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

Percentage Accurate: 99.7% → 99.7%

Time: 7.6s

Alternatives: 9

Speedup: 1.0×

• 20.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y * 6.0 + N[(x * (-6.0)), $MachinePrecision]), $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. Step-by-step derivation

   1. *-commutative 99.8%

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

   2. sub-neg 99.8%

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

   3. distribute-rgt-in 99.8%

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

   4. fma-def 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31500000000 \lor \neg \left(y \leq -7 \cdot 10^{-155} \lor \neg \left(y \leq -1.1 \cdot 10^{-170}\right) \land y \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -31500000000.0)
         (not (or (<= y -7e-155) (and (not (<= y -1.1e-170)) (<= y 8e-99)))))
   (+ x (* 6.0 (* y z)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -31500000000.0) || !((y <= -7e-155) || (!(y <= -1.1e-170) && (y <= 8e-99)))) {
		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 ((y <= (-31500000000.0d0)) .or. (.not. (y <= (-7d-155)) .or. (.not. (y <= (-1.1d-170))) .and. (y <= 8d-99))) 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 ((y <= -31500000000.0) || !((y <= -7e-155) || (!(y <= -1.1e-170) && (y <= 8e-99)))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -31500000000.0) or not ((y <= -7e-155) or (not (y <= -1.1e-170) and (y <= 8e-99))):
		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 ((y <= -31500000000.0) || !((y <= -7e-155) || (!(y <= -1.1e-170) && (y <= 8e-99))))
		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 ((y <= -31500000000.0) || ~(((y <= -7e-155) || (~((y <= -1.1e-170)) && (y <= 8e-99)))))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -31500000000.0], N[Not[Or[LessEqual[y, -7e-155], And[N[Not[LessEqual[y, -1.1e-170]], $MachinePrecision], LessEqual[y, 8e-99]]]], $MachinePrecision]], 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 2 regimes

2. if y < -3.15e10 or -7.00000000000000031e-155 < y < -1.10000000000000007e-170 or 8.0000000000000002e-99 < y

   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 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

   if -3.15e10 < y < -7.00000000000000031e-155 or -1.10000000000000007e-170 < y < 8.0000000000000002e-99

   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 90.3%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31500000000 \lor \neg \left(y \leq -7 \cdot 10^{-155} \lor \neg \left(y \leq -1.1 \cdot 10^{-170}\right) \land y \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -280000000000 \lor \neg \left(y \leq -7.5 \cdot 10^{-155} \lor \neg \left(y \leq -1.1 \cdot 10^{-170}\right) \land y \leq 2.7 \cdot 10^{-98}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -280000000000.0)
         (not
          (or (<= y -7.5e-155) (and (not (<= y -1.1e-170)) (<= y 2.7e-98)))))
   (+ x (* 6.0 (* y z)))
   (+ x (* x (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -280000000000.0) || !((y <= -7.5e-155) || (!(y <= -1.1e-170) && (y <= 2.7e-98)))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (x * (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 <= (-280000000000.0d0)) .or. (.not. (y <= (-7.5d-155)) .or. (.not. (y <= (-1.1d-170))) .and. (y <= 2.7d-98))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + (x * (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -280000000000.0) || !((y <= -7.5e-155) || (!(y <= -1.1e-170) && (y <= 2.7e-98)))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (x * (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -280000000000.0) or not ((y <= -7.5e-155) or (not (y <= -1.1e-170) and (y <= 2.7e-98))):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (x * (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -280000000000.0) || !((y <= -7.5e-155) || (!(y <= -1.1e-170) && (y <= 2.7e-98))))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -280000000000.0) || ~(((y <= -7.5e-155) || (~((y <= -1.1e-170)) && (y <= 2.7e-98)))))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (x * (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -280000000000.0], N[Not[Or[LessEqual[y, -7.5e-155], And[N[Not[LessEqual[y, -1.1e-170]], $MachinePrecision], LessEqual[y, 2.7e-98]]]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e11 or -7.5000000000000006e-155 < y < -1.10000000000000007e-170 or 2.6999999999999999e-98 < y

   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 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

   if -2.8e11 < y < -7.5000000000000006e-155 or -1.10000000000000007e-170 < y < 2.6999999999999999e-98

   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 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r* 90.3%

