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

Percentage Accurate: 99.5% → 99.7%

Time: 10.4s

Alternatives: 12

Speedup: 1.2×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.9× 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. Add Preprocessing

5. Taylor expanded in z around 0 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-288}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -6.2e-12)
     t_0
     (if (<= z -6.4e-260)
       (* x -3.0)
       (if (<= z -2.5e-288) (* 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 <= -6.2e-12) {
		tmp = t_0;
	} else if (z <= -6.4e-260) {
		tmp = x * -3.0;
	} else if (z <= -2.5e-288) {
		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 <= (-6.2d-12)) then
        tmp = t_0
    else if (z <= (-6.4d-260)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.5d-288)) 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 <= -6.2e-12) {
		tmp = t_0;
	} else if (z <= -6.4e-260) {
		tmp = x * -3.0;
	} else if (z <= -2.5e-288) {
		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 <= -6.2e-12:
		tmp = t_0
	elif z <= -6.4e-260:
		tmp = x * -3.0
	elif z <= -2.5e-288:
		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 <= -6.2e-12)
		tmp = t_0;
	elseif (z <= -6.4e-260)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.5e-288)
		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 <= -6.2e-12)
		tmp = t_0;
	elseif (z <= -6.4e-260)
		tmp = x * -3.0;
	elseif (z <= -2.5e-288)
		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, -6.2e-12], t$95$0, If[LessEqual[z, -6.4e-260], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.5e-288], 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 < -6.2000000000000002e-12 or 0.5 < z

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 95.6%

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

   if -6.2000000000000002e-12 < z < -6.3999999999999999e-260 or -2.50000000000000005e-288 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in x around inf 58.1%

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

      1. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   if -6.3999999999999999e-260 < z < -2.50000000000000005e-288

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 79.2%

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

      1. *-commutative 79.2%

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

   8. Simplified 79.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-288}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6 - 3\right)\\ t_1 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -440000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-259}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-290}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 136000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -440000.0)
     t_1
     (if (<= z -1.04e-259)
       t_0
       (if (<= z -4.5e-290) (* y 4.0) (if (<= z 136000.0) 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 <= -440000.0) {
		tmp = t_1;
	} else if (z <= -1.04e-259) {
		tmp = t_0;
	} else if (z <= -4.5e-290) {
		tmp = y * 4.0;
	} else if (z <= 136000.0) {
		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 <= (-440000.0d0)) then
        tmp = t_1
    else if (z <= (-1.04d-259)) then
        tmp = t_0
    else if (z <= (-4.5d-290)) then
        tmp = y * 4.0d0
    else if (z <= 136000.0d0) 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 <= -440000.0) {
		tmp = t_1;
	} else if (z <= -1.04e-259) {
		tmp = t_0;
	} else if (z <= -4.5e-290) {
		tmp = y * 4.0;
	} else if (z <= 136000.0) {
		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 <= -440000.0:
		tmp = t_1
	elif z <= -1.04e-259:
		tmp = t_0
	elif z <= -4.5e-290:
		tmp = y * 4.0
	elif z <= 136000.0:
		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 <= -440000.0)
		tmp = t_1;
	elseif (z <= -1.04e-259)
		tmp = t_0;
	elseif (z <= -4.5e-290)
		tmp = Float64(y * 4.0);
	elseif (z <= 136000.0)
		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 <= -440000.0)
		tmp = t_1;
	elseif (z <= -1.04e-259)
		tmp = t_0;
	elseif (z <= -4.5e-290)
		tmp = y * 4.0;
	elseif (z <= 136000.0)
		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, -440000.0], t$95$1, If[LessEqual[z, -1.04e-259], t$95$0, If[LessEqual[z, -4.5e-290], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 136000.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4e5 or 136000 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 99.1%

