Data.Colour.RGB:hslsv from colour-2.3.3, D

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))

C

double code(double x, double y) {
	return (x - y) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (x + y);
}

Python

def code(x, y):
	return (x - y) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (x + y);
end

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))

C

double code(double x, double y) {
	return (x - y) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (x + y);
}

Python

def code(x, y):
	return (x - y) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (x + y);
end

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))

C

double code(double x, double y) {
	return (x - y) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (x + y);
}

Python

def code(x, y):
	return (x - y) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (x + y);
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{x + y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{x + y} \leq -0.5:\\ \;\;\;\;-1 + \frac{x + x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (+ x y)) -0.5) (+ -1.0 (/ (+ x x) y)) (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= -0.5) {
		tmp = -1.0 + ((x + x) / y);
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x - y) / (x + y)) <= (-0.5d0)) then
        tmp = (-1.0d0) + ((x + x) / y)
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= -0.5) {
		tmp = -1.0 + ((x + x) / y);
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (x + y)) <= -0.5:
		tmp = -1.0 + ((x + x) / y)
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(x + y)) <= -0.5)
		tmp = Float64(-1.0 + Float64(Float64(x + x) / y));
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x - y) / (x + y)) <= -0.5)
		tmp = -1.0 + ((x + x) / y);
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -0.5], N[(-1.0 + N[(N[(x + x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (+.f64 x y)) < -0.5

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y} - 1} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y} + \left(\mathsf{neg}\left(1\right)\right)} \]

      2. *-lft-identity N/A

         \[\leadsto 2 \cdot \frac{\color{blue}{1 \cdot x}}{y} + \left(\mathsf{neg}\left(1\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\frac{1}{y} \cdot x\right)} + \left(\mathsf{neg}\left(1\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{y}\right) \cdot x} + \left(\mathsf{neg}\left(1\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \left(2 \cdot \frac{1}{y}\right) \cdot x + \color{blue}{-1} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{-1 + \left(2 \cdot \frac{1}{y}\right) \cdot x} \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{-1 + \left(2 \cdot \frac{1}{y}\right) \cdot x} \]

      8. associate-*r/ N/A

         \[\leadsto -1 + \color{blue}{\frac{2 \cdot 1}{y}} \cdot x \]

      9. metadata-eval N/A

         \[\leadsto -1 + \frac{\color{blue}{2}}{y} \cdot x \]

      10. associate-*l/ N/A

          \[\leadsto -1 + \color{blue}{\frac{2 \cdot x}{y}} \]

      11. metadata-eval N/A

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

      12. distribute-rgt1-in N/A

          \[\leadsto -1 + \frac{\color{blue}{x + 1 \cdot x}}{y} \]

      13. metadata-eval N/A

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

      14. cancel-sign-sub-inv N/A

          \[\leadsto -1 + \frac{\color{blue}{x - -1 \cdot x}}{y} \]

      15. /-lowering-/.f64 N/A

          \[\leadsto -1 + \color{blue}{\frac{x - -1 \cdot x}{y}} \]

      16. cancel-sign-sub-inv N/A

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

      17. metadata-eval N/A

          \[\leadsto -1 + \frac{x + \color{blue}{1} \cdot x}{y} \]

      18. *-lft-identity N/A

          \[\leadsto -1 + \frac{x + \color{blue}{x}}{y} \]

      19. +-lowering-+.f64 99.6

          \[\leadsto -1 + \frac{\color{blue}{x + x}}{y} \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{-1 + \frac{x + x}{y}} \]

   if -0.5 < (/.f64 (-.f64 x y) (+.f64 x y))

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 99.6%

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

Alternative 3: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{x + y} \leq -0.5:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (+ x y)) -0.5) (+ -1.0 (/ x y)) (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= -0.5) {
		tmp = -1.0 + (x / y);
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x - y) / (x + y)) <= (-0.5d0)) then
        tmp = (-1.0d0) + (x / y)
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= -0.5) {
		tmp = -1.0 + (x / y);
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (x + y)) <= -0.5:
		tmp = -1.0 + (x / y)
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(x + y)) <= -0.5)
		tmp = Float64(-1.0 + Float64(x / y));
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x - y) / (x + y)) <= -0.5)
		tmp = -1.0 + (x / y);
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -0.5], N[(-1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (+.f64 x y)) < -0.5

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 98.0%

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

      1. div-sub N/A

         \[\leadsto \color{blue}{\frac{x}{y} - \frac{y}{y}} \]

      2. *-inverses N/A

         \[\leadsto \frac{x}{y} - \color{blue}{1} \]

      3. metadata-eval N/A

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

      4. --lowering--.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. metadata-eval 98.0

         \[\leadsto \frac{x}{y} - \color{blue}{1} \]

   7. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\frac{x}{y} - 1} \]

   if -0.5 < (/.f64 (-.f64 x y) (+.f64 x y))

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 99.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{x + y} \leq -0.5:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{x + y} \leq -0.5:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (+ x y)) -0.5) (+ -1.0 (/ x y)) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= -0.5) {
		tmp = -1.0 + (x / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x - y) / (x + y)) <= (-0.5d0)) then
        tmp = (-1.0d0) + (x / y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= -0.5) {
		tmp = -1.0 + (x / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (x + y)) <= -0.5:
		tmp = -1.0 + (x / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(x + y)) <= -0.5)
		tmp = Float64(-1.0 + Float64(x / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x - y) / (x + y)) <= -0.5)
		tmp = -1.0 + (x / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -0.5], N[(-1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (+.f64 x y)) < -0.5

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 98.0%

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

      1. div-sub N/A

         \[\leadsto \color{blue}{\frac{x}{y} - \frac{y}{y}} \]

      2. *-inverses N/A

         \[\leadsto \frac{x}{y} - \color{blue}{1} \]

      3. metadata-eval N/A

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

      4. --lowering--.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. metadata-eval 98.0

         \[\leadsto \frac{x}{y} - \color{blue}{1} \]

   7. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\frac{x}{y} - 1} \]

   if -0.5 < (/.f64 (-.f64 x y) (+.f64 x y))

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 99.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{x + y} \leq -0.5:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{x + y} \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= (/ (- x y) (+ x y)) -0.5) -1.0 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= -0.5) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x - y) / (x + y)) <= (-0.5d0)) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x - y) / (x + y)) <= -0.5) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (x + y)) <= -0.5:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(x + y)) <= -0.5)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x - y) / (x + y)) <= -0.5)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -0.5], -1.0, 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (+.f64 x y)) < -0.5

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 97.9%

      \[\leadsto \color{blue}{-1} \]

   if -0.5 < (/.f64 (-.f64 x y) (+.f64 x y))

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 99.6%

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

Alternative 6: 49.7% accurate, 18.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{x + y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Simplified 52.4%

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

Developer Target 1: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} - \frac{y}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ x (+ x y)) (/ y (+ x y))))

C

double code(double x, double y) {
	return (x / (x + y)) - (y / (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / (x + y)) - (y / (x + y))
end function

Java

public static double code(double x, double y) {
	return (x / (x + y)) - (y / (x + y));
}

Python

def code(x, y):
	return (x / (x + y)) - (y / (x + y))

Julia

function code(x, y)
	return Float64(Float64(x / Float64(x + y)) - Float64(y / Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x / (x + y)) - (y / (x + y));
end

Wolfram

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

Reproduce

herbie shell --seed 2024204 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (+ x y)) (/ y (+ x y))))

  (/ (- x y) (+ x y)))