Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 95.8% → 97.6%

Time: 9.6s

Alternatives: 11

Speedup: 1.1×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * 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 * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * 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 * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq 10^{+301}:\\ \;\;\;\;\mathsf{fma}\left(\left(y + -1\right) \cdot z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z (- 1.0 y)) 1e+301) (fma (* (+ y -1.0) z) x x) (* y (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * (1.0 - y)) <= 1e+301) {
		tmp = fma(((y + -1.0) * z), x, x);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * Float64(1.0 - y)) <= 1e+301)
		tmp = fma(Float64(Float64(y + -1.0) * z), x, x);
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1e+301], N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] * x + x), $MachinePrecision], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1.00000000000000005e301

   1. Initial program 98.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 98.4%

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

   if 1.00000000000000005e301 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 60.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 100.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq 10^{+301}:\\ \;\;\;\;\mathsf{fma}\left(\left(y + -1\right) \cdot z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ t_1 := x \cdot \left(y \cdot z - z\right)\\ \mathbf{if}\;t\_0 \leq -20000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 20000000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, x, x\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))) (t_1 (* x (- (* y z) z))))
   (if (<= t_0 -20000000000000.0)
     t_1
     (if (<= t_0 20000000.0)
       (fma (* y z) x x)
       (if (<= t_0 1e+301) t_1 (* y (* z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double t_1 = x * ((y * z) - z);
	double tmp;
	if (t_0 <= -20000000000000.0) {
		tmp = t_1;
	} else if (t_0 <= 20000000.0) {
		tmp = fma((y * z), x, x);
	} else if (t_0 <= 1e+301) {
		tmp = t_1;
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	t_1 = Float64(x * Float64(Float64(y * z) - z))
	tmp = 0.0
	if (t_0 <= -20000000000000.0)
		tmp = t_1;
	elseif (t_0 <= 20000000.0)
		tmp = fma(Float64(y * z), x, x);
	elseif (t_0 <= 1e+301)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -20000000000000.0], t$95$1, If[LessEqual[t$95$0, 20000000.0], N[(N[(y * z), $MachinePrecision] * x + x), $MachinePrecision], If[LessEqual[t$95$0, 1e+301], t$95$1, N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -2e13 or 2e7 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1.00000000000000005e301

   1. Initial program 97.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 96.2

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

   5. Applied rewrites 96.2%

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

   if -2e13 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 2e7

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 97.7

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

   7. Applied rewrites 97.7%

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

   if 1.00000000000000005e301 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 60.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 100.0%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -20000000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - z\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 20000000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, x, x\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 10^{+301}:\\ \;\;\;\;x \cdot \left(y \cdot z - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y \cdot z, x, x\right)\\ \mathbf{if}\;y \leq -260000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* y z) x x)))
   (if (<= y -260000000000.0) t_0 (if (<= y 1.0) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((y * z), x, x);
	double tmp;
	if (y <= -260000000000.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(y * z), x, x)
	tmp = 0.0
	if (y <= -260000000000.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * z), $MachinePrecision] * x + x), $MachinePrecision]}, If[LessEqual[y, -260000000000.0], t$95$0, If[LessEqual[y, 1.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e11 or 1 < y

   1. Initial program 92.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 92.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.6

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

   7. Applied rewrites 91.6%

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

   if -2.6e11 < y < 1

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 98.8

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

   5. Applied rewrites 98.8%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -260000000000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, x, x\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e+36)
   (* y (* z x))
   (if (<= y 8.4e+36) (* x (- 1.0 z)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+36) {
		tmp = y * (z * x);
	} else if (y <= 8.4e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (y * 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 (y <= (-1.65d+36)) then
        tmp = y * (z * x)
    else if (y <= 8.4d+36) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+36) {
		tmp = y * (z * x);
	} else if (y <= 8.4e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e+36:
		tmp = y * (z * x)
	elif y <= 8.4e+36:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e+36)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 8.4e+36)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.65e+36)
		tmp = y * (z * x);
	elseif (y <= 8.4e+36)
		tmp = x * (1.0 - z);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e+36], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.4e+36], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999e36

