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

Percentage Accurate: 99.6% → 99.6%

Time: 10.9s

Alternatives: 10

Speedup: 1.0×

• 21.0% 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: 99.6% 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: 99.6% 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 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-74} \lor \neg \left(y \leq 2150000000000\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e-74) (not (<= y 2150000000000.0)))
   (+ x (* 6.0 (* y z)))
   (* x (+ 1.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-74) || !(y <= 2150000000000.0)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x * (1.0 + (z * -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 ((y <= (-6.5d-74)) .or. (.not. (y <= 2150000000000.0d0))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-74) || !(y <= 2150000000000.0)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x * (1.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e-74) or not (y <= 2150000000000.0):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x * (1.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e-74) || !(y <= 2150000000000.0))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e-74) || ~((y <= 2150000000000.0)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x * (1.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e-74], N[Not[LessEqual[y, 2150000000000.0]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000002e-74 or 2.15e12 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 91.1%

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

   if -6.5000000000000002e-74 < y < 2.15e12

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 90.7%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-74} \lor \neg \left(y \leq 2150000000000\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]

Alternative 3: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-73} \lor \neg \left(y \leq 2200000000000\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{x}{-0.16666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.8e-73) (not (<= y 2200000000000.0)))
   (+ x (* 6.0 (* y z)))
   (+ x (* z (/ x -0.16666666666666666)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e-73) || !(y <= 2200000000000.0)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (z * (x / -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 ((y <= (-2.8d-73)) .or. (.not. (y <= 2200000000000.0d0))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + (z * (x / (-0.16666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e-73) || !(y <= 2200000000000.0)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (z * (x / -0.16666666666666666));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.8e-73) or not (y <= 2200000000000.0):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (z * (x / -0.16666666666666666))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.8e-73) || !(y <= 2200000000000.0))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(x / -0.16666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.8e-73) || ~((y <= 2200000000000.0)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (z * (x / -0.16666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.8e-73], N[Not[LessEqual[y, 2200000000000.0]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x / -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.80000000000000012e-73 or 2.2e12 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 91.1%

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

   if -2.80000000000000012e-73 < y < 2.2e12

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. flip-- 71.4%

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

      3. clear-num 71.3%

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

      4. un-div-inv 71.3%

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

      5. clear-num 71.3%

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

      6. flip-- 99.7%

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

   3. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{6}{\frac{1}{y - x}}} \cdot z \]
   4. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.7%

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

      4. associate-/l/ 99.8%

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

      5. associate-/r* 99.8%

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

      6. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\frac{z}{\frac{0.16666666666666666}{y - x}}} \]
   6. Step-by-step derivation

      1. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around 0 90.7%

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

      1. associate-*r* 90.8%

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

      2. *-commutative 90.8%

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

      3. *-commutative 90.8%

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

      4. /-rgt-identity 90.8%

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

      5. associate-*r* 90.7%

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

      6. associate-/l* 90.7%

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

      7. *-commutative 90.7%

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

      8. metadata-eval 90.7%

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

      9. associate-*l/ 90.8%

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

      10. *-commutative 90.8%

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

   10. Simplified 90.8%

       \[\leadsto x + \color{blue}{z \cdot \frac{x}{-0.16666666666666666}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-73} \lor \neg \left(y \leq 2200000000000\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{x}{-0.16666666666666666}\\ \end{array} \]

Alternative 4: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-73}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 2150000000000:\\ \;\;\;\;x + z \cdot \frac{x}{-0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e-73)
   (+ x (* z (* y 6.0)))
   (if (<= y 2150000000000.0)
     (+ x (* z (/ x -0.16666666666666666)))
     (+ x (* 6.0 (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e-73) {
		tmp = x + (z * (y * 6.0));
	} else if (y <= 2150000000000.0) {
		tmp = x + (z * (x / -0.16666666666666666));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.8d-73)) then
        tmp = x + (z * (y * 6.0d0))
    else if (y <= 2150000000000.0d0) then
        tmp = x + (z * (x / (-0.16666666666666666d0)))
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e-73) {
		tmp = x + (z * (y * 6.0));
	} else if (y <= 2150000000000.0) {
		tmp = x + (z * (x / -0.16666666666666666));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e-73:
		tmp = x + (z * (y * 6.0))
	elif y <= 2150000000000.0:
		tmp = x + (z * (x / -0.16666666666666666))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e-73)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	elseif (y <= 2150000000000.0)
		tmp = Float64(x + Float64(z * Float64(x / -0.16666666666666666)));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e-73)
		tmp = x + (z * (y * 6.0));
	elseif (y <= 2150000000000.0)
		tmp = x + (z * (x / -0.16666666666666666));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e-73], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2150000000000.0], N[(x + N[(z * N[(x / -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.80000000000000012e-73

