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

Percentage Accurate: 99.6% → 99.6%

Time: 7.8s

Alternatives: 7

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+109} \lor \neg \left(x \leq -2.8 \cdot 10^{+55} \lor \neg \left(x \leq -0.17\right) \land x \leq 4.6 \cdot 10^{+21}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.3e+109)
         (not (or (<= x -2.8e+55) (and (not (<= x -0.17)) (<= x 4.6e+21)))))
   (+ x (* -6.0 (* x z)))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e+109) || !((x <= -2.8e+55) || (!(x <= -0.17) && (x <= 4.6e+21)))) {
		tmp = x + (-6.0 * (x * z));
	} 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 ((x <= (-4.3d+109)) .or. (.not. (x <= (-2.8d+55)) .or. (.not. (x <= (-0.17d0))) .and. (x <= 4.6d+21))) then
        tmp = x + ((-6.0d0) * (x * z))
    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 ((x <= -4.3e+109) || !((x <= -2.8e+55) || (!(x <= -0.17) && (x <= 4.6e+21)))) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.3e+109) or not ((x <= -2.8e+55) or (not (x <= -0.17) and (x <= 4.6e+21))):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.3e+109) || !((x <= -2.8e+55) || (!(x <= -0.17) && (x <= 4.6e+21))))
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	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 ((x <= -4.3e+109) || ~(((x <= -2.8e+55) || (~((x <= -0.17)) && (x <= 4.6e+21)))))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.3e+109], N[Not[Or[LessEqual[x, -2.8e+55], And[N[Not[LessEqual[x, -0.17]], $MachinePrecision], LessEqual[x, 4.6e+21]]]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3000000000000001e109 or -2.8000000000000001e55 < x < -0.170000000000000012 or 4.6e21 < 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 94.0%

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

   if -4.3000000000000001e109 < x < -2.8000000000000001e55 or -0.170000000000000012 < x < 4.6e21

   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 89.5%

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

      1. *-commutative 89.5%

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

   5. Simplified 89.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+109} \lor \neg \left(x \leq -2.8 \cdot 10^{+55} \lor \neg \left(x \leq -0.17\right) \land x \leq 4.6 \cdot 10^{+21}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+109}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+57} \lor \neg \left(x \leq -245\right) \land x \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e+109)
   (+ x (* x (* z -6.0)))
   (if (or (<= x -1.6e+57) (and (not (<= x -245.0)) (<= x 2.5e+19)))
     (+ x (* 6.0 (* y z)))
     (+ x (* -6.0 (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+109) {
		tmp = x + (x * (z * -6.0));
	} else if ((x <= -1.6e+57) || (!(x <= -245.0) && (x <= 2.5e+19))) {
		tmp = x + (6.0 * (y * z));
	} 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 (x <= (-4.6d+109)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if ((x <= (-1.6d+57)) .or. (.not. (x <= (-245.0d0))) .and. (x <= 2.5d+19)) then
        tmp = x + (6.0d0 * (y * z))
    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 (x <= -4.6e+109) {
		tmp = x + (x * (z * -6.0));
	} else if ((x <= -1.6e+57) || (!(x <= -245.0) && (x <= 2.5e+19))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e+109:
		tmp = x + (x * (z * -6.0))
	elif (x <= -1.6e+57) or (not (x <= -245.0) and (x <= 2.5e+19)):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e+109)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif ((x <= -1.6e+57) || (!(x <= -245.0) && (x <= 2.5e+19)))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	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 (x <= -4.6e+109)
		tmp = x + (x * (z * -6.0));
	elseif ((x <= -1.6e+57) || (~((x <= -245.0)) && (x <= 2.5e+19)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e+109], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.6e+57], And[N[Not[LessEqual[x, -245.0]], $MachinePrecision], LessEqual[x, 2.5e+19]]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.60000000000000021e109

   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 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-*r* 96.0%

