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

Percentage Accurate: 99.7% → 99.8%

Time: 9.9s

Alternatives: 11

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot z\right)}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot z\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot z\right)}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot z\right)\right)\right) \]

   5. *-lowering-*.f64 99.8%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{*.f64}\left(6, \color{blue}{z}\right)\right)\right) \]

3. Simplified 99.8%

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

Alternative 2: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.4e+16)
   (* z (* x -6.0))
   (if (<= z -3.4e-54)
     (* y (* 6.0 z))
     (if (<= z 1.35e-27) x (* z (* y 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.4e+16) {
		tmp = z * (x * -6.0);
	} else if (z <= -3.4e-54) {
		tmp = y * (6.0 * z);
	} else if (z <= 1.35e-27) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	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 <= (-6.4d+16)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-3.4d-54)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 1.35d-27) then
        tmp = x
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.4e+16) {
		tmp = z * (x * -6.0);
	} else if (z <= -3.4e-54) {
		tmp = y * (6.0 * z);
	} else if (z <= 1.35e-27) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.4e+16:
		tmp = z * (x * -6.0)
	elif z <= -3.4e-54:
		tmp = y * (6.0 * z)
	elif z <= 1.35e-27:
		tmp = x
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.4e+16)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -3.4e-54)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 1.35e-27)
		tmp = x;
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.4e+16)
		tmp = z * (x * -6.0);
	elseif (z <= -3.4e-54)
		tmp = y * (6.0 * z);
	elseif (z <= 1.35e-27)
		tmp = x;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.4e+16], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e-54], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-27], x, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.4e16

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 99.7%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-6 \cdot x\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{-6}\right)\right) \]

      5. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{-6}\right)\right) \]

   8. Simplified 56.2%

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

   if -6.4e16 < z < -3.39999999999999987e-54

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 68.8%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 68.8%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 59.8%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. metadata-eval N/A

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

      5. div-inv N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{\frac{1}{6}}\right), \color{blue}{y}\right) \]

      8. /-lowering-/.f64 59.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \frac{1}{6}\right), y\right) \]

   10. Applied egg-rr 59.6%

       \[\leadsto \color{blue}{\frac{z}{0.16666666666666666} \cdot y} \]
   11. Step-by-step derivation

       1. div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot \frac{1}{\frac{1}{6}}\right), y\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot 6\right), y\right) \]

       3. *-lowering-*.f64 60.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 6\right), y\right) \]

   12. Applied egg-rr 60.1%

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

   if -3.39999999999999987e-54 < z < 1.34999999999999994e-27

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 71.4%

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

   if 1.34999999999999994e-27 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot y\right)}\right) \]

      4. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(6, \color{blue}{y}\right)\right) \]

   5. Simplified 57.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot 6\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y 6.0))))
   (if (<= z -6.8e+17)
     (* z (* x -6.0))
     (if (<= z -2.3e-54) t_0 (if (<= z 2.2e-27) x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * 6.0);
	double tmp;
	if (z <= -6.8e+17) {
		tmp = z * (x * -6.0);
	} else if (z <= -2.3e-54) {
		tmp = t_0;
	} else if (z <= 2.2e-27) {
		tmp = x;
	} 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 * (y * 6.0d0)
    if (z <= (-6.8d+17)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-2.3d-54)) then
        tmp = t_0
    else if (z <= 2.2d-27) then
        tmp = x
    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 * (y * 6.0);
	double tmp;
	if (z <= -6.8e+17) {
		tmp = z * (x * -6.0);
	} else if (z <= -2.3e-54) {
		tmp = t_0;
	} else if (z <= 2.2e-27) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * 6.0)
	tmp = 0
	if z <= -6.8e+17:
		tmp = z * (x * -6.0)
	elif z <= -2.3e-54:
		tmp = t_0
	elif z <= 2.2e-27:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * 6.0))
	tmp = 0.0
	if (z <= -6.8e+17)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -2.3e-54)
		tmp = t_0;
	elseif (z <= 2.2e-27)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * 6.0);
	tmp = 0.0;
	if (z <= -6.8e+17)
		tmp = z * (x * -6.0);
	elseif (z <= -2.3e-54)
		tmp = t_0;
	elseif (z <= 2.2e-27)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+17], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-54], t$95$0, If[LessEqual[z, 2.2e-27], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e17

