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

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 7

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, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{x + y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. div-sub N/A

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

   4. lower--.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. lower-+.f64 N/A

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

   9. lower-/.f64 100.0

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

   10. lift-+.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-+.f64 100.0

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

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\frac{x}{y + x} - \frac{y}{y + x}} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{y + x} \leq -0.5:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{y}, x, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x}, -2, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (+ y x)) -0.5)
   (fma (/ 2.0 y) x -1.0)
   (fma (/ y x) -2.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (y + x)) <= -0.5) {
		tmp = fma((2.0 / y), x, -1.0);
	} else {
		tmp = fma((y / x), -2.0, 1.0);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(y + x)) <= -0.5)
		tmp = fma(Float64(2.0 / y), x, -1.0);
	else
		tmp = fma(Float64(y / x), -2.0, 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision], -0.5], N[(N[(2.0 / y), $MachinePrecision] * x + -1.0), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * -2.0 + 1.0), $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 y around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

      6. metadata-eval N/A

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

      7. distribute-rgt1-in N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. associate-*l/ N/A

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

      14. associate-*l* N/A

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

      15. lower-fma.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{2}}{y}, x, -1\right) \]

      18. lower-/.f64 98.2

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{2}{y}}, x, -1\right) \]

   5. Applied rewrites 98.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{y}, x, -1\right)} \]

   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 y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x}, -2, 1\right)} \]

      4. lower-/.f64 98.6

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{x}}, -2, 1\right) \]

   5. Applied rewrites 98.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{y + x} \leq -0.5:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{y}, x, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x}, -2, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{y + x} \leq -0.5:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{y}, x, -1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (+ y x)) -0.5) (fma (/ 2.0 y) x -1.0) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (y + x)) <= -0.5) {
		tmp = fma((2.0 / y), x, -1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(y + x)) <= -0.5)
		tmp = fma(Float64(2.0 / y), x, -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision], -0.5], N[(N[(2.0 / y), $MachinePrecision] * x + -1.0), $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 y around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

      6. metadata-eval N/A

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

      7. distribute-rgt1-in N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. associate-*l/ N/A

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

      14. associate-*l* N/A

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

      15. lower-fma.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{2}}{y}, x, -1\right) \]

      18. lower-/.f64 98.2

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{2}{y}}, x, -1\right) \]

   5. Applied rewrites 98.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{y}, x, -1\right)} \]

   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 y around 0

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

   5. Applied rewrites 98.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{y + x} \leq -0.5:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{y}, x, -1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (y + x)) <= -0.5) {
		tmp = -y / (y + x);
	} 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) / (y + x)) <= (-0.5d0)) then
        tmp = -y / (y + x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 97.1

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

   5. Applied rewrites 97.1%

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

   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 y around 0

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

   5. Applied rewrites 98.2%

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

4. Final simplification 97.6%

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

Alternative 5: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{y + x} \leq -1 \cdot 10^{-309}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (+ y x)) -1e-309) -1.0 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (y + x)) <= -1e-309) {
		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) / (y + x)) <= (-1d-309)) 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) / (y + x)) <= -1e-309) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (y + x)) <= -1e-309:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(y + x)) <= -1e-309)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x - y) / (y + x)) <= -1e-309)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision], -1e-309], -1.0, 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (+.f64 x y)) < -1.000000000000002e-309

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 97.0%

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

   if -1.000000000000002e-309 < (/.f64 (-.f64 x y) (+.f64 x y))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 98.2%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{y + x} \leq -1 \cdot 10^{-309}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 7: 49.1% 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 y around inf

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

5. Applied rewrites 50.4%

   \[\leadsto \color{blue}{-1} \]
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 2024254 
(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)))