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

      3. *-commutative 96.0%

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

   5. Simplified 96.0%

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

   if -4.60000000000000021e109 < x < -1.60000000000000015e57 or -245 < x < 2.5e19

   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 89.5%

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

      1. *-commutative 89.5%

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

   5. Simplified 89.5%

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

   if -1.60000000000000015e57 < x < -245 or 2.5e19 < 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 92.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+109}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+57} \lor \neg \left(x \leq -245\right) \land x \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq -6.1 \cdot 10^{+57}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -10.6 \lor \neg \left(x \leq 1.1 \cdot 10^{+21}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e+109)
   (+ x (* x (* z -6.0)))
   (if (<= x -6.1e+57)
     (+ x (* 6.0 (* y z)))
     (if (or (<= x -10.6) (not (<= x 1.1e+21)))
       (+ x (* -6.0 (* x z)))
       (+ x (* y (* 6.0 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e+109) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= -6.1e+57) {
		tmp = x + (6.0 * (y * z));
	} else if ((x <= -10.6) || !(x <= 1.1e+21)) {
		tmp = x + (-6.0 * (x * z));
	} 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 (x <= (-5.5d+109)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if (x <= (-6.1d+57)) then
        tmp = x + (6.0d0 * (y * z))
    else if ((x <= (-10.6d0)) .or. (.not. (x <= 1.1d+21))) then
        tmp = x + ((-6.0d0) * (x * z))
    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 (x <= -5.5e+109) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= -6.1e+57) {
		tmp = x + (6.0 * (y * z));
	} else if ((x <= -10.6) || !(x <= 1.1e+21)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5e+109:
		tmp = x + (x * (z * -6.0))
	elif x <= -6.1e+57:
		tmp = x + (6.0 * (y * z))
	elif (x <= -10.6) or not (x <= 1.1e+21):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e+109)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif (x <= -6.1e+57)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif ((x <= -10.6) || !(x <= 1.1e+21))
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	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 (x <= -5.5e+109)
		tmp = x + (x * (z * -6.0));
	elseif (x <= -6.1e+57)
		tmp = x + (6.0 * (y * z));
	elseif ((x <= -10.6) || ~((x <= 1.1e+21)))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e+109], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.1e+57], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -10.6], N[Not[LessEqual[x, 1.1e+21]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.4999999999999998e109

   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 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-*r* 96.0%

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

      3. *-commutative 96.0%

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

   5. Simplified 96.0%

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

   if -5.4999999999999998e109 < x < -6.09999999999999975e57

   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 inf 92.9%

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

      1. *-commutative 92.9%

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

   5. Simplified 92.9%

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

   if -6.09999999999999975e57 < x < -10.5999999999999996 or 1.1e21 < 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 92.7%

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

   if -10.5999999999999996 < x < 1.1e21

   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 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-*r* 89.2%

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

   5. Simplified 89.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq -6.1 \cdot 10^{+57}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -10.6 \lor \neg \left(x \leq 1.1 \cdot 10^{+21}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+109}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq -6.1 \cdot 10^{+57}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -75 \lor \neg \left(x \leq 2.4 \cdot 10^{+21}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.3e+109)
   (+ x (* x (* z -6.0)))
   (if (<= x -6.1e+57)
     (+ x (* 6.0 (* y z)))
     (if (or (<= x -75.0) (not (<= x 2.4e+21)))
       (+ x (* -6.0 (* x z)))
       (+ x (* z (* y 6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.3e+109) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= -6.1e+57) {
		tmp = x + (6.0 * (y * z));
	} else if ((x <= -75.0) || !(x <= 2.4e+21)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (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 <= (-4.3d+109)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if (x <= (-6.1d+57)) then
        tmp = x + (6.0d0 * (y * z))
    else if ((x <= (-75.0d0)) .or. (.not. (x <= 2.4d+21))) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = x + (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 <= -4.3e+109) {
		tmp = x + (x * (z * -6.0));
	} else if (x <= -6.1e+57) {
		tmp = x + (6.0 * (y * z));
	} else if ((x <= -75.0) || !(x <= 2.4e+21)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.3e+109:
		tmp = x + (x * (z * -6.0))
	elif x <= -6.1e+57:
		tmp = x + (6.0 * (y * z))
	elif (x <= -75.0) or not (x <= 2.4e+21):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.3e+109)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif (x <= -6.1e+57)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif ((x <= -75.0) || !(x <= 2.4e+21))
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.3e+109)
		tmp = x + (x * (z * -6.0));
	elseif (x <= -6.1e+57)
		tmp = x + (6.0 * (y * z));
	elseif ((x <= -75.0) || ~((x <= 2.4e+21)))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.3e+109], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.1e+57], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -75.0], N[Not[LessEqual[x, 2.4e+21]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.3000000000000001e109

   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 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-*r* 96.0%

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

      3. *-commutative 96.0%

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

   5. Simplified 96.0%

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

   if -4.3000000000000001e109 < x < -6.09999999999999975e57

   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 inf 92.9%

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

      1. *-commutative 92.9%

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

   5. Simplified 92.9%

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

   if -6.09999999999999975e57 < x < -75 or 2.4e21 < 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 92.7%

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

   if -75 < x < 2.4e21

   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 89.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+109}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq -6.1 \cdot 10^{+57}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -75 \lor \neg \left(x \leq 2.4 \cdot 10^{+21}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 98.2%

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

   1. +-commutative 98.2%

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

   2. associate-*r* 98.3%

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

   3. *-commutative 98.3%

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

   4. associate-*r* 98.3%

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

   5. metadata-eval 98.3%

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

   6. cancel-sign-sub-inv 98.3%

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

   7. *-commutative 98.3%

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

   8. associate-*r* 98.3%

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

   9. *-commutative 98.3%

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

   10. distribute-lft-out-- 99.8%

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

   11. associate-*r* 99.8%

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

5. Simplified 99.8%

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

6. Final simplification 99.8%

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

Alternative 7: 62.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 65.8%

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

4. Final simplification 65.8%

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

Developer target: 99.7% 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 2024115 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (- x (* (* 6.0 z) (- x y)))

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