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

      3. *-commutative 90.3%

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

   5. Simplified 90.3%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -280000000000 \lor \neg \left(y \leq -7.5 \cdot 10^{-155} \lor \neg \left(y \leq -1.1 \cdot 10^{-170}\right) \land y \leq 2.7 \cdot 10^{-98}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -125000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-155}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-170} \lor \neg \left(y \leq 2.2 \cdot 10^{-98}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* 6.0 (* y z)))))
   (if (<= y -125000000000.0)
     t_0
     (if (<= y -8.5e-155)
       (+ x (* x (* z -6.0)))
       (if (or (<= y -1.1e-170) (not (<= y 2.2e-98)))
         t_0
         (+ x (* z (* x -6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (6.0 * (y * z));
	double tmp;
	if (y <= -125000000000.0) {
		tmp = t_0;
	} else if (y <= -8.5e-155) {
		tmp = x + (x * (z * -6.0));
	} else if ((y <= -1.1e-170) || !(y <= 2.2e-98)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x + (6.0d0 * (y * z))
    if (y <= (-125000000000.0d0)) then
        tmp = t_0
    else if (y <= (-8.5d-155)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if ((y <= (-1.1d-170)) .or. (.not. (y <= 2.2d-98))) then
        tmp = t_0
    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 t_0 = x + (6.0 * (y * z));
	double tmp;
	if (y <= -125000000000.0) {
		tmp = t_0;
	} else if (y <= -8.5e-155) {
		tmp = x + (x * (z * -6.0));
	} else if ((y <= -1.1e-170) || !(y <= 2.2e-98)) {
		tmp = t_0;
	} else {
		tmp = x + (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (6.0 * (y * z))
	tmp = 0
	if y <= -125000000000.0:
		tmp = t_0
	elif y <= -8.5e-155:
		tmp = x + (x * (z * -6.0))
	elif (y <= -1.1e-170) or not (y <= 2.2e-98):
		tmp = t_0
	else:
		tmp = x + (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(6.0 * Float64(y * z)))
	tmp = 0.0
	if (y <= -125000000000.0)
		tmp = t_0;
	elseif (y <= -8.5e-155)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif ((y <= -1.1e-170) || !(y <= 2.2e-98))
		tmp = t_0;
	else
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (6.0 * (y * z));
	tmp = 0.0;
	if (y <= -125000000000.0)
		tmp = t_0;
	elseif (y <= -8.5e-155)
		tmp = x + (x * (z * -6.0));
	elseif ((y <= -1.1e-170) || ~((y <= 2.2e-98)))
		tmp = t_0;
	else
		tmp = x + (z * (x * -6.0));
	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]}, If[LessEqual[y, -125000000000.0], t$95$0, If[LessEqual[y, -8.5e-155], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.1e-170], N[Not[LessEqual[y, 2.2e-98]], $MachinePrecision]], t$95$0, N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e11 or -8.4999999999999996e-155 < y < -1.10000000000000007e-170 or 2.19999999999999996e-98 < y

   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 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

   if -1.25e11 < y < -8.4999999999999996e-155

   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 0 82.2%

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

      1. *-commutative 82.2%

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

      2. associate-*r* 82.2%

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

      3. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   if -1.10000000000000007e-170 < y < 2.19999999999999996e-98

   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 95.0%

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

      1. associate-*r* 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -125000000000:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-155}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-170} \lor \neg \left(y \leq 2.2 \cdot 10^{-98}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \left(y \cdot 6\right)\\ \mathbf{if}\;y \leq -31500000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-155}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-98}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (* y 6.0)))))
   (if (<= y -31500000000.0)
     t_0
     (if (<= y -7e-155)
       (+ x (* x (* z -6.0)))
       (if (<= y -1.1e-170)
         t_0
         (if (<= y 1.1e-98) (+ x (* z (* x -6.0))) (+ x (* 6.0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * (y * 6.0));
	double tmp;
	if (y <= -31500000000.0) {
		tmp = t_0;
	} else if (y <= -7e-155) {
		tmp = x + (x * (z * -6.0));
	} else if (y <= -1.1e-170) {
		tmp = t_0;
	} else if (y <= 1.1e-98) {
		tmp = x + (z * (x * -6.0));
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x + (z * (y * 6.0d0))
    if (y <= (-31500000000.0d0)) then
        tmp = t_0
    else if (y <= (-7d-155)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if (y <= (-1.1d-170)) then
        tmp = t_0
    else if (y <= 1.1d-98) then
        tmp = x + (z * (x * (-6.0d0)))
    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 t_0 = x + (z * (y * 6.0));
	double tmp;
	if (y <= -31500000000.0) {
		tmp = t_0;
	} else if (y <= -7e-155) {
		tmp = x + (x * (z * -6.0));
	} else if (y <= -1.1e-170) {
		tmp = t_0;
	} else if (y <= 1.1e-98) {
		tmp = x + (z * (x * -6.0));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * (y * 6.0))
	tmp = 0
	if y <= -31500000000.0:
		tmp = t_0
	elif y <= -7e-155:
		tmp = x + (x * (z * -6.0))
	elif y <= -1.1e-170:
		tmp = t_0
	elif y <= 1.1e-98:
		tmp = x + (z * (x * -6.0))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z * Float64(y * 6.0)))
	tmp = 0.0
	if (y <= -31500000000.0)
		tmp = t_0;
	elseif (y <= -7e-155)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif (y <= -1.1e-170)
		tmp = t_0;
	elseif (y <= 1.1e-98)
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (z * (y * 6.0));
	tmp = 0.0;
	if (y <= -31500000000.0)
		tmp = t_0;
	elseif (y <= -7e-155)
		tmp = x + (x * (z * -6.0));
	elseif (y <= -1.1e-170)
		tmp = t_0;
	elseif (y <= 1.1e-98)
		tmp = x + (z * (x * -6.0));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -31500000000.0], t$95$0, If[LessEqual[y, -7e-155], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-170], t$95$0, If[LessEqual[y, 1.1e-98], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.15e10 or -7.00000000000000031e-155 < y < -1.10000000000000007e-170

