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

Percentage Accurate: 99.7% → 99.7%

Time: 6.9s

Alternatives: 8

Speedup: 1.0×

• 21.4% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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%

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

   2. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-69} \lor \neg \left(y \leq 2.4 \cdot 10^{+29}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.25e-69) (not (<= y 2.4e+29)))
   (+ x (* 6.0 (* y z)))
   (* x (+ 1.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e-69) || !(y <= 2.4e+29)) {
		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 <= (-1.25d-69)) .or. (.not. (y <= 2.4d+29))) 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 <= -1.25e-69) || !(y <= 2.4e+29)) {
		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 <= -1.25e-69) or not (y <= 2.4e+29):
		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 <= -1.25e-69) || !(y <= 2.4e+29))
		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 <= -1.25e-69) || ~((y <= 2.4e+29)))
		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, -1.25e-69], N[Not[LessEqual[y, 2.4e+29]], $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 < -1.25000000000000008e-69 or 2.4000000000000001e29 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 88.0%

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

      1. *-commutative 88.0%

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

   4. Simplified 88.0%

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

   if -1.25000000000000008e-69 < y < 2.4000000000000001e29

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 90.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-69} \lor \neg \left(y \leq 2.4 \cdot 10^{+29}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]

Alternative 3: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.12e-69)
   (+ x (* 6.0 (* y z)))
   (if (<= y 4.4e+27) (* x (+ 1.0 (* z -6.0))) (+ x (* y (* 6.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.12e-69) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 4.4e+27) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = x + (y * (6.0 * 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 <= (-1.12d-69)) then
        tmp = x + (6.0d0 * (y * z))
    else if (y <= 4.4d+27) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.12e-69) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 4.4e+27) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.12e-69:
		tmp = x + (6.0 * (y * z))
	elif y <= 4.4e+27:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.12e-69)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif (y <= 4.4e+27)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.12e-69)
		tmp = x + (6.0 * (y * z));
	elseif (y <= 4.4e+27)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.12e-69], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+27], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e-69

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 86.2%

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

      1. *-commutative 86.2%

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

   4. Simplified 86.2%

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

   if -1.12e-69 < y < 4.3999999999999997e27

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 90.4%

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

   if 4.3999999999999997e27 < y

   1. Initial program 99.7%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. flip-- 57.0%

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

      4. associate-*r/ 50.3%

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

   3. Applied egg-rr 50.3%

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

      1. associate-/l* 57.0%

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

      2. associate-/l* 57.0%

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

      3. difference-of-squares 59.4%

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

      4. associate-/r* 99.8%

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

      5. *-inverses 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

      3. div-inv 99.5%

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

      4. associate-/l/ 99.5%

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

      5. metadata-eval 99.5%

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

   7. Applied egg-rr 99.5%

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

      1. unpow-1 99.5%

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

      2. associate-/r* 99.5%

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

      3. clear-num 99.6%

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

      4. /-rgt-identity 99.6%

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

   9. Applied egg-rr 99.6%

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

       1. associate-/l* 99.7%

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

   11. Simplified 99.7%

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

   12. Taylor expanded in y around inf 90.4%

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

       1. *-commutative 90.4%

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

       2. associate-*r* 90.6%

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

       3. *-commutative 90.6%

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

   14. Simplified 90.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 4: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-69}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e-69)
   (+ x (* z (* y 6.0)))
   (if (<= y 1.9e+30) (* x (+ 1.0 (* z -6.0))) (+ x (* y (* 6.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e-69) {
		tmp = x + (z * (y * 6.0));
	} else if (y <= 1.9e+30) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = x + (y * (6.0 * 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 <= (-1.35d-69)) then
        tmp = x + (z * (y * 6.0d0))
    else if (y <= 1.9d+30) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e-69) {
		tmp = x + (z * (y * 6.0));
	} else if (y <= 1.9e+30) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e-69:
		tmp = x + (z * (y * 6.0))
	elif y <= 1.9e+30:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e-69)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	elseif (y <= 1.9e+30)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.35e-69)
		tmp = x + (z * (y * 6.0));
	elseif (y <= 1.9e+30)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e-69], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+30], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3499999999999999e-69

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 86.3%

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

   if -1.3499999999999999e-69 < y < 1.9000000000000001e30

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 90.4%

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

   if 1.9000000000000001e30 < y

   1. Initial program 99.7%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. flip-- 57.0%

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

      4. associate-*r/ 50.3%

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

   3. Applied egg-rr 50.3%

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

      1. associate-/l* 57.0%

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

      2. associate-/l* 57.0%

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

      3. difference-of-squares 59.4%

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

      4. associate-/r* 99.8%

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

      5. *-inverses 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

      3. div-inv 99.5%

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

      4. associate-/l/ 99.5%

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

      5. metadata-eval 99.5%

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

   7. Applied egg-rr 99.5%

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

      1. unpow-1 99.5%

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

      2. associate-/r* 99.5%

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

      3. clear-num 99.6%

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

      4. /-rgt-identity 99.6%

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

   9. Applied egg-rr 99.6%

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

       1. associate-/l* 99.7%

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

   11. Simplified 99.7%

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

   12. Taylor expanded in y around inf 90.4%

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

       1. *-commutative 90.4%

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

       2. associate-*r* 90.6%

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

       3. *-commutative 90.6%

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

   14. Simplified 90.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-69}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 5: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-5} \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.2e-5) (not (<= z 0.165))) (* x (* z -6.0)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.2e-5) || !(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 <= (-8.2d-5)) .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 <= -8.2e-5) || !(z <= 0.165)) {
		tmp = x * (z * -6.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.2e-5) 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 <= -8.2e-5) || !(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 <= -8.2e-5) || ~((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, -8.2e-5], 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 < -8.20000000000000009e-5 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 63.3%

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

   3. Taylor expanded in z around inf 61.4%

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

   if -8.20000000000000009e-5 < 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 64.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-5} \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 7: 62.6% 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 64.4%

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

3. Final simplification 64.4%

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

Alternative 8: 36.7% 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 34.3%

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

3. Final simplification 34.3%

   \[\leadsto x \]

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 2023293 
(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)))