= (-1850.0d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-1.6d-208)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.6d-185) then
        tmp = y * 4.0d0
    else if (z <= 6.2d-33) then
        tmp = x * (-3.0d0)
    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 <= -1850.0) {
		tmp = x * (z * 6.0);
	} else if (z <= -1.6e-208) {
		tmp = x * -3.0;
	} else if (z <= 2.6e-185) {
		tmp = y * 4.0;
	} else if (z <= 6.2e-33) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1850.0:
		tmp = x * (z * 6.0)
	elif z <= -1.6e-208:
		tmp = x * -3.0
	elif z <= 2.6e-185:
		tmp = y * 4.0
	elif z <= 6.2e-33:
		tmp = x * -3.0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1850.0)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -1.6e-208)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.6e-185)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.2e-33)
		tmp = Float64(x * -3.0);
	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 <= -1850.0)
		tmp = x * (z * 6.0);
	elseif (z <= -1.6e-208)
		tmp = x * -3.0;
	elseif (z <= 2.6e-185)
		tmp = y * 4.0;
	elseif (z <= 6.2e-33)
		tmp = x * -3.0;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1850.0], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-208], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.6e-185], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.2e-33], N[(x * -3.0), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1850

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around inf 57.6%

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

   6. Taylor expanded in z around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-*r* 57.6%

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

   8. Simplified 57.6%

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

   if -1850 < z < -1.6000000000000001e-208 or 2.59999999999999985e-185 < z < 6.19999999999999994e-33

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 97.9%

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

   5. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

   7. Simplified 68.3%

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

   if -1.6000000000000001e-208 < z < 2.59999999999999985e-185

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if 6.19999999999999994e-33 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around inf 44.6%

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

   6. Taylor expanded in z around inf 44.9%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-208}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-185}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 7: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -1850:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))))
   (if (<= z -1850.0)
     t_0
     (if (<= z -2.2e-209)
       (* x -3.0)
       (if (<= z 9.2e-181) (* y 4.0) (if (<= z 6.2e-33) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (z <= -1850.0) {
		tmp = t_0;
	} else if (z <= -2.2e-209) {
		tmp = x * -3.0;
	} else if (z <= 9.2e-181) {
		tmp = y * 4.0;
	} else if (z <= 6.2e-33) {
		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 = z * (x * 6.0d0)
    if (z <= (-1850.0d0)) then
        tmp = t_0
    else if (z <= (-2.2d-209)) then
        tmp = x * (-3.0d0)
    else if (z <= 9.2d-181) then
        tmp = y * 4.0d0
    else if (z <= 6.2d-33) 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 = z * (x * 6.0);
	double tmp;
	if (z <= -1850.0) {
		tmp = t_0;
	} else if (z <= -2.2e-209) {
		tmp = x * -3.0;
	} else if (z <= 9.2e-181) {
		tmp = y * 4.0;
	} else if (z <= 6.2e-33) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	tmp = 0
	if z <= -1850.0:
		tmp = t_0
	elif z <= -2.2e-209:
		tmp = x * -3.0
	elif z <= 9.2e-181:
		tmp = y * 4.0
	elif z <= 6.2e-33:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -1850.0)
		tmp = t_0;
	elseif (z <= -2.2e-209)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.2e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.2e-33)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -1850.0)
		tmp = t_0;
	elseif (z <= -2.2e-209)
		tmp = x * -3.0;
	elseif (z <= 9.2e-181)
		tmp = y * 4.0;
	elseif (z <= 6.2e-33)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1850.0], t$95$0, If[LessEqual[z, -2.2e-209], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.2e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.2e-33], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1850 or 6.19999999999999994e-33 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around inf 51.6%

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

   6. Taylor expanded in z around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 51.9%

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

   8. Simplified 51.9%

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

   if -1850 < z < -2.2000000000000001e-209 or 9.19999999999999963e-181 < z < 6.19999999999999994e-33

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 97.9%

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

   5. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

   7. Simplified 68.3%

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

   if -2.2000000000000001e-209 < z < 9.19999999999999963e-181

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 8: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* -6.0 (* z (- y x)))
   (if (<= z 0.58) (+ (* y 4.0) (* x -3.0)) (+ x (* z (* -6.0 (- y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.58) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = x + (z * (-6.0 * (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 <= (-0.58d0)) then
        tmp = (-6.0d0) * (z * (y - x))
    else if (z <= 0.58d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = x + (z * ((-6.0d0) * (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.58) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = x + (z * (-6.0 * (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = -6.0 * (z * (y - x))
	elif z <= 0.58:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = x + (z * (-6.0 * (y - x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.58)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(x + Float64(z * Float64(-6.0 * Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = -6.0 * (z * (y - x));
	elseif (z <= 0.58)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = x + (z * (-6.0 * (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.58], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.3%

