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

Percentage Accurate: 99.7% → 99.7%

Time: 9.1s

Alternatives: 10

Speedup: 1.0×

• 20.7% 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: 99.7% 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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3700000000:\\ \;\;\;\;x \cdot \frac{z}{-0.16666666666666666}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3700000000.0)
   (* x (/ z -0.16666666666666666))
   (if (<= z -1.7e-34)
     (* 6.0 (* y z))
     (if (<= z 1.55e-67) x (* z (* y 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3700000000.0) {
		tmp = x * (z / -0.16666666666666666);
	} else if (z <= -1.7e-34) {
		tmp = 6.0 * (y * z);
	} else if (z <= 1.55e-67) {
		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 <= (-3700000000.0d0)) then
        tmp = x * (z / (-0.16666666666666666d0))
    else if (z <= (-1.7d-34)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 1.55d-67) 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 <= -3700000000.0) {
		tmp = x * (z / -0.16666666666666666);
	} else if (z <= -1.7e-34) {
		tmp = 6.0 * (y * z);
	} else if (z <= 1.55e-67) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3700000000.0:
		tmp = x * (z / -0.16666666666666666)
	elif z <= -1.7e-34:
		tmp = 6.0 * (y * z)
	elif z <= 1.55e-67:
		tmp = x
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3700000000.0)
		tmp = Float64(x * Float64(z / -0.16666666666666666));
	elseif (z <= -1.7e-34)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 1.55e-67)
		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 <= -3700000000.0)
		tmp = x * (z / -0.16666666666666666);
	elseif (z <= -1.7e-34)
		tmp = 6.0 * (y * z);
	elseif (z <= 1.55e-67)
		tmp = x;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3700000000.0], N[(x * N[(z / -0.16666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-34], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-67], x, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7e9

   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 99.4%

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

   5. Simplified 99.4%

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

   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 58.6%

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

   8. Simplified 58.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 58.5%

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

   10. Applied egg-rr 58.5%

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

       1. metadata-eval N/A

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

       2. metadata-eval N/A

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

       3. div-inv N/A

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

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

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

       5. metadata-eval 58.6%

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

   12. Applied egg-rr 58.6%

       \[\leadsto \color{blue}{\frac{z}{-0.16666666666666666}} \cdot x \]

   if -3.7e9 < z < -1.7e-34

   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 71.9%

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

   5. Simplified 71.9%

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

   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 63.9%

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

   if -1.7e-34 < z < 1.5500000000000001e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 79.0%

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

   if 1.5500000000000001e-67 < 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 53.1%

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

   5. Simplified 53.1%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3700000000:\\ \;\;\;\;x \cdot \frac{z}{-0.16666666666666666}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -29000000000:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-35}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -29000000000.0)
   (* z (* x -6.0))
   (if (<= z -8.6e-35) (* 6.0 (* y z)) (if (<= z 1.9e-67) x (* z (* y 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -29000000000.0) {
		tmp = z * (x * -6.0);
	} else if (z <= -8.6e-35) {
		tmp = 6.0 * (y * z);
	} else if (z <= 1.9e-67) {
		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 <= (-29000000000.0d0)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-8.6d-35)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 1.9d-67) 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 <= -29000000000.0) {
		tmp = z * (x * -6.0);
	} else if (z <= -8.6e-35) {
		tmp = 6.0 * (y * z);
	} else if (z <= 1.9e-67) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -29000000000.0:
		tmp = z * (x * -6.0)
	elif z <= -8.6e-35:
		tmp = 6.0 * (y * z)
	elif z <= 1.9e-67:
		tmp = x
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -29000000000.0)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -8.6e-35)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 1.9e-67)
		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 <= -29000000000.0)
		tmp = z * (x * -6.0);
	elseif (z <= -8.6e-35)
		tmp = 6.0 * (y * z);
	elseif (z <= 1.9e-67)
		tmp = x;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -29000000000.0], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e-35], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-67], x, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9e10

   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 99.4%

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

   5. Simplified 99.4%

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

   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 58.6%

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

   8. Simplified 58.6%

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

   if -2.9e10 < z < -8.6000000000000004e-35

   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 71.9%

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

   5. Simplified 71.9%

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

   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 63.9%

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

   if -8.6000000000000004e-35 < z < 1.89999999999999994e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 79.0%

