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

Percentage Accurate: 99.7% → 99.7%

Time: 8.7s

Alternatives: 8

Speedup: 1.0×

• 21.8% 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 99.9%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
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: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+96} \lor \neg \left(y \leq -4.8 \cdot 10^{+57}\right) \land \left(y \leq -2.4 \cdot 10^{-57} \lor \neg \left(y \leq 2.05 \cdot 10^{-18}\right)\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.2e+96)
         (and (not (<= y -4.8e+57))
              (or (<= y -2.4e-57) (not (<= y 2.05e-18)))))
   (+ x (* 6.0 (* y z)))
   (* x (+ 1.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.2e+96) || (!(y <= -4.8e+57) && ((y <= -2.4e-57) || !(y <= 2.05e-18)))) {
		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 <= (-8.2d+96)) .or. (.not. (y <= (-4.8d+57))) .and. (y <= (-2.4d-57)) .or. (.not. (y <= 2.05d-18))) 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 <= -8.2e+96) || (!(y <= -4.8e+57) && ((y <= -2.4e-57) || !(y <= 2.05e-18)))) {
		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 <= -8.2e+96) or (not (y <= -4.8e+57) and ((y <= -2.4e-57) or not (y <= 2.05e-18))):
		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 <= -8.2e+96) || (!(y <= -4.8e+57) && ((y <= -2.4e-57) || !(y <= 2.05e-18))))
		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 <= -8.2e+96) || (~((y <= -4.8e+57)) && ((y <= -2.4e-57) || ~((y <= 2.05e-18)))))
		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, -8.2e+96], And[N[Not[LessEqual[y, -4.8e+57]], $MachinePrecision], Or[LessEqual[y, -2.4e-57], N[Not[LessEqual[y, 2.05e-18]], $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 < -8.19999999999999996e96 or -4.80000000000000009e57 < y < -2.40000000000000006e-57 or 2.0499999999999999e-18 < y

   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 inf 93.4%

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

      1. *-commutative 93.4%

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

   5. Simplified 93.4%

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

   if -8.19999999999999996e96 < y < -4.80000000000000009e57 or -2.40000000000000006e-57 < y < 2.0499999999999999e-18

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 88.3%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+96} \lor \neg \left(y \leq -4.8 \cdot 10^{+57}\right) \land \left(y \leq -2.4 \cdot 10^{-57} \lor \neg \left(y \leq 2.05 \cdot 10^{-18}\right)\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + z \cdot -6\right)\\ t_1 := x + z \cdot \left(y \cdot 6\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-57}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-21}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* z -6.0)))) (t_1 (+ x (* z (* y 6.0)))))
   (if (<= y -8.2e+96)
     t_1
     (if (<= y -6.2e+62)
       t_0
       (if (<= y -3.4e-57)
         (+ x (* 6.0 (* y z)))
         (if (<= y 1.36e-21) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * -6.0));
	double t_1 = x + (z * (y * 6.0));
	double tmp;
	if (y <= -8.2e+96) {
		tmp = t_1;
	} else if (y <= -6.2e+62) {
		tmp = t_0;
	} else if (y <= -3.4e-57) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 1.36e-21) {
		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 * (1.0d0 + (z * (-6.0d0)))
    t_1 = x + (z * (y * 6.0d0))
    if (y <= (-8.2d+96)) then
        tmp = t_1
    else if (y <= (-6.2d+62)) then
        tmp = t_0
    else if (y <= (-3.4d-57)) then
        tmp = x + (6.0d0 * (y * z))
    else if (y <= 1.36d-21) 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 * (1.0 + (z * -6.0));
	double t_1 = x + (z * (y * 6.0));
	double tmp;
	if (y <= -8.2e+96) {
		tmp = t_1;
	} else if (y <= -6.2e+62) {
		tmp = t_0;
	} else if (y <= -3.4e-57) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 1.36e-21) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (z * -6.0))
	t_1 = x + (z * (y * 6.0))
	tmp = 0
	if y <= -8.2e+96:
		tmp = t_1
	elif y <= -6.2e+62:
		tmp = t_0
	elif y <= -3.4e-57:
		tmp = x + (6.0 * (y * z))
	elif y <= 1.36e-21:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(z * -6.0)))
	t_1 = Float64(x + Float64(z * Float64(y * 6.0)))
	tmp = 0.0
	if (y <= -8.2e+96)
		tmp = t_1;
	elseif (y <= -6.2e+62)
		tmp = t_0;
	elseif (y <= -3.4e-57)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif (y <= 1.36e-21)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 + (z * -6.0));
	t_1 = x + (z * (y * 6.0));
	tmp = 0.0;
	if (y <= -8.2e+96)
		tmp = t_1;
	elseif (y <= -6.2e+62)
		tmp = t_0;
	elseif (y <= -3.4e-57)
		tmp = x + (6.0 * (y * z));
	elseif (y <= 1.36e-21)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+96], t$95$1, If[LessEqual[y, -6.2e+62], t$95$0, If[LessEqual[y, -3.4e-57], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.36e-21], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.19999999999999996e96 or 1.3599999999999999e-21 < y

