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

Percentage Accurate: 99.6% → 99.6%

Time: 9.6s

Alternatives: 11

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: 99.6% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-115} \lor \neg \left(x \leq 3.3 \cdot 10^{-99}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e-115) (not (<= x 3.3e-99)))
   (+ x (* -6.0 (* x z)))
   (* z (* y 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e-115) || !(x <= 3.3e-99)) {
		tmp = x + (-6.0 * (x * z));
	} 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 ((x <= (-9d-115)) .or. (.not. (x <= 3.3d-99))) then
        tmp = x + ((-6.0d0) * (x * z))
    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 ((x <= -9e-115) || !(x <= 3.3e-99)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e-115) or not (x <= 3.3e-99):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e-115) || !(x <= 3.3e-99))
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9e-115) || ~((x <= 3.3e-99)))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e-115], N[Not[LessEqual[x, 3.3e-99]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.00000000000000046e-115 or 3.29999999999999986e-99 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.9%

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

   if -9.00000000000000046e-115 < x < 3.29999999999999986e-99

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-*r* 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in x around inf 68.1%

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

   7. Taylor expanded in x around 0 76.8%

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

      1. associate-*r* 76.9%

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

      2. *-commutative 76.9%

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

   9. Simplified 76.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-115} \lor \neg \left(x \leq 3.3 \cdot 10^{-99}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-113} \lor \neg \left(x \leq 2.3 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.18e-113) (not (<= x 2.3e-99)))
   (* x (+ (* z -6.0) 1.0))
   (* z (* y 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.18e-113) || !(x <= 2.3e-99)) {
		tmp = x * ((z * -6.0) + 1.0);
	} 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 ((x <= (-1.18d-113)) .or. (.not. (x <= 2.3d-99))) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    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 ((x <= -1.18e-113) || !(x <= 2.3e-99)) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.18e-113) or not (x <= 2.3e-99):
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.18e-113) || !(x <= 2.3e-99))
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.18e-113) || ~((x <= 2.3e-99)))
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.18e-113], N[Not[LessEqual[x, 2.3e-99]], $MachinePrecision]], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.18e-113 or 2.2999999999999998e-99 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 80.8%

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

      1. +-commutative 80.8%

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

   5. Simplified 80.8%

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

   if -1.18e-113 < x < 2.2999999999999998e-99

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-*r* 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in x around inf 68.1%

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

   7. Taylor expanded in x around 0 76.8%

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

      1. associate-*r* 76.9%

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

      2. *-commutative 76.9%

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

   9. Simplified 76.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-113} \lor \neg \left(x \leq 2.3 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+128}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.5e+128)
   (+ x (* -6.0 (* x z)))
   (if (<= x 5.3e+17) (+ x (* z (* y 6.0))) (+ x (* z (* x -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e+128) {
		tmp = x + (-6.0 * (x * z));
	} else if (x <= 5.3e+17) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = x + (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 (x <= (-6.5d+128)) then
        tmp = x + ((-6.0d0) * (x * z))
    else if (x <= 5.3d+17) then
        tmp = x + (z * (y * 6.0d0))
    else
        tmp = x + (z * (x * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e+128) {
		tmp = x + (-6.0 * (x * z));
	} else if (x <= 5.3e+17) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = x + (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.5e+128:
		tmp = x + (-6.0 * (x * z))
	elif x <= 5.3e+17:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = x + (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.5e+128)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	elseif (x <= 5.3e+17)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	else
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.5e+128)
		tmp = x + (-6.0 * (x * z));
	elseif (x <= 5.3e+17)
		tmp = x + (z * (y * 6.0));
	else
		tmp = x + (z * (x * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.5e+128], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.3e+17], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5000000000000003e128

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -6.5000000000000003e128 < x < 5.3e17

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 90.1%

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

   if 5.3e17 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.5%

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

      1. associate-*r* 90.6%

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

   5. Simplified 90.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+128}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+128}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+17}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.8e+128)
   (+ x (* -6.0 (* x z)))
   (if (<= x 2.55e+17) (+ x (* 6.0 (* y z))) (+ x (* z (* x -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e+128) {
		tmp = x + (-6.0 * (x * z));
	} else if (x <= 2.55e+17) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (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 (x <= (-5.8d+128)) then
        tmp = x + ((-6.0d0) * (x * z))
    else if (x <= 2.55d+17) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + (z * (x * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e+128) {
		tmp = x + (-6.0 * (x * z));
	} else if (x <= 2.55e+17) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.8e+128:
		tmp = x + (-6.0 * (x * z))
	elif x <= 2.55e+17:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.8e+128)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	elseif (x <= 2.55e+17)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.8e+128)
		tmp = x + (-6.0 * (x * z));
	elseif (x <= 2.55e+17)
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (z * (x * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.8e+128], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.55e+17], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.8000000000000001e128

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -5.8000000000000001e128 < x < 2.55e17