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 86.4%

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

   if -2.80000000000000012e-73 < y < 2.15e12

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. flip-- 71.4%

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

      3. clear-num 71.3%

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

      4. un-div-inv 71.3%

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

      5. clear-num 71.3%

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

      6. flip-- 99.7%

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

   3. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{6}{\frac{1}{y - x}}} \cdot z \]
   4. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.7%

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

      4. associate-/l/ 99.8%

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

      5. associate-/r* 99.8%

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

      6. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\frac{z}{\frac{0.16666666666666666}{y - x}}} \]
   6. Step-by-step derivation

      1. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around 0 90.7%

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

      1. associate-*r* 90.8%

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

      2. *-commutative 90.8%

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

      3. *-commutative 90.8%

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

      4. /-rgt-identity 90.8%

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

      5. associate-*r* 90.7%

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

      6. associate-/l* 90.7%

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

      7. *-commutative 90.7%

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

      8. metadata-eval 90.7%

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

      9. associate-*l/ 90.8%

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

      10. *-commutative 90.8%

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

   10. Simplified 90.8%

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

   if 2.15e12 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 97.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-73}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 2150000000000:\\ \;\;\;\;x + z \cdot \frac{x}{-0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -96000000000 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -96000000000.0) (not (<= z 0.165))) (* x (* z -6.0)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -96000000000.0) || !(z <= 0.165)) {
		tmp = x * (z * -6.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-96000000000.0d0)) .or. (.not. (z <= 0.165d0))) then
        tmp = x * (z * (-6.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -96000000000.0) || !(z <= 0.165)) {
		tmp = x * (z * -6.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -96000000000.0) or not (z <= 0.165):
		tmp = x * (z * -6.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -96000000000.0) || !(z <= 0.165))
		tmp = Float64(x * Float64(z * -6.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -96000000000.0) || ~((z <= 0.165)))
		tmp = x * (z * -6.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -96000000000.0], N[Not[LessEqual[z, 0.165]], $MachinePrecision]], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.6e10 or 0.165000000000000008 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 58.3%

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

   3. Taylor expanded in z around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   if -9.6e10 < z < 0.165000000000000008

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.1%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -96000000000 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -96000000000:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{-0.16666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -96000000000.0)
   (* x (* z -6.0))
   (if (<= z 0.165) x (* z (/ x -0.16666666666666666)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -96000000000.0) {
		tmp = x * (z * -6.0);
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = z * (x / -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 <= (-96000000000.0d0)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 0.165d0) then
        tmp = x
    else
        tmp = z * (x / (-0.16666666666666666d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -96000000000.0) {
		tmp = x * (z * -6.0);
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = z * (x / -0.16666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -96000000000.0:
		tmp = x * (z * -6.0)
	elif z <= 0.165:
		tmp = x
	else:
		tmp = z * (x / -0.16666666666666666)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -96000000000.0)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= 0.165)
		tmp = x;
	else
		tmp = Float64(z * Float64(x / -0.16666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -96000000000.0)
		tmp = x * (z * -6.0);
	elseif (z <= 0.165)
		tmp = x;
	else
		tmp = z * (x / -0.16666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -96000000000.0], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.165], x, N[(z * N[(x / -0.16666666666666666), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.6e10

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 50.3%

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

   3. Taylor expanded in z around inf 50.3%

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

      1. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   if -9.6e10 < z < 0.165000000000000008

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.1%

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

   if 0.165000000000000008 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 66.1%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. *-commutative 66.1%