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

   if -4.4e5 < z < -1.03999999999999997e-259 or -4.5e-290 < z < 136000

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in x around inf 59.4%

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

   if -1.03999999999999997e-259 < z < -4.5e-290

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 79.2%

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

      1. *-commutative 79.2%

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

   8. Simplified 79.2%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -440000:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-290}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 136000:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+156}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+73}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -42000 \lor \neg \left(z \leq 0.58\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))))
   (if (<= z -1.7e+156)
     t_0
     (if (<= z -4.6e+73)
       (* 6.0 (* x z))
       (if (or (<= z -42000.0) (not (<= z 0.58))) t_0 (* x -3.0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double tmp;
	if (z <= -1.7e+156) {
		tmp = t_0;
	} else if (z <= -4.6e+73) {
		tmp = 6.0 * (x * z);
	} else if ((z <= -42000.0) || !(z <= 0.58)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * y)
    if (z <= (-1.7d+156)) then
        tmp = t_0
    else if (z <= (-4.6d+73)) then
        tmp = 6.0d0 * (x * z)
    else if ((z <= (-42000.0d0)) .or. (.not. (z <= 0.58d0))) then
        tmp = t_0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double tmp;
	if (z <= -1.7e+156) {
		tmp = t_0;
	} else if (z <= -4.6e+73) {
		tmp = 6.0 * (x * z);
	} else if ((z <= -42000.0) || !(z <= 0.58)) {
		tmp = t_0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	tmp = 0
	if z <= -1.7e+156:
		tmp = t_0
	elif z <= -4.6e+73:
		tmp = 6.0 * (x * z)
	elif (z <= -42000.0) or not (z <= 0.58):
		tmp = t_0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -1.7e+156)
		tmp = t_0;
	elseif (z <= -4.6e+73)
		tmp = Float64(6.0 * Float64(x * z));
	elseif ((z <= -42000.0) || !(z <= 0.58))
		tmp = t_0;
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	tmp = 0.0;
	if (z <= -1.7e+156)
		tmp = t_0;
	elseif (z <= -4.6e+73)
		tmp = 6.0 * (x * z);
	elseif ((z <= -42000.0) || ~((z <= 0.58)))
		tmp = t_0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+156], t$95$0, If[LessEqual[z, -4.6e+73], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -42000.0], N[Not[LessEqual[z, 0.58]], $MachinePrecision]], t$95$0, N[(x * -3.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e156 or -4.6e73 < z < -42000 or 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in y around inf 61.3%

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

   7. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

   9. Simplified 60.7%

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

   if -1.7e156 < z < -4.6e73

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in x around inf 79.5%

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

   7. Taylor expanded in z around inf 79.5%

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

   if -42000 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 97.1%

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

   6. Taylor expanded in x around inf 53.6%

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

      1. *-commutative 53.6%

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

   8. Simplified 53.6%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+156}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+73}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -42000 \lor \neg \left(z \leq 0.58\right):\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -42000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-288}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))))
   (if (<= z -42000.0)
     t_0
     (if (<= z -3e-260)
       (* x -3.0)
       (if (<= z -3.3e-288) (* y 4.0) (if (<= z 0.55) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double tmp;
	if (z <= -42000.0) {
		tmp = t_0;
	} else if (z <= -3e-260) {
		tmp = x * -3.0;
	} else if (z <= -3.3e-288) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		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)
    if (z <= (-42000.0d0)) then
        tmp = t_0
    else if (z <= (-3d-260)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.3d-288)) then
        tmp = y * 4.0d0
    else if (z <= 0.55d0) 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);
	double tmp;
	if (z <= -42000.0) {
		tmp = t_0;
	} else if (z <= -3e-260) {
		tmp = x * -3.0;
	} else if (z <= -3.3e-288) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	tmp = 0
	if z <= -42000.0:
		tmp = t_0
	elif z <= -3e-260:
		tmp = x * -3.0
	elif z <= -3.3e-288:
		tmp = y * 4.0
	elif z <= 0.55:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -42000.0)
		tmp = t_0;
	elseif (z <= -3e-260)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.3e-288)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.55)
		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);
	tmp = 0.0;
	if (z <= -42000.0)
		tmp = t_0;
	elseif (z <= -3e-260)
		tmp = x * -3.0;
	elseif (z <= -3.3e-288)
		tmp = y * 4.0;
	elseif (z <= 0.55)
		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 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -42000.0], t$95$0, If[LessEqual[z, -3e-260], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.3e-288], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -42000 or 0.55000000000000004 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in y around inf 57.6%

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

   7. Taylor expanded in z around inf 57.1%

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

      1. *-commutative 57.1%

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

   9. Simplified 57.1%

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

   if -42000 < z < -3.0000000000000001e-260 or -3.29999999999999988e-288 < z < 0.55000000000000004

