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

Percentage Accurate: 95.9% → 95.9%

Time: 10.8s

Alternatives: 5

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

   \[x \cdot \left(1 - y \cdot z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. sub-neg N/A

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

   3. distribute-rgt-in N/A

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

   4. *-lft-identity N/A

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

   5. +-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-neg.f64 96.9

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

4. Applied rewrites 96.9%

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

Alternative 2: 93.9% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))) (t_1 (* (* y z) (- x))))
   (if (<= t_0 -10.0) t_1 (if (<= t_0 2.0) x t_1))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double t_1 = (y * z) * -x;
	double tmp;
	if (t_0 <= -10.0) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 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 = 1.0d0 - (y * z)
    t_1 = (y * z) * -x
    if (t_0 <= (-10.0d0)) then
        tmp = t_1
    else if (t_0 <= 2.0d0) then
        tmp = 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 = 1.0 - (y * z);
	double t_1 = (y * z) * -x;
	double tmp;
	if (t_0 <= -10.0) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y * z)
	t_1 = (y * z) * -x
	tmp = 0
	if t_0 <= -10.0:
		tmp = t_1
	elif t_0 <= 2.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	t_1 = Float64(Float64(y * z) * Float64(-x))
	tmp = 0.0
	if (t_0 <= -10.0)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	t_1 = (y * z) * -x;
	tmp = 0.0;
	if (t_0 <= -10.0)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[t$95$0, -10.0], t$95$1, If[LessEqual[t$95$0, 2.0], x, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -10 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 93.3

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

   5. Applied rewrites 93.3%

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

   if -10 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 96.6%

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

      1. *-rgt-identity 96.6

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

   7. Applied rewrites 96.6%

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

4. Final simplification 94.9%

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

Alternative 3: 93.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \cdot z \leq 0.05:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5e+17)
   (* (* y z) (- x))
   (if (<= (* y z) 0.05) x (- (* y (* z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+17) {
		tmp = (y * z) * -x;
	} else if ((y * z) <= 0.05) {
		tmp = x;
	} else {
		tmp = -(y * (z * 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 * z) <= (-5d+17)) then
        tmp = (y * z) * -x
    else if ((y * z) <= 0.05d0) then
        tmp = x
    else
        tmp = -(y * (z * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+17) {
		tmp = (y * z) * -x;
	} else if ((y * z) <= 0.05) {
		tmp = x;
	} else {
		tmp = -(y * (z * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -5e+17:
		tmp = (y * z) * -x
	elif (y * z) <= 0.05:
		tmp = x
	else:
		tmp = -(y * (z * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -5e+17)
		tmp = Float64(Float64(y * z) * Float64(-x));
	elseif (Float64(y * z) <= 0.05)
		tmp = x;
	else
		tmp = Float64(-Float64(y * Float64(z * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -5e+17)
		tmp = (y * z) * -x;
	elseif ((y * z) <= 0.05)
		tmp = x;
	else
		tmp = -(y * (z * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+17], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.05], x, (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5e17

   1. Initial program 93.8%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 93.8

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

   5. Applied rewrites 93.8%

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

   if -5e17 < (*.f64 y z) < 0.050000000000000003

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 96.6%

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

      1. *-rgt-identity 96.6

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

   7. Applied rewrites 96.6%

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

   if 0.050000000000000003 < (*.f64 y z)

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 91.2

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

   5. Applied rewrites 91.2%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \cdot z \leq 0.05:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

Alternative 5: 50.7% accurate, 14.0× 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 96.9%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 48.1%

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

   1. *-rgt-identity 48.1

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

7. Applied rewrites 48.1%

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

Reproduce

herbie shell --seed 2024216 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))