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

   5. Simplified 66.1%

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

      1. *-commutative 66.1%

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

      2. associate-*r* 66.3%

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

      3. metadata-eval 66.3%

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

      4. associate-/r/ 66.2%

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

      5. associate-*r/ 66.1%

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

      6. metadata-eval 66.1%

         \[\leadsto \frac{z \cdot \color{blue}{\frac{1}{0.16666666666666666}}}{\frac{-1}{x}} \]

      7. div-inv 66.2%

         \[\leadsto \frac{\color{blue}{\frac{z}{0.16666666666666666}}}{\frac{-1}{x}} \]

      8. div-inv 66.1%

         \[\leadsto \color{blue}{\frac{z}{0.16666666666666666} \cdot \frac{1}{\frac{-1}{x}}} \]

      9. frac-2neg 66.1%

         \[\leadsto \frac{z}{0.16666666666666666} \cdot \frac{1}{\color{blue}{\frac{--1}{-x}}} \]

      10. metadata-eval 66.1%

          \[\leadsto \frac{z}{0.16666666666666666} \cdot \frac{1}{\frac{\color{blue}{1}}{-x}} \]

      11. remove-double-div 66.2%

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

      12. *-commutative 66.2%

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

      13. clear-num 66.2%

          \[\leadsto \left(-x\right) \cdot \color{blue}{\frac{1}{\frac{0.16666666666666666}{z}}} \]

      14. metadata-eval 66.2%

          \[\leadsto \left(-x\right) \cdot \frac{\color{blue}{--1}}{\frac{0.16666666666666666}{z}} \]

      15. frac-2neg 66.2%

          \[\leadsto \left(-x\right) \cdot \color{blue}{\frac{-\left(--1\right)}{-\frac{0.16666666666666666}{z}}} \]

      16. metadata-eval 66.2%

          \[\leadsto \left(-x\right) \cdot \frac{-\color{blue}{1}}{-\frac{0.16666666666666666}{z}} \]

      17. metadata-eval 66.2%

          \[\leadsto \left(-x\right) \cdot \frac{\color{blue}{-1}}{-\frac{0.16666666666666666}{z}} \]

      18. associate-*r/ 66.2%

          \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot -1}{-\frac{0.16666666666666666}{z}}} \]

      19. distribute-lft-neg-in 66.2%

          \[\leadsto \frac{\color{blue}{-x \cdot -1}}{-\frac{0.16666666666666666}{z}} \]

      20. metadata-eval 66.2%

          \[\leadsto \frac{-x \cdot \color{blue}{\frac{1}{-1}}}{-\frac{0.16666666666666666}{z}} \]

      21. div-inv 66.2%

          \[\leadsto \frac{-\color{blue}{\frac{x}{-1}}}{-\frac{0.16666666666666666}{z}} \]

      22. frac-2neg 66.2%

          \[\leadsto \frac{-\color{blue}{\frac{-x}{--1}}}{-\frac{0.16666666666666666}{z}} \]

      23. distribute-neg-frac 66.2%

          \[\leadsto \frac{\color{blue}{\frac{-\left(-x\right)}{--1}}}{-\frac{0.16666666666666666}{z}} \]

      24. remove-double-neg 66.2%

          \[\leadsto \frac{\frac{\color{blue}{x}}{--1}}{-\frac{0.16666666666666666}{z}} \]

      25. metadata-eval 66.2%

          \[\leadsto \frac{\frac{x}{\color{blue}{1}}}{-\frac{0.16666666666666666}{z}} \]

      26. /-rgt-identity 66.2%

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

      27. distribute-neg-frac 66.2%

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

   7. Applied egg-rr 66.2%

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

   8. Taylor expanded in x around 0 66.1%

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

      1. metadata-eval 66.1%

         \[\leadsto \color{blue}{\frac{1}{-0.16666666666666666}} \cdot \left(x \cdot z\right) \]

      2. *-commutative 66.1%

         \[\leadsto \frac{1}{-0.16666666666666666} \cdot \color{blue}{\left(z \cdot x\right)} \]

      3. associate-/r/ 66.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{-0.16666666666666666}{z \cdot x}}} \]

      4. associate-/r* 66.1%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-0.16666666666666666}{z}}{x}}} \]