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

   if -0.57999999999999996 < z < 0.57999999999999996

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 98.8%

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

   5. Taylor expanded in x around 0 98.8%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 0.57999999999999996 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 9: 38.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+107} \lor \neg \left(x \leq -1.6 \cdot 10^{+71} \lor \neg \left(x \leq -2.2 \cdot 10^{+17}\right) \land x \leq 5.8 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.4e+107)
         (not (or (<= x -1.6e+71) (and (not (<= x -2.2e+17)) (<= x 5.8e-56)))))
   (* x -3.0)
   (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e+107) || !((x <= -1.6e+71) || (!(x <= -2.2e+17) && (x <= 5.8e-56)))) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	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 <= (-2.4d+107)) .or. (.not. (x <= (-1.6d+71)) .or. (.not. (x <= (-2.2d+17))) .and. (x <= 5.8d-56))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e+107) || !((x <= -1.6e+71) || (!(x <= -2.2e+17) && (x <= 5.8e-56)))) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.4e+107) or not ((x <= -1.6e+71) or (not (x <= -2.2e+17) and (x <= 5.8e-56))):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.4e+107) || !((x <= -1.6e+71) || (!(x <= -2.2e+17) && (x <= 5.8e-56))))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.4e+107) || ~(((x <= -1.6e+71) || (~((x <= -2.2e+17)) && (x <= 5.8e-56)))))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.4e+107], N[Not[Or[LessEqual[x, -1.6e+71], And[N[Not[LessEqual[x, -2.2e+17]], $MachinePrecision], LessEqual[x, 5.8e-56]]]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4000000000000001e107 or -1.60000000000000012e71 < x < -2.2e17 or 5.79999999999999982e-56 < x

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 53.6%

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

   5. Taylor expanded in x around inf 44.4%

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

      1. *-commutative 44.4%

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

   7. Simplified 44.4%

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

   if -2.4000000000000001e107 < x < -1.60000000000000012e71 or -2.2e17 < x < 5.79999999999999982e-56

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 55.0%

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

   5. Taylor expanded in x around 0 44.5%

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

      1. *-commutative 44.5%

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

   7. Simplified 44.5%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+107} \lor \neg \left(x \leq -1.6 \cdot 10^{+71} \lor \neg \left(x \leq -2.2 \cdot 10^{+17}\right) \land x \leq 5.8 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]

Alternative 10: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.52)))
   (* -6.0 (* z (- y x)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.52)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	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 ((z <= (-0.58d0)) .or. (.not. (z <= 0.52d0))) then
        tmp = (-6.0d0) * (z * (y - x))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.52)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.52):
		tmp = -6.0 * (z * (y - x))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.52))
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.52)))
		tmp = -6.0 * (z * (y - x));
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.52]], $MachinePrecision]], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.52000000000000002 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.9%

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

   if -0.57999999999999996 < z < 0.52000000000000002

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 98.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]

Alternative 11: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.62\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.62)))
   (* -6.0 (* z (- y x)))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.62)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = (y * 4.0) + (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 ((z <= (-0.6d0)) .or. (.not. (z <= 0.62d0))) then
        tmp = (-6.0d0) * (z * (y - x))
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.62)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.62):
		tmp = -6.0 * (z * (y - x))
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.62))
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.62)))
		tmp = -6.0 * (z * (y - x));
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.62]], $MachinePrecision]], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.619999999999999996 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.9%

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

   if -0.599999999999999978 < z < 0.619999999999999996

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 98.8%

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

   5. Taylor expanded in x around 0 98.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.62\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]

Alternative 12: 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 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 13: 99.7% 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 99.6%

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

   1. +-commutative 99.6%

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

   2. *-commutative 99.6%

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

   3. associate-*l* 99.5%

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

   4. fma-def 99.5%

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

   5. metadata-eval 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(6, \left(y - x\right) \cdot \left(0.6666666666666666 - z\right), x\right)} \]
4. Step-by-step derivation

   1. fma-udef 99.5%

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

   2. associate-*r* 99.6%

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

   3. *-commutative 99.6%

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

   4. associate-*l* 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 14: 26.3% 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 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in z around 0 54.3%

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

5. Taylor expanded in x around inf 28.9%

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

   1. *-commutative 28.9%

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

7. Simplified 28.9%

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

8. Final simplification 28.9%

   \[\leadsto x \cdot -3 \]

Alternative 15: 2.6% accurate, 13.0× 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 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
4. Step-by-step derivation

   1. add-cube-cbrt 98.3%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\sqrt[3]{6 \cdot \left(0.6666666666666666 - z\right)} \cdot \sqrt[3]{6 \cdot \left(0.6666666666666666 - z\right)}\right) \cdot \sqrt[3]{6 \cdot \left(0.6666666666666666 - z\right)}}, x\right) \]

   2. pow3 98.3%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\sqrt[3]{6 \cdot \left(0.6666666666666666 - z\right)}\right)}^{3}}, x\right) \]

5. Applied egg-rr 98.3%

   \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\sqrt[3]{6 \cdot \left(0.6666666666666666 - z\right)}\right)}^{3}}, x\right) \]

6. Taylor expanded in z around inf 2.5%

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

7. Final simplification 2.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023318 
(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))))