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

Percentage Accurate: 99.7% → 99.7%

Time: 6.3s

Alternatives: 9

Speedup: 1.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq -28.5 \lor \neg \left(x \leq -6 \cdot 10^{-53}\right) \land x \leq 1860000000000:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+64)
   (* x (+ 1.0 (* z -6.0)))
   (if (or (<= x -28.5) (and (not (<= x -6e-53)) (<= x 1860000000000.0)))
     (+ x (* 6.0 (* y z)))
     (+ x (* z (* x -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+64) {
		tmp = x * (1.0 + (z * -6.0));
	} else if ((x <= -28.5) || (!(x <= -6e-53) && (x <= 1860000000000.0))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (z * (x * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.2d+64)) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else if ((x <= (-28.5d0)) .or. (.not. (x <= (-6d-53))) .and. (x <= 1860000000000.0d0)) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + (z * (x * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+64) {
		tmp = x * (1.0 + (z * -6.0));
	} else if ((x <= -28.5) || (!(x <= -6e-53) && (x <= 1860000000000.0))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.2e+64:
		tmp = x * (1.0 + (z * -6.0))
	elif (x <= -28.5) or (not (x <= -6e-53) and (x <= 1860000000000.0)):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e+64)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	elseif ((x <= -28.5) || (!(x <= -6e-53) && (x <= 1860000000000.0)))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.2e+64)
		tmp = x * (1.0 + (z * -6.0));
	elseif ((x <= -28.5) || (~((x <= -6e-53)) && (x <= 1860000000000.0)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (z * (x * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+64], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -28.5], And[N[Not[LessEqual[x, -6e-53]], $MachinePrecision], LessEqual[x, 1860000000000.0]]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.20000000000000019e64

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.7%

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

   if -3.20000000000000019e64 < x < -28.5 or -6.0000000000000004e-53 < x < 1.86e12

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 94.5%

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

   if -28.5 < x < -6.0000000000000004e-53 or 1.86e12 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 83.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq -28.5 \lor \neg \left(x \leq -6 \cdot 10^{-53}\right) \land x \leq 1860000000000:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 3: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq -30:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-53} \lor \neg \left(x \leq 1220000000000\right):\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+79)
   (* x (+ 1.0 (* z -6.0)))
   (if (<= x -30.0)
     (+ x (* 6.0 (* y z)))
     (if (or (<= x -6e-53) (not (<= x 1220000000000.0)))
       (+ x (* z (* x -6.0)))
       (+ x (* z (* y 6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+79) {
		tmp = x * (1.0 + (z * -6.0));
	} else if (x <= -30.0) {
		tmp = x + (6.0 * (y * z));
	} else if ((x <= -6e-53) || !(x <= 1220000000000.0)) {
		tmp = x + (z * (x * -6.0));
	} 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 <= (-1.3d+79)) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else if (x <= (-30.0d0)) then
        tmp = x + (6.0d0 * (y * z))
    else if ((x <= (-6d-53)) .or. (.not. (x <= 1220000000000.0d0))) then
        tmp = x + (z * (x * (-6.0d0)))
    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 <= -1.3e+79) {
		tmp = x * (1.0 + (z * -6.0));
	} else if (x <= -30.0) {
		tmp = x + (6.0 * (y * z));
	} else if ((x <= -6e-53) || !(x <= 1220000000000.0)) {
		tmp = x + (z * (x * -6.0));
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e+79:
		tmp = x * (1.0 + (z * -6.0))
	elif x <= -30.0:
		tmp = x + (6.0 * (y * z))
	elif (x <= -6e-53) or not (x <= 1220000000000.0):
		tmp = x + (z * (x * -6.0))
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+79)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	elseif (x <= -30.0)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif ((x <= -6e-53) || !(x <= 1220000000000.0))
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	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 <= -1.3e+79)
		tmp = x * (1.0 + (z * -6.0));
	elseif (x <= -30.0)
		tmp = x + (6.0 * (y * z));
	elseif ((x <= -6e-53) || ~((x <= 1220000000000.0)))
		tmp = x + (z * (x * -6.0));
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+79], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -30.0], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -6e-53], N[Not[LessEqual[x, 1220000000000.0]], $MachinePrecision]], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.30000000000000007e79