   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 95.5%

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

   if -3.15e10 < y < -7.00000000000000031e-155

   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 0 82.2%

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

      1. *-commutative 82.2%

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

      2. associate-*r* 82.2%

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

      3. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   if -1.10000000000000007e-170 < y < 1.09999999999999998e-98

   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 95.0%

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

      1. associate-*r* 95.1%

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

   5. Simplified 95.1%

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

   if 1.09999999999999998e-98 < y

   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 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31500000000:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-155}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-170}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-98}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \left(y \cdot 6\right)\\ \mathbf{if}\;y \leq -235000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-155}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-99}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (* y 6.0)))))
   (if (<= y -235000000000.0)
     t_0
     (if (<= y -7e-155)
       (+ x (* x (* z -6.0)))
       (if (<= y -4.8e-171)
         t_0
         (if (<= y 7.2e-99) (+ x (* z (* x -6.0))) (+ x (* y (* 6.0 z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * (y * 6.0));
	double tmp;
	if (y <= -235000000000.0) {
		tmp = t_0;
	} else if (y <= -7e-155) {
		tmp = x + (x * (z * -6.0));
	} else if (y <= -4.8e-171) {
		tmp = t_0;
	} else if (y <= 7.2e-99) {
		tmp = x + (z * (x * -6.0));
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (z * (y * 6.0d0))
    if (y <= (-235000000000.0d0)) then
        tmp = t_0
    else if (y <= (-7d-155)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if (y <= (-4.8d-171)) then
        tmp = t_0
    else if (y <= 7.2d-99) then
        tmp = x + (z * (x * (-6.0d0)))
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (z * (y * 6.0));
	double tmp;
	if (y <= -235000000000.0) {
		tmp = t_0;
	} else if (y <= -7e-155) {
		tmp = x + (x * (z * -6.0));
	} else if (y <= -4.8e-171) {
		tmp = t_0;
	} else if (y <= 7.2e-99) {
		tmp = x + (z * (x * -6.0));
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * (y * 6.0))
	tmp = 0
	if y <= -235000000000.0:
		tmp = t_0
	elif y <= -7e-155:
		tmp = x + (x * (z * -6.0))
	elif y <= -4.8e-171:
		tmp = t_0
	elif y <= 7.2e-99:
		tmp = x + (z * (x * -6.0))
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z * Float64(y * 6.0)))
	tmp = 0.0
	if (y <= -235000000000.0)
		tmp = t_0;
	elseif (y <= -7e-155)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif (y <= -4.8e-171)
		tmp = t_0;
	elseif (y <= 7.2e-99)
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (z * (y * 6.0));
	tmp = 0.0;
	if (y <= -235000000000.0)
		tmp = t_0;
	elseif (y <= -7e-155)
		tmp = x + (x * (z * -6.0));
	elseif (y <= -4.8e-171)
		tmp = t_0;
	elseif (y <= 7.2e-99)
		tmp = x + (z * (x * -6.0));
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -235000000000.0], t$95$0, If[LessEqual[y, -7e-155], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-171], t$95$0, If[LessEqual[y, 7.2e-99], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.35e11 or -7.00000000000000031e-155 < y < -4.79999999999999974e-171

   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 95.5%

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

   if -2.35e11 < y < -7.00000000000000031e-155

   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 0 82.2%

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

      1. *-commutative 82.2%

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

      2. associate-*r* 82.2%

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

      3. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   if -4.79999999999999974e-171 < y < 7.2000000000000001e-99

   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 95.0%

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

      1. associate-*r* 95.1%

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

   5. Simplified 95.1%

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

   if 7.2000000000000001e-99 < y

   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 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

      1. add-sqr-sqrt 50.2%

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

      2. pow2 50.2%

         \[\leadsto x + \color{blue}{{\left(\sqrt{6 \cdot \left(z \cdot y\right)}\right)}^{2}} \]

      3. associate-*r* 50.2%

         \[\leadsto x + {\left(\sqrt{\color{blue}{\left(6 \cdot z\right) \cdot y}}\right)}^{2} \]

      4. *-commutative 50.2%

         \[\leadsto x + {\left(\sqrt{\color{blue}{y \cdot \left(6 \cdot z\right)}}\right)}^{2} \]

   7. Applied egg-rr 50.2%

      \[\leadsto x + \color{blue}{{\left(\sqrt{y \cdot \left(6 \cdot z\right)}\right)}^{2}} \]
   8. Step-by-step derivation

      1. unpow2 50.2%

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

      2. add-sqr-sqrt 95.4%

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

      3. *-commutative 95.4%

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

   9. Applied egg-rr 95.4%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -235000000000:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-155}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-171}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-99}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 8: 62.1% 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 99.8%

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

3. Taylor expanded in y around 0 64.9%

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

4. Final simplification 64.9%

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

Alternative 9: 36.2% 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 40.2%

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

4. Final simplification 40.2%

   \[\leadsto x \]
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 2024019 
(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)))