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

Percentage Accurate: 99.7% → 99.7%

Time: 9.5s

Alternatives: 10

Speedup: 1.0×

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

Specification

Math

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

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot 6\right)\\ t_1 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y 6.0))) (t_1 (* x (* z -6.0))))
   (if (<= z -6.4e+44)
     t_0
     (if (<= z -7.8e-13)
       t_1
       (if (<= z 3.9e-17) x (if (<= z 1.8e+65) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * 6.0);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -6.4e+44) {
		tmp = t_0;
	} else if (z <= -7.8e-13) {
		tmp = t_1;
	} else if (z <= 3.9e-17) {
		tmp = x;
	} else if (z <= 1.8e+65) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * (y * 6.0d0)
    t_1 = x * (z * (-6.0d0))
    if (z <= (-6.4d+44)) then
        tmp = t_0
    else if (z <= (-7.8d-13)) then
        tmp = t_1
    else if (z <= 3.9d-17) then
        tmp = x
    else if (z <= 1.8d+65) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y * 6.0);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -6.4e+44) {
		tmp = t_0;
	} else if (z <= -7.8e-13) {
		tmp = t_1;
	} else if (z <= 3.9e-17) {
		tmp = x;
	} else if (z <= 1.8e+65) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * 6.0)
	t_1 = x * (z * -6.0)
	tmp = 0
	if z <= -6.4e+44:
		tmp = t_0
	elif z <= -7.8e-13:
		tmp = t_1
	elif z <= 3.9e-17:
		tmp = x
	elif z <= 1.8e+65:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * 6.0))
	t_1 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -6.4e+44)
		tmp = t_0;
	elseif (z <= -7.8e-13)
		tmp = t_1;
	elseif (z <= 3.9e-17)
		tmp = x;
	elseif (z <= 1.8e+65)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * 6.0);
	t_1 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -6.4e+44)
		tmp = t_0;
	elseif (z <= -7.8e-13)
		tmp = t_1;
	elseif (z <= 3.9e-17)
		tmp = x;
	elseif (z <= 1.8e+65)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+44], t$95$0, If[LessEqual[z, -7.8e-13], t$95$1, If[LessEqual[z, 3.9e-17], x, If[LessEqual[z, 1.8e+65], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.40000000000000009e44 or 3.89999999999999989e-17 < z < 1.79999999999999989e65

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. flip3-+ 16.2%

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

      3. clear-num 16.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}}} \]

      4. *-un-lft-identity 16.2%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)\right)}}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}} \]

      5. associate-/l* 16.2%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}}}} \]

      6. flip3-+ 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around inf 62.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{y \cdot z}}} \]
   5. Step-by-step derivation

      1. *-commutative 62.4%

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

   6. Simplified 62.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{z \cdot y}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 62.5%

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

      2. *-commutative 62.5%

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

      3. associate-*r* 62.7%

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

      4. metadata-eval 62.7%

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

   8. Applied egg-rr 62.7%

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

   if -6.40000000000000009e44 < z < -7.80000000000000009e-13 or 1.79999999999999989e65 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 75.6%

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

   3. Taylor expanded in z around inf 74.7%

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

      1. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -7.80000000000000009e-13 < z < 3.89999999999999989e-17

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 80.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 3: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-17} \lor \neg \left(z \leq 4.5 \cdot 10^{-17}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e-17) (not (<= z 4.5e-17))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-17) || !(z <= 4.5e-17)) {
		tmp = 6.0 * ((y - 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 <= (-1.7d-17)) .or. (.not. (z <= 4.5d-17))) then
        tmp = 6.0d0 * ((y - 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 <= -1.7e-17) || !(z <= 4.5e-17)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e-17) or not (z <= 4.5e-17):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e-17) || !(z <= 4.5e-17))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e-17) || ~((z <= 4.5e-17)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e-17], N[Not[LessEqual[z, 4.5e-17]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.6999999999999999e-17 or 4.49999999999999978e-17 < z

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. flip3-+ 17.6%

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

      3. clear-num 17.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}}} \]

      4. *-un-lft-identity 17.6%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)\right)}}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}} \]

      5. associate-/l* 17.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}}}} \]

      6. flip3-+ 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 97.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{z \cdot \left(y - x\right)}}} \]
   5. Step-by-step derivation