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.7%

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

   if -1.30000000000000007e79 < x < -30

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 93.9%

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

   if -30 < x < -6.0000000000000004e-53 or 1.22e12 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 83.1%

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

   if -6.0000000000000004e-53 < x < 1.22e12

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 94.6%

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

      1. associate-*r* 94.6%

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

   4. Simplified 94.6%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq -30:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-53} \lor \neg \left(x \leq 1220000000000\right):\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]

Alternative 4: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + 6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -27:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;x \leq 245000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* 6.0 (* y z)))) (t_1 (* x (+ 1.0 (* z -6.0)))))
   (if (<= x -6.5e+77)
     t_1
     (if (<= x -27.0)
       t_0
       (if (<= x -6e-53)
         (* z (* x -6.0))
         (if (<= x 245000000000.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (6.0 * (y * z));
	double t_1 = x * (1.0 + (z * -6.0));
	double tmp;
	if (x <= -6.5e+77) {
		tmp = t_1;
	} else if (x <= -27.0) {
		tmp = t_0;
	} else if (x <= -6e-53) {
		tmp = z * (x * -6.0);
	} else if (x <= 245000000000.0) {
		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 = x + (6.0d0 * (y * z))
    t_1 = x * (1.0d0 + (z * (-6.0d0)))
    if (x <= (-6.5d+77)) then
        tmp = t_1
    else if (x <= (-27.0d0)) then
        tmp = t_0
    else if (x <= (-6d-53)) then
        tmp = z * (x * (-6.0d0))
    else if (x <= 245000000000.0d0) 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 = x + (6.0 * (y * z));
	double t_1 = x * (1.0 + (z * -6.0));
	double tmp;
	if (x <= -6.5e+77) {
		tmp = t_1;
	} else if (x <= -27.0) {
		tmp = t_0;
	} else if (x <= -6e-53) {
		tmp = z * (x * -6.0);
	} else if (x <= 245000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (6.0 * (y * z))
	t_1 = x * (1.0 + (z * -6.0))
	tmp = 0
	if x <= -6.5e+77:
		tmp = t_1
	elif x <= -27.0:
		tmp = t_0
	elif x <= -6e-53:
		tmp = z * (x * -6.0)
	elif x <= 245000000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(6.0 * Float64(y * z)))
	t_1 = Float64(x * Float64(1.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (x <= -6.5e+77)
		tmp = t_1;
	elseif (x <= -27.0)
		tmp = t_0;
	elseif (x <= -6e-53)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (x <= 245000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (6.0 * (y * z));
	t_1 = x * (1.0 + (z * -6.0));
	tmp = 0.0;
	if (x <= -6.5e+77)
		tmp = t_1;
	elseif (x <= -27.0)
		tmp = t_0;
	elseif (x <= -6e-53)
		tmp = z * (x * -6.0);
	elseif (x <= 245000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e+77], t$95$1, If[LessEqual[x, -27.0], t$95$0, If[LessEqual[x, -6e-53], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 245000000000.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5e77 or 2.45e11 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 87.3%

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

   if -6.5e77 < x < -27 or -6.0000000000000004e-53 < x < 2.45e11

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 94.5%

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

   if -27 < x < -6.0000000000000004e-53

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 79.9%

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

   3. Taylor expanded in z around inf 79.9%

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

      1. *-commutative 79.9%

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

      2. associate-*r* 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq -27:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;x \leq 245000000000:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]