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 99.7%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-6 \cdot x\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{-6}\right)\right) \]

      5. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{-6}\right)\right) \]

   8. Simplified 56.2%

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

   if -6.8e17 < z < -2.2999999999999999e-54 or 2.19999999999999987e-27 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot y\right)}\right) \]

      4. *-lowering-*.f64 57.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(6, \color{blue}{y}\right)\right) \]

   5. Simplified 57.8%

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

   if -2.2999999999999999e-54 < z < 2.19999999999999987e-27

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 71.4%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -310000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.8:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -310000.0) t_0 (if (<= z 6.8) (+ x (* y (* 6.0 z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -310000.0) {
		tmp = t_0;
	} else if (z <= 6.8) {
		tmp = x + (y * (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 * ((y - x) * z)
    if (z <= (-310000.0d0)) then
        tmp = t_0
    else if (z <= 6.8d0) then
        tmp = x + (y * (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 * ((y - x) * z);
	double tmp;
	if (z <= -310000.0) {
		tmp = t_0;
	} else if (z <= 6.8) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * ((y - x) * z)
	tmp = 0
	if z <= -310000.0:
		tmp = t_0
	elif z <= 6.8:
		tmp = x + (y * (6.0 * z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -310000.0)
		tmp = t_0;
	elseif (z <= 6.8)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -310000.0)
		tmp = t_0;
	elseif (z <= 6.8)
		tmp = x + (y * (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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -310000.0], t$95$0, If[LessEqual[z, 6.8], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e5 or 6.79999999999999982 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 98.8%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 98.8%

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

   if -3.1e5 < z < 6.79999999999999982

   1. Initial program 98.6%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot z\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot z\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot z\right)\right)\right) \]

      5. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{*.f64}\left(6, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(6, z\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 98.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -310000:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 6.8:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.00056:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{0.16666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.2e-54)
   (* 6.0 (* (- y x) z))
   (if (<= z 0.00056)
     (* x (+ 1.0 (* z -6.0)))
     (* (- y x) (/ z 0.16666666666666666)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e-54) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 0.00056) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = (y - x) * (z / 0.16666666666666666);
	}
	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 <= (-3.2d-54)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 0.00056d0) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else
        tmp = (y - x) * (z / 0.16666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e-54) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 0.00056) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = (y - x) * (z / 0.16666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.2e-54:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 0.00056:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = (y - x) * (z / 0.16666666666666666)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.2e-54)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.00056)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = Float64(Float64(y - x) * Float64(z / 0.16666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.2e-54)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 0.00056)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = (y - x) * (z / 0.16666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.2e-54], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00056], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / 0.16666666666666666), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999998e-54

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 92.3%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 92.3%

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

   if -3.19999999999999998e-54 < z < 5.5999999999999995e-4

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot z\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(z \cdot \color{blue}{-6}\right)\right)\right) \]

      4. *-lowering-*.f64 70.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right) \]

   5. Simplified 70.8%

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

   if 5.5999999999999995e-4 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 98.9%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 98.9%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. associate-/r/ N/A

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

      5. clear-num N/A

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

      6. associate-*l/ N/A

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

      7. div-inv N/A

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

      8. times-frac N/A

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

      9. remove-double-div N/A

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

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{z}{\frac{1}{6}}\right)}\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{z}}{\frac{1}{6}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{1}{6}\right)}\right)\right) \]

      13. metadata-eval 98.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(z, \frac{1}{6}\right)\right) \]