      5. associate-/l* 66.2%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{\frac{-0.16666666666666666}{z}}} \]

      6. associate-*r/ 66.2%

         \[\leadsto \color{blue}{1 \cdot \frac{x}{\frac{-0.16666666666666666}{z}}} \]

      7. *-lft-identity 66.2%

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

      8. associate-/r/ 66.3%

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

      9. *-commutative 66.3%

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

   10. Simplified 66.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -96000000000:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{-0.16666666666666666}\\ \end{array} \]

Alternative 7: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -96000000000:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -96000000000.0)
   (* x (* z -6.0))
   (if (<= z 0.165) x (* z (* x -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -96000000000.0) {
		tmp = x * (z * -6.0);
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = z * (x * -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 <= (-96000000000.0d0)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 0.165d0) then
        tmp = x
    else
        tmp = z * (x * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -96000000000.0) {
		tmp = x * (z * -6.0);
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = z * (x * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -96000000000.0:
		tmp = x * (z * -6.0)
	elif z <= 0.165:
		tmp = x
	else:
		tmp = z * (x * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -96000000000.0)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= 0.165)
		tmp = x;
	else
		tmp = Float64(z * Float64(x * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -96000000000.0)
		tmp = x * (z * -6.0);
	elseif (z <= 0.165)
		tmp = x;
	else
		tmp = z * (x * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -96000000000.0], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.165], x, N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.6e10

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 50.3%

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

   3. Taylor expanded in z around inf 50.3%

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

      1. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   if -9.6e10 < z < 0.165000000000000008

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.1%

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

   if 0.165000000000000008 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 66.1%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. *-commutative 66.1%

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

   5. Simplified 66.1%

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

      1. *-commutative 66.1%

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

      2. associate-*r* 66.3%

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

      3. metadata-eval 66.3%

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

      4. associate-/r/ 66.2%

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

      5. associate-*r/ 66.1%

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

      6. metadata-eval 66.1%

         \[\leadsto \frac{z \cdot \color{blue}{\frac{1}{0.16666666666666666}}}{\frac{-1}{x}} \]

      7. div-inv 66.2%

         \[\leadsto \frac{\color{blue}{\frac{z}{0.16666666666666666}}}{\frac{-1}{x}} \]

      8. div-inv 66.1%

         \[\leadsto \color{blue}{\frac{z}{0.16666666666666666} \cdot \frac{1}{\frac{-1}{x}}} \]

      9. frac-2neg 66.1%

         \[\leadsto \frac{z}{0.16666666666666666} \cdot \frac{1}{\color{blue}{\frac{--1}{-x}}} \]

      10. metadata-eval 66.1%

          \[\leadsto \frac{z}{0.16666666666666666} \cdot \frac{1}{\frac{\color{blue}{1}}{-x}} \]

      11. remove-double-div 66.2%

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

      12. *-commutative 66.2%

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

      13. clear-num 66.2%

          \[\leadsto \left(-x\right) \cdot \color{blue}{\frac{1}{\frac{0.16666666666666666}{z}}} \]

      14. metadata-eval 66.2%

          \[\leadsto \left(-x\right) \cdot \frac{\color{blue}{--1}}{\frac{0.16666666666666666}{z}} \]

      15. frac-2neg 66.2%

          \[\leadsto \left(-x\right) \cdot \color{blue}{\frac{-\left(--1\right)}{-\frac{0.16666666666666666}{z}}} \]

      16. metadata-eval 66.2%

          \[\leadsto \left(-x\right) \cdot \frac{-\color{blue}{1}}{-\frac{0.16666666666666666}{z}} \]

      17. metadata-eval 66.2%

          \[\leadsto \left(-x\right) \cdot \frac{\color{blue}{-1}}{-\frac{0.16666666666666666}{z}} \]

      18. associate-*r/ 66.2%

          \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot -1}{-\frac{0.16666666666666666}{z}}} \]

      19. distribute-lft-neg-in 66.2%

          \[\leadsto \frac{\color{blue}{-x \cdot -1}}{-\frac{0.16666666666666666}{z}} \]

      20. metadata-eval 66.2%

          \[\leadsto \frac{-x \cdot \color{blue}{\frac{1}{-1}}}{-\frac{0.16666666666666666}{z}} \]

