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

Percentage Accurate: 95.9% → 97.9%

Time: 9.6s

Alternatives: 9

Speedup: 1.1×

• 20.3% 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: 95.9% 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: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -inf.0

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 70.7

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

   5. Simplified 70.7%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 100.0

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

   7. Applied egg-rr 100.0%

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

   if -inf.0 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 98.4%

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

   4. Applied egg-rr 98.4%

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

4. Final simplification 98.5%

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

Alternative 2: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;1 - y \leq -2 \cdot 10^{+69}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - y \leq 2 \cdot 10^{+119}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= (- 1.0 y) -2e+69)
     t_0
     (if (<= (- 1.0 y) 2e+119) (- x (* z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if ((1.0 - y) <= -2e+69) {
		tmp = t_0;
	} else if ((1.0 - y) <= 2e+119) {
		tmp = x - (z * x);
	} 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 * (y * z)
    if ((1.0d0 - y) <= (-2d+69)) then
        tmp = t_0
    else if ((1.0d0 - y) <= 2d+119) then
        tmp = x - (z * x)
    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 * (y * z);
	double tmp;
	if ((1.0 - y) <= -2e+69) {
		tmp = t_0;
	} else if ((1.0 - y) <= 2e+119) {
		tmp = x - (z * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if (1.0 - y) <= -2e+69:
		tmp = t_0
	elif (1.0 - y) <= 2e+119:
		tmp = x - (z * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (Float64(1.0 - y) <= -2e+69)
		tmp = t_0;
	elseif (Float64(1.0 - y) <= 2e+119)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	tmp = 0.0;
	if ((1.0 - y) <= -2e+69)
		tmp = t_0;
	elseif ((1.0 - y) <= 2e+119)
		tmp = x - (z * x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 - y), $MachinePrecision], -2e+69], t$95$0, If[LessEqual[N[(1.0 - y), $MachinePrecision], 2e+119], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -2.0000000000000001e69 or 1.99999999999999989e119 < (-.f64 #s(literal 1 binary64) y)

   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 inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 83.0

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

   5. Simplified 83.0%

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

   if -2.0000000000000001e69 < (-.f64 #s(literal 1 binary64) y) < 1.99999999999999989e119

   1. Initial program 98.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. --lowering--.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 91.3

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

   5. Simplified 91.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;1 - y \leq 2 \cdot 10^{+119}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y, z \cdot x, x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.185:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma y (* z x) x)))
   (if (<= y -1.0) t_0 (if (<= y 0.185) (- x (* z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(y, (z * x), x);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.185) {
		tmp = x - (z * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(y, Float64(z * x), x)
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 0.185)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 0.185], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.185 < y

   1. Initial program 93.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 94.7%

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

   if -1 < y < 0.185

   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

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   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. --lowering--.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 98.5

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

   5. Simplified 98.5%

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

Alternative 4: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+49}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.7e+66)
   (* y (* z x))
   (if (<= y 9.5e+49) (- x (* z x)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.7e+66) {
		tmp = y * (z * x);
	} else if (y <= 9.5e+49) {
		tmp = x - (z * x);
	} 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 <= (-4.7d+66)) then
        tmp = y * (z * x)
    else if (y <= 9.5d+49) then
        tmp = x - (z * x)
    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 <= -4.7e+66) {
		tmp = y * (z * x);
	} else if (y <= 9.5e+49) {
		tmp = x - (z * x);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.7e+66:
		tmp = y * (z * x)
	elif y <= 9.5e+49:
		tmp = x - (z * x)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.7e+66)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 9.5e+49)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.7e+66)
		tmp = y * (z * x);
	elseif (y <= 9.5e+49)
		tmp = x - (z * x);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.7e+66], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+49], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7000000000000002e66

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 80.9

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

   5. Simplified 80.9%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 87.0

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

   7. Applied egg-rr 87.0%

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

   if -4.7000000000000002e66 < y < 9.49999999999999969e49

   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

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
   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. --lowering--.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 94.3

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

   5. Simplified 94.3%

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

   if 9.49999999999999969e49 < y

   1. Initial program 91.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 81.6

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

   5. Simplified 81.6%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+49}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+49}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y x))))
   (if (<= y -1.95e+119) t_0 (if (<= y 1.15e+49) (- x (* z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * x);
	double tmp;
	if (y <= -1.95e+119) {
		tmp = t_0;
	} else if (y <= 1.15e+49) {
		tmp = x - (z * x);
	} 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 <= (-1.95d+119)) then
        tmp = t_0
    else if (y <= 1.15d+49) then
        tmp = x - (z * x)
    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 <= -1.95e+119) {
		tmp = t_0;
	} else if (y <= 1.15e+49) {
		tmp = x - (z * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * x)
	tmp = 0
	if y <= -1.95e+119:
		tmp = t_0
	elif y <= 1.15e+49:
		tmp = x - (z * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * x))
	tmp = 0.0
	if (y <= -1.95e+119)
		tmp = t_0;
	elseif (y <= 1.15e+49)
		tmp = Float64(x - Float64(z * x));
	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 <= -1.95e+119)
		tmp = t_0;
	elseif (y <= 1.15e+49)
		tmp = x - (z * x);
	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, -1.95e+119], t$95$0, If[LessEqual[y, 1.15e+49], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9499999999999999e119 or 1.15000000000000001e49 < y

   1. Initial program 92.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 85.5

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

   5. Simplified 85.5%

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

   if -1.9499999999999999e119 < y < 1.15000000000000001e49

   1. Initial program 99.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. --lowering--.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 92.3

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

   5. Simplified 92.3%

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

Alternative 6: 65.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 93.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. --lowering--.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. *-lowering-*.f64 93.1

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

   5. Simplified 93.1%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. neg-lowering-neg.f64 60.7

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

   8. Simplified 60.7%

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

   if -1 < z < 1

   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

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

   5. Simplified 72.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-z \cdot x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.1% 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 96.7%

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

4. Applied egg-rr 98.1%

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

Alternative 8: 66.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ x - z \cdot x \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
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. --lowering--.f64 N/A

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

   4. *-commutative N/A

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

   5. *-lowering-*.f64 67.1

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

5. Simplified 67.1%

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

Alternative 9: 39.1% accurate, 17.0× 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 96.7%

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

3. Taylor expanded in z around 0

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

5. Simplified 35.9%

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

Developer Target 1: 99.8% 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 2024199 
(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))))