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

Percentage Accurate: 99.7% → 99.7%

Time: 7.4s

Alternatives: 8

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: 99.7% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 72.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+57}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+34} \lor \neg \left(y \leq -5.8 \cdot 10^{-78}\right) \land y \leq 3.1 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.06e+57)
   (* 6.0 (* y z))
   (if (or (<= y -2.2e+34) (and (not (<= y -5.8e-78)) (<= y 3.1e+65)))
     (* x (+ (* z -6.0) 1.0))
     (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.06e+57) {
		tmp = 6.0 * (y * z);
	} else if ((y <= -2.2e+34) || (!(y <= -5.8e-78) && (y <= 3.1e+65))) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = 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 (y <= (-1.06d+57)) then
        tmp = 6.0d0 * (y * z)
    else if ((y <= (-2.2d+34)) .or. (.not. (y <= (-5.8d-78))) .and. (y <= 3.1d+65)) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.06e+57) {
		tmp = 6.0 * (y * z);
	} else if ((y <= -2.2e+34) || (!(y <= -5.8e-78) && (y <= 3.1e+65))) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.06e+57:
		tmp = 6.0 * (y * z)
	elif (y <= -2.2e+34) or (not (y <= -5.8e-78) and (y <= 3.1e+65)):
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.06e+57)
		tmp = Float64(6.0 * Float64(y * z));
	elseif ((y <= -2.2e+34) || (!(y <= -5.8e-78) && (y <= 3.1e+65)))
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.06e+57)
		tmp = 6.0 * (y * z);
	elseif ((y <= -2.2e+34) || (~((y <= -5.8e-78)) && (y <= 3.1e+65)))
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.06e+57], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.2e+34], And[N[Not[LessEqual[y, -5.8e-78]], $MachinePrecision], LessEqual[y, 3.1e+65]]], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e57

   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 93.1%

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

      1. *-commutative 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + 6 \cdot \frac{y \cdot z}{x}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 74.6%

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

      2. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in x around 0 78.3%

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

   if -1.06e57 < y < -2.2000000000000002e34 or -5.8000000000000001e-78 < y < 3.09999999999999991e65

   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 85.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 85.2%

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

   5. Simplified 85.2%

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

   if -2.2000000000000002e34 < y < -5.8000000000000001e-78 or 3.09999999999999991e65 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in x around inf 70.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + 6 \cdot \frac{y \cdot z}{x}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 70.5%

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

      2. associate-/l* 68.1%

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

   8. Simplified 68.1%

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

   9. Taylor expanded in x around 0 74.8%

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

       1. associate-*r* 74.9%

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

       2. *-commutative 74.9%

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

   11. Simplified 74.9%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+57}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+34} \lor \neg \left(y \leq -5.8 \cdot 10^{-78}\right) \land y \leq 3.1 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+100} \lor \neg \left(x \leq 1.7 \cdot 10^{+148}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e+100) (not (<= x 1.7e+148)))
   (* x (+ (* z -6.0) 1.0))
   (+ x (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e+100) || !(x <= 1.7e+148)) {
		tmp = x * ((z * -6.0) + 1.0);
	} 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 <= (-5.2d+100)) .or. (.not. (x <= 1.7d+148))) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    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 <= -5.2e+100) || !(x <= 1.7e+148)) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e+100) or not (x <= 1.7e+148):
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e+100) || !(x <= 1.7e+148))
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	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 <= -5.2e+100) || ~((x <= 1.7e+148)))
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e+100], N[Not[LessEqual[x, 1.7e+148]], $MachinePrecision]], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2000000000000003e100 or 1.7000000000000001e148 < x

   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 92.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 92.6%

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

   5. Simplified 92.6%

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

   if -5.2000000000000003e100 < x < 1.7000000000000001e148

   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 89.4%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+100} \lor \neg \left(x \leq 1.7 \cdot 10^{+148}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.06 \cdot 10^{+101} \lor \neg \left(x \leq 2.8 \cdot 10^{+148}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.06e+101) (not (<= x 2.8e+148)))
   (* x (+ (* z -6.0) 1.0))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.06e+101) || !(x <= 2.8e+148)) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.06d+101)) .or. (.not. (x <= 2.8d+148))) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.06e+101) || !(x <= 2.8e+148)) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.06e+101) or not (x <= 2.8e+148):
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.06e+101) || !(x <= 2.8e+148))
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.06e+101) || ~((x <= 2.8e+148)))
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.06e+101], N[Not[LessEqual[x, 2.8e+148]], $MachinePrecision]], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05999999999999993e101 or 2.7999999999999998e148 < x