      21. div-inv 66.2%

          \[\leadsto \frac{-\color{blue}{\frac{x}{-1}}}{-\frac{0.16666666666666666}{z}} \]

      22. frac-2neg 66.2%

          \[\leadsto \frac{-\color{blue}{\frac{-x}{--1}}}{-\frac{0.16666666666666666}{z}} \]

      23. distribute-neg-frac 66.2%

          \[\leadsto \frac{\color{blue}{\frac{-\left(-x\right)}{--1}}}{-\frac{0.16666666666666666}{z}} \]

      24. remove-double-neg 66.2%

          \[\leadsto \frac{\frac{\color{blue}{x}}{--1}}{-\frac{0.16666666666666666}{z}} \]

      25. metadata-eval 66.2%

          \[\leadsto \frac{\frac{x}{\color{blue}{1}}}{-\frac{0.16666666666666666}{z}} \]

      26. /-rgt-identity 66.2%

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

      27. distribute-neg-frac 66.2%

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

   7. Applied egg-rr 66.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{-0.16666666666666666}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 66.3%

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

      2. div-inv 66.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{-0.16666666666666666}\right)} \cdot z \]

      3. metadata-eval 66.3%

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

   9. Applied egg-rr 66.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -96000000000:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 8: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -96000000000:\\ \;\;\;\;\frac{z}{\frac{-0.16666666666666666}{x}}\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -96000000000.0)
   (/ z (/ -0.16666666666666666 x))
   (if (<= z 0.165) x (* z (* x -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -96000000000.0) {
		tmp = z / (-0.16666666666666666 / x);
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = z * (x * -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 <= (-96000000000.0d0)) then
        tmp = z / ((-0.16666666666666666d0) / x)
    else if (z <= 0.165d0) then
        tmp = x
    else
        tmp = z * (x * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -96000000000.0) {
		tmp = z / (-0.16666666666666666 / x);
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = z * (x * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -96000000000.0:
		tmp = z / (-0.16666666666666666 / x)
	elif z <= 0.165:
		tmp = x
	else:
		tmp = z * (x * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -96000000000.0)
		tmp = Float64(z / Float64(-0.16666666666666666 / x));
	elseif (z <= 0.165)
		tmp = x;
	else
		tmp = Float64(z * Float64(x * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -96000000000.0)
		tmp = z / (-0.16666666666666666 / x);
	elseif (z <= 0.165)
		tmp = x;
	else
		tmp = z * (x * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -96000000000.0], N[(z / N[(-0.16666666666666666 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.165], x, N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.6e10

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 50.3%

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

   3. Taylor expanded in z around inf 50.3%

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

      1. *-commutative 50.3%

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

   5. Simplified 50.3%

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

      1. *-commutative 50.3%

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

      2. associate-*r* 50.3%

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

      3. metadata-eval 50.3%

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

      4. associate-/r/ 50.2%

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

      5. associate-*r/ 50.2%

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

      6. associate-/l* 50.3%

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

      7. div-inv 50.3%

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

      8. metadata-eval 50.3%

         \[\leadsto \frac{z}{\frac{-1}{x} \cdot \color{blue}{0.16666666666666666}} \]

      9. associate-*l/ 50.3%

         \[\leadsto \frac{z}{\color{blue}{\frac{-1 \cdot 0.16666666666666666}{x}}} \]

      10. metadata-eval 50.3%

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

   7. Applied egg-rr 50.3%

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

   if -9.6e10 < z < 0.165000000000000008

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.1%

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

   if 0.165000000000000008 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 66.1%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. *-commutative 66.1%

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

   5. Simplified 66.1%

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

      1. *-commutative 66.1%

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

      2. associate-*r* 66.3%

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

      3. metadata-eval 66.3%

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

      4. associate-/r/ 66.2%

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

      5. associate-*r/ 66.1%

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

      6. metadata-eval 66.1%

         \[\leadsto \frac{z \cdot \color{blue}{\frac{1}{0.16666666666666666}}}{\frac{-1}{x}} \]

      7. div-inv 66.2%

         \[\leadsto \frac{\color{blue}{\frac{z}{0.16666666666666666}}}{\frac{-1}{x}} \]

