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

Percentage Accurate: 96.3% → 98.1%

Time: 7.3s

Alternatives: 9

Speedup: 1.1×

• 21.6% 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: 96.3% 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: 98.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

4. Applied rewrites 97.6%

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

5. Final simplification 97.6%

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

Alternative 2: 96.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ t_1 := \left(x \cdot \left(y - 1\right)\right) \cdot z\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(-1, x \cdot z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)) (t_1 (* (* x (- y 1.0)) z)))
   (if (<= t_0 -5e+15) t_1 (if (<= t_0 2e-6) (fma -1.0 (* x z) x) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double t_1 = (x * (y - 1.0)) * z;
	double tmp;
	if (t_0 <= -5e+15) {
		tmp = t_1;
	} else if (t_0 <= 2e-6) {
		tmp = fma(-1.0, (x * z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	t_1 = Float64(Float64(x * Float64(y - 1.0)) * z)
	tmp = 0.0
	if (t_0 <= -5e+15)
		tmp = t_1;
	elseif (t_0 <= 2e-6)
		tmp = fma(-1.0, Float64(x * z), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+15], t$95$1, If[LessEqual[t$95$0, 2e-6], N[(-1.0 * N[(x * z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -5e15 or 1.99999999999999991e-6 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. *-commutative N/A

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

      7. cancel-sign-sub N/A

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

      8. mul-1-neg N/A

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

      9. *-rgt-identity N/A

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

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

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

      11. mul-1-neg N/A

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

      12. distribute-lft-neg-in N/A

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

      13. *-commutative N/A

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

      14. associate-*r* N/A

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

      15. distribute-rgt-neg-in N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

   5. Applied rewrites 95.4%

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

   if -5e15 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1.99999999999999991e-6

   1. Initial program 100.0%

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 97.9%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\left(x \cdot \left(y - 1\right)\right) \cdot z\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(-1, x \cdot z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y - 1\right)\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;1 - y \leq 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(-1, x \cdot z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 y) -2e+19)
   (* (* x z) y)
   (if (<= (- 1.0 y) 1e+31) (fma -1.0 (* x z) x) (* (* z y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - y) <= -2e+19) {
		tmp = (x * z) * y;
	} else if ((1.0 - y) <= 1e+31) {
		tmp = fma(-1.0, (x * z), x);
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - y) <= -2e+19)
		tmp = Float64(Float64(x * z) * y);
	elseif (Float64(1.0 - y) <= 1e+31)
		tmp = fma(-1.0, Float64(x * z), x);
	else
		tmp = Float64(Float64(z * y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(1.0 - y), $MachinePrecision], -2e+19], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(1.0 - y), $MachinePrecision], 1e+31], N[(-1.0 * N[(x * z), $MachinePrecision] + x), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -2e19

   1. Initial program 90.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 76.8

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

   5. Applied rewrites 76.8%

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

   if -2e19 < (-.f64 #s(literal 1 binary64) y) < 9.9999999999999996e30

   1. Initial program 100.0%

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 98.0%

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

   if 9.9999999999999996e30 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 96.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lower-*.f64 75.7

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

   5. Applied rewrites 75.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;1 - y \leq 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(-1, x \cdot z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;1 - y \leq 10^{+31}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 y) -2e+19)
   (* (* x z) y)
   (if (<= (- 1.0 y) 1e+31) (* (- 1.0 z) x) (* (* z y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - y) <= -2e+19) {
		tmp = (x * z) * y;
	} else if ((1.0 - y) <= 1e+31) {
		tmp = (1.0 - 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 ((1.0d0 - y) <= (-2d+19)) then
        tmp = (x * z) * y
    else if ((1.0d0 - y) <= 1d+31) then
        tmp = (1.0d0 - 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 ((1.0 - y) <= -2e+19) {
		tmp = (x * z) * y;
	} else if ((1.0 - y) <= 1e+31) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (z * y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (1.0 - y) <= -2e+19:
		tmp = (x * z) * y
	elif (1.0 - y) <= 1e+31:
		tmp = (1.0 - z) * x
	else:
		tmp = (z * y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - y) <= -2e+19)
		tmp = Float64(Float64(x * z) * y);
	elseif (Float64(1.0 - y) <= 1e+31)
		tmp = Float64(Float64(1.0 - z) * x);
	else
		tmp = Float64(Float64(z * y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((1.0 - y) <= -2e+19)
		tmp = (x * z) * y;
	elseif ((1.0 - y) <= 1e+31)
		tmp = (1.0 - z) * x;
	else
		tmp = (z * y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(1.0 - y), $MachinePrecision], -2e+19], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(1.0 - y), $MachinePrecision], 1e+31], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -2e19

   1. Initial program 90.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 76.8

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

   5. Applied rewrites 76.8%

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

   if -2e19 < (-.f64 #s(literal 1 binary64) y) < 9.9999999999999996e30

   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 98.0

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

   5. Applied rewrites 98.0%

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

   if 9.9999999999999996e30 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 96.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lower-*.f64 75.7