   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. Add Preprocessing

   5. Taylor expanded in z around 0 96.9%

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

   6. Taylor expanded in x around inf 56.4%

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

      1. *-commutative 56.4%

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

   8. Simplified 56.4%

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

   if -3.0000000000000001e-260 < z < -3.29999999999999988e-288

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 79.2%

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

      1. *-commutative 79.2%

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

   8. Simplified 79.2%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -42000:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-288}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-69} \lor \neg \left(y \leq 3 \cdot 10^{-27}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.3e-69) (not (<= y 3e-27)))
   (* y (+ 4.0 (* -6.0 z)))
   (* x (- (* z 6.0) 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.3e-69) || !(y <= 3e-27)) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x * ((z * 6.0) - 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 ((y <= (-1.3d-69)) .or. (.not. (y <= 3d-27))) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = x * ((z * 6.0d0) - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.3e-69) || !(y <= 3e-27)) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x * ((z * 6.0) - 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.3e-69) or not (y <= 3e-27):
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = x * ((z * 6.0) - 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.3e-69) || !(y <= 3e-27))
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = Float64(x * Float64(Float64(z * 6.0) - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.3e-69) || ~((y <= 3e-27)))
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = x * ((z * 6.0) - 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.3e-69], N[Not[LessEqual[y, 3e-27]], $MachinePrecision]], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3000000000000001e-69 or 3.0000000000000001e-27 < y

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in y around inf 81.4%

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

   if -1.3000000000000001e-69 < y < 3.0000000000000001e-27

   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. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in x around inf 81.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-69} \lor \neg \left(y \leq 3 \cdot 10^{-27}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.54\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.54)))
   (* -6.0 (* z (- y x)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.54)) {
		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 <= (-0.6d0)) .or. (.not. (z <= 0.54d0))) 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 <= -0.6) || !(z <= 0.54)) {
		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 <= -0.6) or not (z <= 0.54):
		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 <= -0.6) || !(z <= 0.54))
		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 <= -0.6) || ~((z <= 0.54)))
		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, -0.6], N[Not[LessEqual[z, 0.54]], $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 < -0.599999999999999978 or 0.54000000000000004 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 96.9%

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

   if -0.599999999999999978 < z < 0.54000000000000004

   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. Add Preprocessing

   5. Taylor expanded in z around 0 98.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.54\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.54 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.54) (not (<= z 0.65)))
   (* -6.0 (* z (- y x)))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.54) || !(z <= 0.65)) {
		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 <= (-0.54d0)) .or. (.not. (z <= 0.65d0))) 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 <= -0.54) || !(z <= 0.65)) {
		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 <= -0.54) or not (z <= 0.65):
		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 <= -0.54) || !(z <= 0.65))
		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 <= -0.54) || ~((z <= 0.65)))
		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, -0.54], N[Not[LessEqual[z, 0.65]], $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 < -0.54000000000000004 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. 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 96.9%

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

   if -0.54000000000000004 < z < 0.650000000000000022

   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. Add Preprocessing

   5. Taylor expanded in z around 0 98.9%

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

   6. Taylor expanded in x around 0 99.0%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.54 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-76} \lor \neg \left(y \leq 2.7 \cdot 10^{-38}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.95e-76) (not (<= y 2.7e-38))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.95e-76) || !(y <= 2.7e-38)) {
		tmp = y * 4.0;
	} 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 ((y <= (-1.95d-76)) .or. (.not. (y <= 2.7d-38))) then
        tmp = y * 4.0d0
    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 ((y <= -1.95e-76) || !(y <= 2.7e-38)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.95e-76) or not (y <= 2.7e-38):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.95e-76) || !(y <= 2.7e-38))
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.95e-76) || ~((y <= 2.7e-38)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.95e-76], N[Not[LessEqual[y, 2.7e-38]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95000000000000013e-76 or 2.70000000000000005e-38 < y

   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. Add Preprocessing

   5. Taylor expanded in z around 0 49.9%

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

   6. Taylor expanded in x around 0 39.8%

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

      1. *-commutative 39.8%

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

   8. Simplified 39.8%

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

   if -1.95000000000000013e-76 < y < 2.70000000000000005e-38

   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. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 60.0%

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

   6. Taylor expanded in x around inf 51.0%

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

      1. *-commutative 51.0%

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

   8. Simplified 51.0%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-76} \lor \neg \left(y \leq 2.7 \cdot 10^{-38}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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. Add Preprocessing

5. Final simplification 99.6%

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

Alternative 11: 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 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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* 99.7%

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

   3. fma-define 99.7%

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

   4. metadata-eval 99.7%

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

3. Simplified 99.7%

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

   1. fma-undefine 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

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

Alternative 12: 26.1% 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. Add Preprocessing

5. Taylor expanded in z around 0 54.6%

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

6. Taylor expanded in x around inf 30.6%

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

   1. *-commutative 30.6%

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

8. Simplified 30.6%

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

9. Final simplification 30.6%

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

Reproduce

herbie shell --seed 2024066 
(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))))