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

Percentage Accurate: 96.3% → 99.9%

Time: 8.5s

Alternatives: 9

Speedup: 1.1×

• 21.9% 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: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ t_1 := \left(x \cdot \left(y - 1\right)\right) \cdot z\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{+262}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(y - 1\right), x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)) (t_1 (* (* x (- y 1.0)) z)))
   (if (<= t_0 -1e+246)
     t_1
     (if (<= t_0 1e+262) (fma (* z (- y 1.0)) x 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 <= -1e+246) {
		tmp = t_1;
	} else if (t_0 <= 1e+262) {
		tmp = fma((z * (y - 1.0)), x, 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 <= -1e+246)
		tmp = t_1;
	elseif (t_0 <= 1e+262)
		tmp = fma(Float64(z * Float64(y - 1.0)), x, 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, -1e+246], t$95$1, If[LessEqual[t$95$0, 1e+262], N[(N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] * x + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -1.00000000000000007e246 or 1e262 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 68.5%

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

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

      14. associate-*r* N/A

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

      15. neg-mul-1 N/A

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

      16. distribute-lft-neg-in 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 99.9%

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

   if -1.00000000000000007e246 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1e262

   1. Initial program 99.9%

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

   4. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+246}:\\ \;\;\;\;\left(x \cdot \left(y - 1\right)\right) \cdot z\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 10^{+262}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(y - 1\right), x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y - 1\right)\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(z \cdot y, x, x\right)\\ \mathbf{if}\;1 - y \leq -1000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - y \leq 1:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{elif}\;1 - y \leq 5 \cdot 10^{+232}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* z y) x x)))
   (if (<= (- 1.0 y) -1000.0)
     t_0
     (if (<= (- 1.0 y) 1.0)
       (* (- 1.0 z) x)
       (if (<= (- 1.0 y) 5e+232) t_0 (* (* x z) y))))))

C

double code(double x, double y, double z) {
	double t_0 = fma((z * y), x, x);
	double tmp;
	if ((1.0 - y) <= -1000.0) {
		tmp = t_0;
	} else if ((1.0 - y) <= 1.0) {
		tmp = (1.0 - z) * x;
	} else if ((1.0 - y) <= 5e+232) {
		tmp = t_0;
	} else {
		tmp = (x * z) * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(z * y), x, x)
	tmp = 0.0
	if (Float64(1.0 - y) <= -1000.0)
		tmp = t_0;
	elseif (Float64(1.0 - y) <= 1.0)
		tmp = Float64(Float64(1.0 - z) * x);
	elseif (Float64(1.0 - y) <= 5e+232)
		tmp = t_0;
	else
		tmp = Float64(Float64(x * z) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * y), $MachinePrecision] * x + x), $MachinePrecision]}, If[LessEqual[N[(1.0 - y), $MachinePrecision], -1000.0], t$95$0, If[LessEqual[N[(1.0 - y), $MachinePrecision], 1.0], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(1.0 - y), $MachinePrecision], 5e+232], t$95$0, N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -1e3 or 1 < (-.f64 #s(literal 1 binary64) y) < 4.99999999999999987e232

   1. Initial program 93.2%

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

   4. Applied rewrites 93.3%

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

   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. lower-*.f64 91.7

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

   7. Applied rewrites 91.7%

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

   if -1e3 < (-.f64 #s(literal 1 binary64) 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 99.2

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

   5. Applied rewrites 99.2%

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

   if 4.99999999999999987e232 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 89.2%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 84.4

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

   5. Applied rewrites 84.4%

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

   7. Applied rewrites 86.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -1000:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x, x\right)\\ \mathbf{elif}\;1 - y \leq 1:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{elif}\;1 - y \leq 5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \]
5. 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 2024230 
(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))))