Alternative 5: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq -27:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-53}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;x \leq 900000000000:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.1e+81)
   (* x (+ 1.0 (* z -6.0)))
   (if (<= x -27.0)
     (+ x (* 6.0 (* y z)))
     (if (<= x -6e-53)
       (+ x (* z (* x -6.0)))
       (if (<= x 900000000000.0)
         (+ x (* z (* y 6.0)))
         (+ x (* -6.0 (* x z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.1e+81) {
		tmp = x * (1.0 + (z * -6.0));
	} else if (x <= -27.0) {
		tmp = x + (6.0 * (y * z));
	} else if (x <= -6e-53) {
		tmp = x + (z * (x * -6.0));
	} else if (x <= 900000000000.0) {
		tmp = x + (z * (y * 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 (x <= (-7.1d+81)) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    else if (x <= (-27.0d0)) then
        tmp = x + (6.0d0 * (y * z))
    else if (x <= (-6d-53)) then
        tmp = x + (z * (x * (-6.0d0)))
    else if (x <= 900000000000.0d0) then
        tmp = x + (z * (y * 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 (x <= -7.1e+81) {
		tmp = x * (1.0 + (z * -6.0));
	} else if (x <= -27.0) {
		tmp = x + (6.0 * (y * z));
	} else if (x <= -6e-53) {
		tmp = x + (z * (x * -6.0));
	} else if (x <= 900000000000.0) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.1e+81:
		tmp = x * (1.0 + (z * -6.0))
	elif x <= -27.0:
		tmp = x + (6.0 * (y * z))
	elif x <= -6e-53:
		tmp = x + (z * (x * -6.0))
	elif x <= 900000000000.0:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.1e+81)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	elseif (x <= -27.0)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif (x <= -6e-53)
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	elseif (x <= 900000000000.0)
		tmp = Float64(x + Float64(z * Float64(y * 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 (x <= -7.1e+81)
		tmp = x * (1.0 + (z * -6.0));
	elseif (x <= -27.0)
		tmp = x + (6.0 * (y * z));
	elseif (x <= -6e-53)
		tmp = x + (z * (x * -6.0));
	elseif (x <= 900000000000.0)
		tmp = x + (z * (y * 6.0));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.1e+81], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -27.0], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-53], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 900000000000.0], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.09999999999999967e81

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.7%

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

   if -7.09999999999999967e81 < x < -27

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 93.9%

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

   if -27 < x < -6.0000000000000004e-53

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 80.1%

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

   if -6.0000000000000004e-53 < x < 9e11

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 94.6%

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

      1. associate-*r* 94.6%

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

   4. Simplified 94.6%

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

   if 9e11 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 83.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right) + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq -27:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-53}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;x \leq 900000000000:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.16 \lor \neg \left(z \leq 51000\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.16) (not (<= z 51000.0))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.16) || !(z <= 51000.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.16d0)) .or. (.not. (z <= 51000.0d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.16) || !(z <= 51000.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.16) or not (z <= 51000.0):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.16) || !(z <= 51000.0))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.16) || ~((z <= 51000.0)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.16], N[Not[LessEqual[z, 51000.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.160000000000000003 or 51000 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 48.0%

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

   3. Taylor expanded in z around inf 47.3%

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

   if -0.160000000000000003 < z < 51000

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 62.1%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.16 \lor \neg \left(z \leq 51000\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 51000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.16) (* -6.0 (* x z)) (if (<= z 51000.0) x (* z (* x -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.16) {
		tmp = -6.0 * (x * z);
	} else if (z <= 51000.0) {
		tmp = x;
	} else {
		tmp = z * (x * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.16d0)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 51000.0d0) then
        tmp = x
    else
        tmp = z * (x * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.16) {
		tmp = -6.0 * (x * z);
	} else if (z <= 51000.0) {
		tmp = x;
	} else {
		tmp = z * (x * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.16:
		tmp = -6.0 * (x * z)
	elif z <= 51000.0:
		tmp = x
	else:
		tmp = z * (x * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.16)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 51000.0)
		tmp = x;
	else
		tmp = Float64(z * Float64(x * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.16)
		tmp = -6.0 * (x * z);
	elseif (z <= 51000.0)
		tmp = x;
	else
		tmp = z * (x * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.16], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 51000.0], x, N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.160000000000000003

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 43.2%

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

   3. Taylor expanded in z around inf 42.3%

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

   if -0.160000000000000003 < z < 51000

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 62.1%

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

   if 51000 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 54.6%

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

   3. Taylor expanded in z around inf 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*r* 54.3%

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

   5. Simplified 54.3%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 51000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 8: 61.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 + (z * (-6.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around inf 54.8%

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

3. Final simplification 54.8%

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

Alternative 9: 36.4% 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 30.7%

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

3. Final simplification 30.7%

   \[\leadsto x \]

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 2023229 
(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)))