   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 92.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 92.6%

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

   5. Simplified 92.6%

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

   if -2.05999999999999993e101 < x < 2.7999999999999998e148

   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 89.4%

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

      1. *-commutative 89.4%

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

   5. Simplified 89.4%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.06 \cdot 10^{+101} \lor \neg \left(x \leq 2.8 \cdot 10^{+148}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-34} \lor \neg \left(z \leq 1.58 \cdot 10^{-58}\right):\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e-34) (not (<= z 1.58e-58))) (* z (* y 6.0)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-34) || !(z <= 1.58e-58)) {
		tmp = z * (y * 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 <= (-4d-34)) .or. (.not. (z <= 1.58d-58))) then
        tmp = z * (y * 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 <= -4e-34) || !(z <= 1.58e-58)) {
		tmp = z * (y * 6.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e-34) or not (z <= 1.58e-58):
		tmp = z * (y * 6.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e-34) || !(z <= 1.58e-58))
		tmp = Float64(z * Float64(y * 6.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4e-34) || ~((z <= 1.58e-58)))
		tmp = z * (y * 6.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e-34], N[Not[LessEqual[z, 1.58e-58]], $MachinePrecision]], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999971e-34 or 1.57999999999999997e-58 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 66.2%

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

      1. *-commutative 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in x around inf 49.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + 6 \cdot \frac{y \cdot z}{x}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 49.5%

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

      2. associate-/l* 46.4%

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

   8. Simplified 46.4%

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

   9. Taylor expanded in x around 0 62.7%

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

       1. associate-*r* 62.7%

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

       2. *-commutative 62.7%

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

   11. Simplified 62.7%

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

   if -3.99999999999999971e-34 < z < 1.57999999999999997e-58

   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 76.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-34} \lor \neg \left(z \leq 1.58 \cdot 10^{-58}\right):\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{-33} \lor \neg \left(z \leq 1.46 \cdot 10^{-61}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.95e-33) (not (<= z 1.46e-61))) (* 6.0 (* y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.95e-33) || !(z <= 1.46e-61)) {
		tmp = 6.0 * (y * 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 <= (-2.95d-33)) .or. (.not. (z <= 1.46d-61))) then
        tmp = 6.0d0 * (y * 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 <= -2.95e-33) || !(z <= 1.46e-61)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.95e-33) or not (z <= 1.46e-61):
		tmp = 6.0 * (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.95e-33) || !(z <= 1.46e-61))
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.95e-33) || ~((z <= 1.46e-61)))
		tmp = 6.0 * (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.95e-33], N[Not[LessEqual[z, 1.46e-61]], $MachinePrecision]], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.94999999999999993e-33 or 1.46e-61 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 66.2%

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

      1. *-commutative 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in x around inf 49.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + 6 \cdot \frac{y \cdot z}{x}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 49.5%

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

      2. associate-/l* 46.4%

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

   8. Simplified 46.4%

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

   9. Taylor expanded in x around 0 62.7%

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

   if -2.94999999999999993e-33 < z < 1.46e-61

   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 76.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{-33} \lor \neg \left(z \leq 1.46 \cdot 10^{-61}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.166))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.166)) {
		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 <= (-0.165d0)) .or. (.not. (z <= 0.166d0))) 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 <= -0.165) || !(z <= 0.166)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 0.166):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.166))
		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 <= -0.165) || ~((z <= 0.166)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 0.166]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 0.166000000000000009 < z

   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 0 95.2%

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

      1. fma-define 95.2%

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

      2. *-commutative 95.2%

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

      3. associate-*r* 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in x around inf 43.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   7. Step-by-step derivation

      1. +-commutative 43.5%

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

      2. *-commutative 43.5%

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

   8. Simplified 43.5%

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

   9. Taylor expanded in z around inf 41.8%

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

   10. Taylor expanded in x around 0 41.7%

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

   if -0.165000000000000008 < z < 0.166000000000000009

   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 66.5%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.3% 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. Add Preprocessing

3. Taylor expanded in z around 0 33.2%

   \[\leadsto \color{blue}{x} \]
4. 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 2024091 
(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)))