      1. *-commutative 97.0%

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

      2. associate-/r* 97.0%

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

   6. Simplified 97.0%

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

   7. Taylor expanded in z around 0 97.1%

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

   if -1.6999999999999999e-17 < z < 4.49999999999999978e-17

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-17} \lor \neg \left(z \leq 4.5 \cdot 10^{-17}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-17} \lor \neg \left(z \leq 1.4 \cdot 10^{-9}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e-17) (not (<= z 1.4e-9)))
   (* 6.0 (* (- y x) z))
   (* x (+ 1.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-17) || !(z <= 1.4e-9)) {
		tmp = 6.0 * ((y - x) * 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 ((z <= (-2.3d-17)) .or. (.not. (z <= 1.4d-9))) then
        tmp = 6.0d0 * ((y - x) * 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 ((z <= -2.3e-17) || !(z <= 1.4e-9)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x * (1.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.3e-17) or not (z <= 1.4e-9):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x * (1.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.3e-17) || !(z <= 1.4e-9))
		tmp = Float64(6.0 * Float64(Float64(y - x) * 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 ((z <= -2.3e-17) || ~((z <= 1.4e-9)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x * (1.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e-17], N[Not[LessEqual[z, 1.4e-9]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.30000000000000009e-17 or 1.39999999999999992e-9 < z

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. flip3-+ 17.9%

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

      3. clear-num 17.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}}} \]

      4. *-un-lft-identity 17.9%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)\right)}}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}} \]

      5. associate-/l* 17.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}}}} \]

      6. flip3-+ 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 97.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{z \cdot \left(y - x\right)}}} \]
   5. Step-by-step derivation

      1. *-commutative 97.7%

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

      2. associate-/r* 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in z around 0 97.9%

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

   if -2.30000000000000009e-17 < z < 1.39999999999999992e-9

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 80.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-17} \lor \neg \left(z \leq 1.4 \cdot 10^{-9}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]

Alternative 5: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-17} \lor \neg \left(z \leq 1.2 \cdot 10^{-9}\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e-17) (not (<= z 1.2e-9)))
   (* z (* (- y x) 6.0))
   (* x (+ 1.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e-17) || !(z <= 1.2e-9)) {
		tmp = z * ((y - x) * 6.0);
	} 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 ((z <= (-2.2d-17)) .or. (.not. (z <= 1.2d-9))) then
        tmp = z * ((y - x) * 6.0d0)
    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 ((z <= -2.2e-17) || !(z <= 1.2e-9)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x * (1.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.2e-17) or not (z <= 1.2e-9):
		tmp = z * ((y - x) * 6.0)
	else:
		tmp = x * (1.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e-17) || !(z <= 1.2e-9))
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	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 ((z <= -2.2e-17) || ~((z <= 1.2e-9)))
		tmp = z * ((y - x) * 6.0);
	else
		tmp = x * (1.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e-17], N[Not[LessEqual[z, 1.2e-9]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e-17 or 1.2e-9 < z

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. flip3-+ 17.9%

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

      3. clear-num 17.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}}} \]

      4. *-un-lft-identity 17.9%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)\right)}}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}} \]

      5. associate-/l* 17.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}}}} \]

      6. flip3-+ 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 97.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{z \cdot \left(y - x\right)}}} \]
   5. Step-by-step derivation

      1. *-commutative 97.7%

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

      2. associate-/r* 97.8%

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

   6. Simplified 97.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{0.16666666666666666}{y - x}}{z}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 97.8%

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

      2. associate-/r/ 97.9%

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

      3. metadata-eval 97.9%

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

   8. Applied egg-rr 97.9%

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

   if -2.2e-17 < z < 1.2e-9

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 80.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-17} \lor \neg \left(z \leq 1.2 \cdot 10^{-9}\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]