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

   if 1.89999999999999994e-67 < 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 53.1%

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

   5. Simplified 53.1%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -29000000000:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-35}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot \frac{z}{0.16666666666666666}\\ \mathbf{if}\;z \leq -0.195:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) (/ z 0.16666666666666666))))
   (if (<= z -0.195) t_0 (if (<= z 0.165) (+ x (* y (* 6.0 z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * (z / 0.16666666666666666);
	double tmp;
	if (z <= -0.195) {
		tmp = t_0;
	} else if (z <= 0.165) {
		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 = (y - x) * (z / 0.16666666666666666d0)
    if (z <= (-0.195d0)) then
        tmp = t_0
    else if (z <= 0.165d0) 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 = (y - x) * (z / 0.16666666666666666);
	double tmp;
	if (z <= -0.195) {
		tmp = t_0;
	} else if (z <= 0.165) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * (z / 0.16666666666666666)
	tmp = 0
	if z <= -0.195:
		tmp = t_0
	elif z <= 0.165:
		tmp = x + (y * (6.0 * z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * Float64(z / 0.16666666666666666))
	tmp = 0.0
	if (z <= -0.195)
		tmp = t_0;
	elseif (z <= 0.165)
		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 = (y - x) * (z / 0.16666666666666666);
	tmp = 0.0;
	if (z <= -0.195)
		tmp = t_0;
	elseif (z <= 0.165)
		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[(N[(y - x), $MachinePrecision] * N[(z / 0.16666666666666666), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.195], t$95$0, If[LessEqual[z, 0.165], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.19500000000000001 or 0.165000000000000008 < 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 99.4%

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

   5. Simplified 99.4%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   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 99.5%

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

   7. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z}{0.16666666666666666}} \]

   if -0.19500000000000001 < z < 0.165000000000000008

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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 98.0%

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

Alternative 5: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot \frac{z}{0.16666666666666666}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) (/ z 0.16666666666666666))))
   (if (<= z -5.2e-35) t_0 (if (<= z 1.9e-67) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * (z / 0.16666666666666666);
	double tmp;
	if (z <= -5.2e-35) {
		tmp = t_0;
	} else if (z <= 1.9e-67) {
		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 = (y - x) * (z / 0.16666666666666666d0)
    if (z <= (-5.2d-35)) then
        tmp = t_0
    else if (z <= 1.9d-67) 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 = (y - x) * (z / 0.16666666666666666);
	double tmp;
	if (z <= -5.2e-35) {
		tmp = t_0;
	} else if (z <= 1.9e-67) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * (z / 0.16666666666666666)
	tmp = 0
	if z <= -5.2e-35:
		tmp = t_0
	elif z <= 1.9e-67:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * Float64(z / 0.16666666666666666))
	tmp = 0.0
	if (z <= -5.2e-35)
		tmp = t_0;
	elseif (z <= 1.9e-67)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * (z / 0.16666666666666666);
	tmp = 0.0;
	if (z <= -5.2e-35)
		tmp = t_0;
	elseif (z <= 1.9e-67)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * N[(z / 0.16666666666666666), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-35], t$95$0, If[LessEqual[z, 1.9e-67], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000009e-35 or 1.89999999999999994e-67 < 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 94.0%

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

   5. Simplified 94.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   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 94.1%

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

   7. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z}{0.16666666666666666}} \]

   if -5.20000000000000009e-35 < z < 1.89999999999999994e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 79.0%

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

Alternative 6: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -4.4e-35) t_0 (if (<= z 1.9e-67) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -4.4e-35) {
		tmp = t_0;
	} else if (z <= 1.9e-67) {
		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 <= (-4.4d-35)) then
        tmp = t_0
    else if (z <= 1.9d-67) 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 <= -4.4e-35) {
		tmp = t_0;
	} else if (z <= 1.9e-67) {
		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 <= -4.4e-35:
		tmp = t_0
	elif z <= 1.9e-67:
		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 <= -4.4e-35)
		tmp = t_0;
	elseif (z <= 1.9e-67)
		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 <= -4.4e-35)
		tmp = t_0;
	elseif (z <= 1.9e-67)
		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, -4.4e-35], t$95$0, If[LessEqual[z, 1.9e-67], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999987e-35 or 1.89999999999999994e-67 < 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 94.0%