      8. div-inv 66.1%

         \[\leadsto \color{blue}{\frac{z}{0.16666666666666666} \cdot \frac{1}{\frac{-1}{x}}} \]

      9. frac-2neg 66.1%

         \[\leadsto \frac{z}{0.16666666666666666} \cdot \frac{1}{\color{blue}{\frac{--1}{-x}}} \]

      10. metadata-eval 66.1%

          \[\leadsto \frac{z}{0.16666666666666666} \cdot \frac{1}{\frac{\color{blue}{1}}{-x}} \]

      11. remove-double-div 66.2%

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

      12. *-commutative 66.2%

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

      13. clear-num 66.2%

          \[\leadsto \left(-x\right) \cdot \color{blue}{\frac{1}{\frac{0.16666666666666666}{z}}} \]

      14. metadata-eval 66.2%

          \[\leadsto \left(-x\right) \cdot \frac{\color{blue}{--1}}{\frac{0.16666666666666666}{z}} \]

      15. frac-2neg 66.2%

          \[\leadsto \left(-x\right) \cdot \color{blue}{\frac{-\left(--1\right)}{-\frac{0.16666666666666666}{z}}} \]

      16. metadata-eval 66.2%

          \[\leadsto \left(-x\right) \cdot \frac{-\color{blue}{1}}{-\frac{0.16666666666666666}{z}} \]

      17. metadata-eval 66.2%

          \[\leadsto \left(-x\right) \cdot \frac{\color{blue}{-1}}{-\frac{0.16666666666666666}{z}} \]

      18. associate-*r/ 66.2%

          \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot -1}{-\frac{0.16666666666666666}{z}}} \]

      19. distribute-lft-neg-in 66.2%

          \[\leadsto \frac{\color{blue}{-x \cdot -1}}{-\frac{0.16666666666666666}{z}} \]

      20. metadata-eval 66.2%

          \[\leadsto \frac{-x \cdot \color{blue}{\frac{1}{-1}}}{-\frac{0.16666666666666666}{z}} \]

      21. div-inv 66.2%

          \[\leadsto \frac{-\color{blue}{\frac{x}{-1}}}{-\frac{0.16666666666666666}{z}} \]

      22. frac-2neg 66.2%

          \[\leadsto \frac{-\color{blue}{\frac{-x}{--1}}}{-\frac{0.16666666666666666}{z}} \]

      23. distribute-neg-frac 66.2%

          \[\leadsto \frac{\color{blue}{\frac{-\left(-x\right)}{--1}}}{-\frac{0.16666666666666666}{z}} \]

      24. remove-double-neg 66.2%

          \[\leadsto \frac{\frac{\color{blue}{x}}{--1}}{-\frac{0.16666666666666666}{z}} \]

      25. metadata-eval 66.2%

          \[\leadsto \frac{\frac{x}{\color{blue}{1}}}{-\frac{0.16666666666666666}{z}} \]

      26. /-rgt-identity 66.2%

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

      27. distribute-neg-frac 66.2%

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

   7. Applied egg-rr 66.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{-0.16666666666666666}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 66.3%

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

      2. div-inv 66.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{-0.16666666666666666}\right)} \cdot z \]

      3. metadata-eval 66.3%

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

   9. Applied egg-rr 66.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -96000000000:\\ \;\;\;\;\frac{z}{\frac{-0.16666666666666666}{x}}\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 9: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 + z \cdot -6\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (+ 1.0 (* z -6.0))))

C

double code(double x, double y, double z) {
	return x * (1.0 + (z * -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 * (1.0d0 + (z * (-6.0d0)))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 + (z * -6.0));
}

Python

def code(x, y, z):
	return x * (1.0 + (z * -6.0))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 + Float64(z * -6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 + (z * -6.0));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around inf 66.5%

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

3. Final simplification 66.5%

   \[\leadsto x \cdot \left(1 + z \cdot -6\right) \]

Alternative 10: 35.6% 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 99.8%

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

2. Taylor expanded in z around 0 38.1%

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

3. Final simplification 38.1%

   \[\leadsto x \]

Developer target: 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 2023297 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

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