   1. Initial program 94.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 84.0

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

   5. Applied rewrites 84.0%

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

   7. Applied rewrites 87.3%

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

   if -1.6499999999999999e36 < y < 8.40000000000000018e36

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 94.3

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

   5. Applied rewrites 94.3%

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

   if 8.40000000000000018e36 < y

   1. Initial program 90.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 71.7

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

   5. Applied rewrites 71.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+36}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y x))))
   (if (<= y -1.65e+36) t_0 (if (<= y 8.4e+36) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * x);
	double tmp;
	if (y <= -1.65e+36) {
		tmp = t_0;
	} else if (y <= 8.4e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_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 = z * (y * x)
    if (y <= (-1.65d+36)) then
        tmp = t_0
    else if (y <= 8.4d+36) then
        tmp = x * (1.0d0 - z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y * x);
	double tmp;
	if (y <= -1.65e+36) {
		tmp = t_0;
	} else if (y <= 8.4e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * x)
	tmp = 0
	if y <= -1.65e+36:
		tmp = t_0
	elif y <= 8.4e+36:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * x))
	tmp = 0.0
	if (y <= -1.65e+36)
		tmp = t_0;
	elseif (y <= 8.4e+36)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * x);
	tmp = 0.0;
	if (y <= -1.65e+36)
		tmp = t_0;
	elseif (y <= 8.4e+36)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+36], t$95$0, If[LessEqual[y, 8.4e+36], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6499999999999999e36 or 8.40000000000000018e36 < y

   1. Initial program 91.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if -1.6499999999999999e36 < y < 8.40000000000000018e36

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 94.3

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

   5. Applied rewrites 94.3%

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

Alternative 6: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 165:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -1.0) t_0 (if (<= z 165.0) (* x 1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 165.0) {
		tmp = x * 1.0;
	} else {
		tmp = t_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 * -z
    if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 165.0d0) then
        tmp = x * 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 165.0) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -1.0:
		tmp = t_0
	elif z <= 165.0:
		tmp = x * 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 165.0)
		tmp = Float64(x * 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 165.0)
		tmp = x * 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 165.0], N[(x * 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 165 < z

   1. Initial program 92.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 55.8

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

   5. Applied rewrites 55.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 54.2%

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

   if -1 < z < 165

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 70.1%

      \[\leadsto x \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -7000:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 y) -7000.0) (fma x z x) (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - y) <= -7000.0) {
		tmp = fma(x, z, x);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - y) <= -7000.0)
		tmp = fma(x, z, x);
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(1.0 - y), $MachinePrecision], -7000.0], N[(x * z + x), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -7e3

   1. Initial program 91.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 89.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{1}{\mathsf{fma}\left(z, 1 + y, 1\right)}}} \]

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

         \[\leadsto \color{blue}{x \cdot z + x \cdot 1} \]

      3. *-rgt-identity N/A

         \[\leadsto x \cdot z + \color{blue}{x} \]

      4. lower-fma.f64 39.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, z, x\right)} \]

   7. Applied rewrites 39.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, z, x\right)} \]

   if -7e3 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 98.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot z} \]

      2. *-rgt-identity N/A

         \[\leadsto \color{blue}{x} - x \cdot z \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - x \cdot z} \]

      4. *-commutative N/A

         \[\leadsto x - \color{blue}{z \cdot x} \]

      5. lower-*.f64 77.2

         \[\leadsto x - \color{blue}{z \cdot x} \]

   5. Applied rewrites 77.2%

      \[\leadsto \color{blue}{x - z \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 68.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.0) (* x (- 1.0 z)) (fma x z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < 1

   1. Initial program 98.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if 1 < y

   1. Initial program 91.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 89.4%

      \[\leadsto \color{blue}{\frac{x}{\frac{1}{\mathsf{fma}\left(z, 1 + y, 1\right)}}} \]

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

         \[\leadsto \color{blue}{x \cdot z + x \cdot 1} \]

      3. *-rgt-identity N/A

         \[\leadsto x \cdot z + \color{blue}{x} \]

      4. lower-fma.f64 40.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, z, x\right)} \]

   7. Applied rewrites 40.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, z, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 98.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y + -1, z \cdot x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.6%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

4. Applied rewrites 97.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y + -1, z \cdot x, x\right)} \]
5. Add Preprocessing

Alternative 10: 40.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, z, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x z x))

C

double code(double x, double y, double z) {
	return fma(x, z, x);
}

Julia

function code(x, y, z)
	return fma(x, z, x)
end

Wolfram

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

Derivation

1. Initial program 96.6%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

4. Applied rewrites 71.0%

   \[\leadsto \color{blue}{\frac{x}{\frac{1}{\mathsf{fma}\left(z, 1 + y, 1\right)}}} \]

5. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. distribute-lft-in N/A

      \[\leadsto \color{blue}{x \cdot z + x \cdot 1} \]

   3. *-rgt-identity N/A

      \[\leadsto x \cdot z + \color{blue}{x} \]

   4. lower-fma.f64 41.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, z, x\right)} \]

7. Applied rewrites 41.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, z, x\right)} \]
8. Add Preprocessing

Alternative 11: 38.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ x \cdot 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 1.0))

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto x \cdot \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 39.2%

   \[\leadsto x \cdot \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t\_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} 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 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    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 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024232 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- 1 (* (- 1 y) z))) -161819597360704900000000000000000000000000000000000) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 389223764966390300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x))))))

  (* x (- 1.0 (* (- 1.0 y) z))))