   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 inf 95.2%

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

   if -8.19999999999999996e96 < y < -6.20000000000000029e62 or -3.40000000000000016e-57 < y < 1.3599999999999999e-21

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 88.3%

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

   if -6.20000000000000029e62 < y < -3.40000000000000016e-57

   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 86.0%

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

      1. *-commutative 86.0%

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

   5. Simplified 86.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+96}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-57}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 0.165000000000000008 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 90.1%

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

   4. Taylor expanded in z around inf 89.6%

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

      1. *-commutative 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in y around 0 50.7%

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

   if -0.170000000000000012 < z < 0.165000000000000008

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 66.6%

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

4. Final simplification 59.5%

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

Alternative 5: 60.9% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17) (* x (* z -6.0)) (if (<= z 0.165) x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = x * (z * -6.0);
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = -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 <= (-0.17d0)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 0.165d0) then
        tmp = x
    else
        tmp = (-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 <= -0.17) {
		tmp = x * (z * -6.0);
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = x * (z * -6.0)
	elif z <= 0.165:
		tmp = x
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.165], x, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 55.8%

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

   4. Taylor expanded in z around inf 55.8%

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

      1. *-commutative 94.5%

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

   6. Simplified 55.8%

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

   if -0.170000000000000012 < z < 0.165000000000000008

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 66.6%

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

   if 0.165000000000000008 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.5%

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

   4. Taylor expanded in z around inf 84.5%

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

      1. *-commutative 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in y around 0 45.4%

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

4. Final simplification 59.5%

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

Alternative 6: 60.9% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17) (* x (* z -6.0)) (if (<= z 0.165) x (* z (* x -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = x * (z * -6.0);
	} else if (z <= 0.165) {
		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 <= (-0.17d0)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 0.165d0) 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 <= -0.17) {
		tmp = x * (z * -6.0);
	} else if (z <= 0.165) {
		tmp = x;
	} else {
		tmp = z * (x * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = x * (z * -6.0)
	elif z <= 0.165:
		tmp = x
	else:
		tmp = z * (x * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= 0.165)
		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 <= -0.17)
		tmp = x * (z * -6.0);
	elseif (z <= 0.165)
		tmp = x;
	else
		tmp = z * (x * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.165], x, N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 55.8%

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

   4. Taylor expanded in z around inf 55.8%

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

      1. *-commutative 94.5%

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

   6. Simplified 55.8%

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

   if -0.170000000000000012 < z < 0.165000000000000008

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 66.6%

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

   if 0.165000000000000008 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.5%

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

   4. Taylor expanded in z around inf 84.5%

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

      1. *-commutative 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in y around 0 45.4%

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

      1. associate-*r* 45.4%

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

      2. *-commutative 45.4%

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

      3. *-commutative 45.4%

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

   9. Simplified 45.4%

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

4. Final simplification 59.5%

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

Alternative 7: 62.0% 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 99.9%

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

3. Taylor expanded in x around inf 60.9%

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

4. Final simplification 60.9%

   \[\leadsto x \cdot \left(1 + z \cdot -6\right) \]
5. Add Preprocessing

Alternative 8: 35.9% 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 99.9%

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

3. Taylor expanded in z around 0 38.3%

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

4. Final simplification 38.3%

   \[\leadsto x \]
5. Add Preprocessing

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 2024045 
(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)))