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

   5. Applied rewrites 75.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;1 - y \leq 10^{+31}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;1 - y \leq 10^{+31}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 y) -2e+19)
   (* (* x z) y)
   (if (<= (- 1.0 y) 1e+31) (* (- 1.0 z) x) (* (* x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - y) <= -2e+19) {
		tmp = (x * z) * y;
	} else if ((1.0 - y) <= 1e+31) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (x * y) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((1.0d0 - y) <= (-2d+19)) then
        tmp = (x * z) * y
    else if ((1.0d0 - y) <= 1d+31) then
        tmp = (1.0d0 - z) * x
    else
        tmp = (x * y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - y) <= -2e+19) {
		tmp = (x * z) * y;
	} else if ((1.0 - y) <= 1e+31) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = (x * y) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (1.0 - y) <= -2e+19:
		tmp = (x * z) * y
	elif (1.0 - y) <= 1e+31:
		tmp = (1.0 - z) * x
	else:
		tmp = (x * y) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - y) <= -2e+19)
		tmp = Float64(Float64(x * z) * y);
	elseif (Float64(1.0 - y) <= 1e+31)
		tmp = Float64(Float64(1.0 - z) * x);
	else
		tmp = Float64(Float64(x * y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((1.0 - y) <= -2e+19)
		tmp = (x * z) * y;
	elseif ((1.0 - y) <= 1e+31)
		tmp = (1.0 - z) * x;
	else
		tmp = (x * y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(1.0 - y), $MachinePrecision], -2e+19], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(1.0 - y), $MachinePrecision], 1e+31], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -2e19

   1. Initial program 90.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 76.8

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

   5. Applied rewrites 76.8%

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

   if -2e19 < (-.f64 #s(literal 1 binary64) y) < 9.9999999999999996e30

   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 98.0

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

   5. Applied rewrites 98.0%

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

   if 9.9999999999999996e30 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 96.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 72.6

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

   5. Applied rewrites 72.6%

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

   7. Applied rewrites 74.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;1 - y \leq 10^{+31}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot z\right) \cdot y\\ \mathbf{if}\;1 - y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - y \leq 10^{+31}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* x z) y)))
   (if (<= (- 1.0 y) -2e+19)
     t_0
     (if (<= (- 1.0 y) 1e+31) (* (- 1.0 z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * z) * y;
	double tmp;
	if ((1.0 - y) <= -2e+19) {
		tmp = t_0;
	} else if ((1.0 - y) <= 1e+31) {
		tmp = (1.0 - 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 * z) * y
    if ((1.0d0 - y) <= (-2d+19)) then
        tmp = t_0
    else if ((1.0d0 - y) <= 1d+31) then
        tmp = (1.0d0 - 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 * z) * y;
	double tmp;
	if ((1.0 - y) <= -2e+19) {
		tmp = t_0;
	} else if ((1.0 - y) <= 1e+31) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * z) * y
	tmp = 0
	if (1.0 - y) <= -2e+19:
		tmp = t_0
	elif (1.0 - y) <= 1e+31:
		tmp = (1.0 - z) * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * z) * y)
	tmp = 0.0
	if (Float64(1.0 - y) <= -2e+19)
		tmp = t_0;
	elseif (Float64(1.0 - y) <= 1e+31)
		tmp = Float64(Float64(1.0 - z) * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * z) * y;
	tmp = 0.0;
	if ((1.0 - y) <= -2e+19)
		tmp = t_0;
	elseif ((1.0 - y) <= 1e+31)
		tmp = (1.0 - z) * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(1.0 - y), $MachinePrecision], -2e+19], t$95$0, If[LessEqual[N[(1.0 - y), $MachinePrecision], 1e+31], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -2e19 or 9.9999999999999996e30 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 93.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

   if -2e19 < (-.f64 #s(literal 1 binary64) y) < 9.9999999999999996e30

   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 98.0

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

   5. Applied rewrites 98.0%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \mathbf{elif}\;1 - y \leq 10^{+31}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot x\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-12}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) x)))
   (if (<= z -1.0) t_0 (if (<= z 8.2e-12) (* 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 <= 8.2e-12) {
		tmp = 1.0 * 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 <= 8.2d-12) then
        tmp = 1.0d0 * 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 <= 8.2e-12) {
		tmp = 1.0 * 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 <= 8.2e-12:
		tmp = 1.0 * 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 <= 8.2e-12)
		tmp = Float64(1.0 * 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 <= 8.2e-12)
		tmp = 1.0 * 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, 8.2e-12], N[(1.0 * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 8.19999999999999979e-12 < z

   1. Initial program 93.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 54.3

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

   5. Applied rewrites 54.3%

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

   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 53.2%

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

   if -1 < z < 8.19999999999999979e-12

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 69.5

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

   5. Applied rewrites 69.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 68.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-12}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.3% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
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 63.0

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

5. Applied rewrites 63.0%

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

6. Final simplification 63.0%

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

Alternative 9: 39.0% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
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 63.0

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

5. Applied rewrites 63.0%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 40.7%

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

9. Final simplification 40.7%

   \[\leadsto 1 \cdot x \]
10. 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 2024331 
(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))))