Alternative 6: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-17} \lor \neg \left(z \leq 1.45 \cdot 10^{-10}\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e-17) (not (<= z 1.45e-10)))
   (* z (* (- y x) 6.0))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e-17) || !(z <= 1.45e-10)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x + (-6.0 * (x * 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 <= (-1.5d-17)) .or. (.not. (z <= 1.45d-10))) then
        tmp = z * ((y - x) * 6.0d0)
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e-17) || !(z <= 1.45e-10)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e-17) or not (z <= 1.45e-10):
		tmp = z * ((y - x) * 6.0)
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e-17) || !(z <= 1.45e-10))
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5e-17) || ~((z <= 1.45e-10)))
		tmp = z * ((y - x) * 6.0);
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e-17], N[Not[LessEqual[z, 1.45e-10]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000003e-17 or 1.4499999999999999e-10 < z

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. flip3-+ 17.9%

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

      3. clear-num 17.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}}} \]

      4. *-un-lft-identity 17.9%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)\right)}}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}} \]

      5. associate-/l* 17.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}}}} \]

      6. flip3-+ 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 97.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{z \cdot \left(y - x\right)}}} \]
   5. Step-by-step derivation

      1. *-commutative 97.7%

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

      2. associate-/r* 97.8%

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

   6. Simplified 97.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{0.16666666666666666}{y - x}}{z}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 97.8%

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

      2. associate-/r/ 97.9%

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

      3. metadata-eval 97.9%

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

   8. Applied egg-rr 97.9%

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

   if -1.50000000000000003e-17 < z < 1.4499999999999999e-10

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-17} \lor \neg \left(z \leq 1.45 \cdot 10^{-10}\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 7: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.155 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.155) (not (<= z 0.17)))
   (* z (* (- y x) 6.0))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.155) || !(z <= 0.17)) {
		tmp = z * ((y - x) * 6.0);
	} 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 ((z <= (-0.155d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = z * ((y - x) * 6.0d0)
    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 ((z <= -0.155) || !(z <= 0.17)) {
		tmp = z * ((y - x) * 6.0);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.155) or not (z <= 0.17):
		tmp = z * ((y - x) * 6.0)
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.155) || !(z <= 0.17))
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	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 ((z <= -0.155) || ~((z <= 0.17)))
		tmp = z * ((y - x) * 6.0);
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.155], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.154999999999999999 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

      1. associate-*r* 99.7%

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

      2. flip3-+ 17.2%

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

      3. clear-num 17.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}}} \]

      4. *-un-lft-identity 17.2%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)\right)}}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}} \]

      5. associate-/l* 17.2%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(6 \cdot z\right)\right)\right)}}}} \]

      6. flip3-+ 99.7%

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

      7. +-commutative 99.7%

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

      8. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 99.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{z \cdot \left(y - x\right)}}} \]
   5. Step-by-step derivation

      1. *-commutative 99.1%

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

      2. associate-/r* 99.2%

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

   6. Simplified 99.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{0.16666666666666666}{y - x}}{z}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 99.2%

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

      2. associate-/r/ 99.4%

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

      3. metadata-eval 99.4%

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

   8. Applied egg-rr 99.4%

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

   if -0.154999999999999999 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.2%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.155 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-13} \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.8e-13) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.8e-13) || !(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 <= (-7.8d-13)) .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 <= -7.8e-13) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.8e-13) 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 <= -7.8e-13) || !(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 <= -7.8e-13) || ~((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, -7.8e-13], 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 < -7.80000000000000009e-13 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 55.1%

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

   3. Taylor expanded in z around inf 54.8%

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

   if -7.80000000000000009e-13 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-13} \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.8e-13) (* -6.0 (* x z)) (if (<= z 0.17) x (* x (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e-13) {
		tmp = -6.0 * (x * z);
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = x * (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 (z <= (-7.8d-13)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 0.17d0) then
        tmp = x
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e-13) {
		tmp = -6.0 * (x * z);
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.8e-13:
		tmp = -6.0 * (x * z)
	elif z <= 0.17:
		tmp = x
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.8e-13)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.8e-13)
		tmp = -6.0 * (x * z);
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.8e-13], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], x, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.80000000000000009e-13

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 46.2%

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

   3. Taylor expanded in z around inf 45.4%

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

   if -7.80000000000000009e-13 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.7%

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

   if 0.170000000000000012 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 64.3%

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

   3. Taylor expanded in z around inf 64.2%

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

      1. *-commutative 64.2%

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

   5. Simplified 64.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 10: 35.5% 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 41.6%

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

3. Final simplification 41.6%

   \[\leadsto x \]

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 2023301 
(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)))