   7. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z}{0.16666666666666666}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.00056:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{0.16666666666666666}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.00056:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -3e-54) t_0 (if (<= z 0.00056) (* x (+ 1.0 (* z -6.0))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -3e-54) {
		tmp = t_0;
	} else if (z <= 0.00056) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * ((y - x) * z)
    if (z <= (-3d-54)) then
        tmp = t_0
    else if (z <= 0.00056d0) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -3e-54) {
		tmp = t_0;
	} else if (z <= 0.00056) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * ((y - x) * z)
	tmp = 0
	if z <= -3e-54:
		tmp = t_0
	elif z <= 0.00056:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -3e-54)
		tmp = t_0;
	elseif (z <= 0.00056)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -3e-54)
		tmp = t_0;
	elseif (z <= 0.00056)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e-54], t$95$0, If[LessEqual[z, 0.00056], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000009e-54 or 5.5999999999999995e-4 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 94.9%

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

   if -3.00000000000000009e-54 < z < 5.5999999999999995e-4

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot z\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(z \cdot \color{blue}{-6}\right)\right)\right) \]

      4. *-lowering-*.f64 70.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right) \]

   5. Simplified 70.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + z \cdot -6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.00056:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -2.8e-54) t_0 (if (<= z 8.5e-28) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2.8e-54) {
		tmp = t_0;
	} else if (z <= 8.5e-28) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * ((y - x) * z)
    if (z <= (-2.8d-54)) then
        tmp = t_0
    else if (z <= 8.5d-28) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2.8e-54) {
		tmp = t_0;
	} else if (z <= 8.5e-28) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * ((y - x) * z)
	tmp = 0
	if z <= -2.8e-54:
		tmp = t_0
	elif z <= 8.5e-28:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -2.8e-54)
		tmp = t_0;
	elseif (z <= 8.5e-28)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -2.8e-54)
		tmp = t_0;
	elseif (z <= 8.5e-28)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-54], t$95$0, If[LessEqual[z, 8.5e-28], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000002e-54 or 8.49999999999999925e-28 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 93.6%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 93.6%

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

   if -2.8000000000000002e-54 < z < 8.49999999999999925e-28

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 71.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.4e-54) (* 6.0 (* y z)) (if (<= z 2.9e-28) x (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.4e-54) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.9e-28) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	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 <= (-3.4d-54)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 2.9d-28) then
        tmp = x
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.4e-54) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.9e-28) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.4e-54:
		tmp = 6.0 * (y * z)
	elif z <= 2.9e-28:
		tmp = x
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.4e-54)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 2.9e-28)
		tmp = x;
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.4e-54)
		tmp = 6.0 * (y * z);
	elseif (z <= 2.9e-28)
		tmp = x;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.4e-54], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-28], x, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.39999999999999987e-54

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 92.3%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 92.3%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 51.1%

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

   if -3.39999999999999987e-54 < z < 2.90000000000000013e-28

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 71.4%

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

   if 2.90000000000000013e-28 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot y\right)}\right) \]

      4. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(6, \color{blue}{y}\right)\right) \]

   5. Simplified 57.2%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z)))) (if (<= z -3e-54) t_0 (if (<= z 3e-28) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -3e-54) {
		tmp = t_0;
	} else if (z <= 3e-28) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    if (z <= (-3d-54)) then
        tmp = t_0
    else if (z <= 3d-28) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -3e-54) {
		tmp = t_0;
	} else if (z <= 3e-28) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -3e-54:
		tmp = t_0
	elif z <= 3e-28:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3e-54)
		tmp = t_0;
	elseif (z <= 3e-28)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3e-54)
		tmp = t_0;
	elseif (z <= 3e-28)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e-54], t$95$0, If[LessEqual[z, 3e-28], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000009e-54 or 3.00000000000000003e-28 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 93.6%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 93.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 53.6%

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

   if -3.00000000000000009e-54 < z < 3.00000000000000003e-28

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 71.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-54}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

3. Final simplification 99.1%

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

Alternative 11: 36.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in z around 0

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

5. Simplified 38.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (* 6 z) (- x y))))

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