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 90.1%

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

      1. *-commutative 90.1%

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

   5. Simplified 90.1%

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

   if 2.55e17 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.5%

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

      1. associate-*r* 90.6%

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

   5. Simplified 90.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+128}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+17}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+128}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+17}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e+128)
   (+ x (* -6.0 (* x z)))
   (if (<= x 2.2e+17) (+ x (* 6.0 (* y z))) (* x (+ (* z -6.0) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+128) {
		tmp = x + (-6.0 * (x * z));
	} else if (x <= 2.2e+17) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-7.5d+128)) then
        tmp = x + ((-6.0d0) * (x * z))
    else if (x <= 2.2d+17) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+128) {
		tmp = x + (-6.0 * (x * z));
	} else if (x <= 2.2e+17) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e+128:
		tmp = x + (-6.0 * (x * z))
	elif x <= 2.2e+17:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x * ((z * -6.0) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e+128)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	elseif (x <= 2.2e+17)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e+128)
		tmp = x + (-6.0 * (x * z));
	elseif (x <= 2.2e+17)
		tmp = x + (6.0 * (y * z));
	else
		tmp = x * ((z * -6.0) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e+128], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+17], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.50000000000000076e128

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -7.50000000000000076e128 < x < 2.2e17

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 90.1%

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

      1. *-commutative 90.1%

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

   5. Simplified 90.1%

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

   if 2.2e17 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.6%

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

      1. +-commutative 90.6%

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

   5. Simplified 90.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+128}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+17}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-74} \lor \neg \left(z \leq 3.15 \cdot 10^{-26}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.8e-74) (not (<= z 3.15e-26))) (* 6.0 (* y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.8e-74) || !(z <= 3.15e-26)) {
		tmp = 6.0 * (y * z);
	} 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 <= (-6.8d-74)) .or. (.not. (z <= 3.15d-26))) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.8e-74) || !(z <= 3.15e-26)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.8e-74) or not (z <= 3.15e-26):
		tmp = 6.0 * (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.8e-74) || !(z <= 3.15e-26))
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.8e-74) || ~((z <= 3.15e-26)))
		tmp = 6.0 * (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.8e-74], N[Not[LessEqual[z, 3.15e-26]], $MachinePrecision]], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000001e-74 or 3.15e-26 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 65.2%

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

      1. *-commutative 65.2%

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

      2. associate-*r* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in x around inf 48.4%

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

   7. Taylor expanded in x around 0 60.6%

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

   if -6.8000000000000001e-74 < z < 3.15e-26

   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 76.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-74} \lor \neg \left(z \leq 3.15 \cdot 10^{-26}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} 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 <= (-0.165d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 0.17):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.17))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 0.17)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

   4. Taylor expanded in x around inf 47.2%

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

      1. +-commutative 47.2%

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

      2. *-commutative 47.2%

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

   6. Simplified 47.2%

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

   7. Taylor expanded in z around inf 46.3%

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

   if -0.165000000000000008 < z < 0.170000000000000012

   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 72.3%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-75}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e-75) (* z (* y 6.0)) (if (<= z 1e-24) x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e-75) {
		tmp = z * (y * 6.0);
	} else if (z <= 1e-24) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-5.8d-75)) then
        tmp = z * (y * 6.0d0)
    else if (z <= 1d-24) then
        tmp = x
    else
        tmp = 6.0d0 * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e-75) {
		tmp = z * (y * 6.0);
	} else if (z <= 1e-24) {
		tmp = x;
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e-75:
		tmp = z * (y * 6.0)
	elif z <= 1e-24:
		tmp = x
	else:
		tmp = 6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e-75)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= 1e-24)
		tmp = x;
	else
		tmp = Float64(6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.8e-75)
		tmp = z * (y * 6.0);
	elseif (z <= 1e-24)
		tmp = x;
	else
		tmp = 6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e-75], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-24], x, N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000003e-75

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*r* 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in x around inf 49.4%

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

   7. Taylor expanded in x around 0 60.4%

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

      1. associate-*r* 60.4%

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

      2. *-commutative 60.4%

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

   9. Simplified 60.4%

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

   if -5.8000000000000003e-75 < z < 9.99999999999999924e-25

   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 76.5%

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

   if 9.99999999999999924e-25 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r* 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in x around inf 47.1%

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

   7. Taylor expanded in x around 0 61.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-75}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.6e-75) (* y (* 6.0 z)) (if (<= z 6.5e-26) x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e-75) {
		tmp = y * (6.0 * z);
	} else if (z <= 6.5e-26) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-1.6d-75)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 6.5d-26) then
        tmp = x
    else
        tmp = 6.0d0 * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e-75) {
		tmp = y * (6.0 * z);
	} else if (z <= 6.5e-26) {
		tmp = x;
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.6e-75:
		tmp = y * (6.0 * z)
	elif z <= 6.5e-26:
		tmp = x
	else:
		tmp = 6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.6e-75)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 6.5e-26)
		tmp = x;
	else
		tmp = Float64(6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.6e-75)
		tmp = y * (6.0 * z);
	elseif (z <= 6.5e-26)
		tmp = x;
	else
		tmp = 6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.6e-75], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-26], x, N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999988e-75

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*r* 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in x around inf 49.4%

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

   7. Taylor expanded in x around 0 60.4%

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

      1. associate-*r* 60.4%

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

      2. *-commutative 60.4%

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

      3. associate-*r* 60.4%

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

   9. Simplified 60.4%

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

   if -1.59999999999999988e-75 < z < 6.5e-26

   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 76.5%

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

   if 6.5e-26 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r* 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in x around inf 47.1%

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

   7. Taylor expanded in x around 0 61.0%

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

Alternative 11: 37.2% 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. Add Preprocessing

3. Taylor expanded in z around 0 40.2%

   \[\leadsto \color{blue}{x} \]
4. 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 2024118 
(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)))