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

   5. Simplified 94.0%

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

   if -4.39999999999999987e-35 < z < 1.89999999999999994e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 79.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot 6\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-34}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y 6.0))))
   (if (<= z -1.75e-34) t_0 (if (<= z 1.9e-67) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * 6.0);
	double tmp;
	if (z <= -1.75e-34) {
		tmp = t_0;
	} else if (z <= 1.9e-67) {
		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 <= (-1.75d-34)) then
        tmp = t_0
    else if (z <= 1.9d-67) 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 <= -1.75e-34) {
		tmp = t_0;
	} else if (z <= 1.9e-67) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * 6.0)
	tmp = 0
	if z <= -1.75e-34:
		tmp = t_0
	elif z <= 1.9e-67:
		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 <= -1.75e-34)
		tmp = t_0;
	elseif (z <= 1.9e-67)
		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 <= -1.75e-34)
		tmp = t_0;
	elseif (z <= 1.9e-67)
		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, -1.75e-34], t$95$0, If[LessEqual[z, 1.9e-67], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e-34 or 1.89999999999999994e-67 < 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 51.4%

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

   5. Simplified 51.4%

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

   if -1.75e-34 < z < 1.89999999999999994e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 79.0%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{0.16666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.4e-35)
   (* 6.0 (* y z))
   (if (<= z 1.35e-67) x (* y (/ z 0.16666666666666666)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.4e-35) {
		tmp = 6.0 * (y * z);
	} else if (z <= 1.35e-67) {
		tmp = x;
	} else {
		tmp = y * (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 <= (-3.4d-35)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 1.35d-67) then
        tmp = x
    else
        tmp = y * (z / 0.16666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.4e-35) {
		tmp = 6.0 * (y * z);
	} else if (z <= 1.35e-67) {
		tmp = x;
	} else {
		tmp = y * (z / 0.16666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.4e-35:
		tmp = 6.0 * (y * z)
	elif z <= 1.35e-67:
		tmp = x
	else:
		tmp = y * (z / 0.16666666666666666)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.4e-35)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 1.35e-67)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / 0.16666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.4e-35)
		tmp = 6.0 * (y * z);
	elseif (z <= 1.35e-67)
		tmp = x;
	else
		tmp = y * (z / 0.16666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.4e-35], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-67], x, N[(y * N[(z / 0.16666666666666666), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000003e-35

   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 96.0%

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

   5. Simplified 96.0%

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

   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 50.2%

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

   if -3.4000000000000003e-35 < z < 1.35000000000000008e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 79.0%

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

   if 1.35000000000000008e-67 < 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 91.2%

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

   5. Simplified 91.2%

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

   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 53.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

      4. associate-/r/ N/A

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

      5. clear-num N/A

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

      6. associate-*l/ N/A

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

      7. div-inv N/A

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

      8. times-frac N/A

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

      9. remove-double-div N/A

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

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

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

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

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

      12. metadata-eval 53.1%

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

   10. Applied egg-rr 53.1%

       \[\leadsto \color{blue}{y \cdot \frac{z}{0.16666666666666666}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{0.16666666666666666}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-34}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -1.75e-34) t_0 (if (<= z 1.9e-67) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.75e-34) {
		tmp = t_0;
	} else if (z <= 1.9e-67) {
		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 <= (-1.75d-34)) then
        tmp = t_0
    else if (z <= 1.9d-67) 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 <= -1.75e-34) {
		tmp = t_0;
	} else if (z <= 1.9e-67) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -1.75e-34:
		tmp = t_0
	elif z <= 1.9e-67:
		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 <= -1.75e-34)
		tmp = t_0;
	elseif (z <= 1.9e-67)
		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 <= -1.75e-34)
		tmp = t_0;
	elseif (z <= 1.9e-67)
		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, -1.75e-34], t$95$0, If[LessEqual[z, 1.9e-67], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e-34 or 1.89999999999999994e-67 < 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 94.0%

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

   5. Simplified 94.0%

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

   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 51.4%

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

   if -1.75e-34 < z < 1.89999999999999994e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 79.0%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-34}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.9% 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 99.9%

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

3. Taylor expanded in z around 0

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

5. Simplified 40.1%

   \[\leadsto \color{blue}{x} \]
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 2024140 
(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)))