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

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 8

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, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{x + y}{x - y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0 / ((x + y) / (x - y))

Julia

function code(x, y)
	return Float64(1.0 / Float64(Float64(x + y) / Float64(x - y)))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. clear-num N/A

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

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{x + y}{x - y}\right)}\right) \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(x + y\right), \color{blue}{\left(x - y\right)}\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{x} - y\right)\right)\right) \]

   5. --lowering--.f64 100.0%

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x - y}}} \]
5. Add Preprocessing

Alternative 2: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 23000000000000:\\ \;\;\;\;-1 + \frac{x \cdot 2}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot -2}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.1e+27)
   (/ x (+ x y))
   (if (<= x 23000000000000.0)
     (+ -1.0 (/ (* x 2.0) y))
     (+ 1.0 (/ (* y -2.0) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.1e+27) {
		tmp = x / (x + y);
	} else if (x <= 23000000000000.0) {
		tmp = -1.0 + ((x * 2.0) / y);
	} else {
		tmp = 1.0 + ((y * -2.0) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.1d+27)) then
        tmp = x / (x + y)
    else if (x <= 23000000000000.0d0) then
        tmp = (-1.0d0) + ((x * 2.0d0) / y)
    else
        tmp = 1.0d0 + ((y * (-2.0d0)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.1e+27) {
		tmp = x / (x + y);
	} else if (x <= 23000000000000.0) {
		tmp = -1.0 + ((x * 2.0) / y);
	} else {
		tmp = 1.0 + ((y * -2.0) / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.1e+27:
		tmp = x / (x + y)
	elif x <= 23000000000000.0:
		tmp = -1.0 + ((x * 2.0) / y)
	else:
		tmp = 1.0 + ((y * -2.0) / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.1e+27)
		tmp = Float64(x / Float64(x + y));
	elseif (x <= 23000000000000.0)
		tmp = Float64(-1.0 + Float64(Float64(x * 2.0) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y * -2.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.1e+27)
		tmp = x / (x + y);
	elseif (x <= 23000000000000.0)
		tmp = -1.0 + ((x * 2.0) / y);
	else
		tmp = 1.0 + ((y * -2.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.1e+27], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 23000000000000.0], N[(-1.0 + N[(N[(x * 2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * -2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0999999999999999e27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(x, y\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 77.5%

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

   if -1.0999999999999999e27 < x < 2.3e13

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. associate-*l* N/A

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

      6. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(-1, \color{blue}{\left(\left(2 \cdot \frac{1}{y}\right) \cdot x\right)}\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{2 \cdot 1}{y} \cdot x\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{2}{y} \cdot x\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{2 \cdot x}{\color{blue}{y}}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{\left(1 + 1\right) \cdot x}{y}\right)\right) \]

      12. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{x + 1 \cdot x}{y}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{x + \left(\mathsf{neg}\left(-1\right)\right) \cdot x}{y}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{x - -1 \cdot x}{y}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(x - -1 \cdot x\right), \color{blue}{y}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(-1\right)\right) \cdot x\right), y\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(x + 1 \cdot x\right), y\right)\right) \]

      18. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(\left(1 + 1\right) \cdot x\right), y\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(2 \cdot x\right), y\right)\right) \]

      20. *-lowering-*.f64 77.8%

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), y\right)\right) \]

   5. Simplified 77.8%

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

   if 2.3e13 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. div-sub N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1 \cdot y - y}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot y - y\right), \color{blue}{x}\right)\right) \]

      6. *-lft-identity N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot y - 1 \cdot y\right), x\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(-1 - 1\right)\right), x\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot -2\right), x\right)\right) \]

      9. *-lowering-*.f64 84.1%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -2\right), x\right)\right) \]

   5. Simplified 84.1%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 23000000000000:\\ \;\;\;\;-1 + \frac{x \cdot 2}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot -2}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + y}\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 11500000000000:\\ \;\;\;\;-1 + \frac{x \cdot 2}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ x y))))
   (if (<= x -5.4e+33)
     t_0
     (if (<= x 11500000000000.0) (+ -1.0 (/ (* x 2.0) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (x + y);
	double tmp;
	if (x <= -5.4e+33) {
		tmp = t_0;
	} else if (x <= 11500000000000.0) {
		tmp = -1.0 + ((x * 2.0) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (x + y)
    if (x <= (-5.4d+33)) then
        tmp = t_0
    else if (x <= 11500000000000.0d0) then
        tmp = (-1.0d0) + ((x * 2.0d0) / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (x + y);
	double tmp;
	if (x <= -5.4e+33) {
		tmp = t_0;
	} else if (x <= 11500000000000.0) {
		tmp = -1.0 + ((x * 2.0) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (x + y)
	tmp = 0
	if x <= -5.4e+33:
		tmp = t_0
	elif x <= 11500000000000.0:
		tmp = -1.0 + ((x * 2.0) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(x + y))
	tmp = 0.0
	if (x <= -5.4e+33)
		tmp = t_0;
	elseif (x <= 11500000000000.0)
		tmp = Float64(-1.0 + Float64(Float64(x * 2.0) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (x + y);
	tmp = 0.0;
	if (x <= -5.4e+33)
		tmp = t_0;
	elseif (x <= 11500000000000.0)
		tmp = -1.0 + ((x * 2.0) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e+33], t$95$0, If[LessEqual[x, 11500000000000.0], N[(-1.0 + N[(N[(x * 2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999982e33 or 1.15e13 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(x, y\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 80.7%

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

   if -5.39999999999999982e33 < x < 1.15e13

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. associate-*l* N/A

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

      6. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(-1, \color{blue}{\left(\left(2 \cdot \frac{1}{y}\right) \cdot x\right)}\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{2 \cdot 1}{y} \cdot x\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{2}{y} \cdot x\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{2 \cdot x}{\color{blue}{y}}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{\left(1 + 1\right) \cdot x}{y}\right)\right) \]

      12. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{x + 1 \cdot x}{y}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{x + \left(\mathsf{neg}\left(-1\right)\right) \cdot x}{y}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(-1, \left(\frac{x - -1 \cdot x}{y}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(x - -1 \cdot x\right), \color{blue}{y}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(-1\right)\right) \cdot x\right), y\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(x + 1 \cdot x\right), y\right)\right) \]

      18. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(\left(1 + 1\right) \cdot x\right), y\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\left(2 \cdot x\right), y\right)\right) \]

      20. *-lowering-*.f64 77.8%

          \[\leadsto \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), y\right)\right) \]

   5. Simplified 77.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 11500000000000:\\ \;\;\;\;-1 + \frac{x \cdot 2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + y}\\ \mathbf{if}\;x \leq -2.75 \cdot 10^{+29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6200000000000:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ x y))))
   (if (<= x -2.75e+29) t_0 (if (<= x 6200000000000.0) (+ -1.0 (/ x y)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (x + y);
	double tmp;
	if (x <= -2.75e+29) {
		tmp = t_0;
	} else if (x <= 6200000000000.0) {
		tmp = -1.0 + (x / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (x + y)
    if (x <= (-2.75d+29)) then
        tmp = t_0
    else if (x <= 6200000000000.0d0) then
        tmp = (-1.0d0) + (x / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (x + y);
	double tmp;
	if (x <= -2.75e+29) {
		tmp = t_0;
	} else if (x <= 6200000000000.0) {
		tmp = -1.0 + (x / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (x + y)
	tmp = 0
	if x <= -2.75e+29:
		tmp = t_0
	elif x <= 6200000000000.0:
		tmp = -1.0 + (x / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(x + y))
	tmp = 0.0
	if (x <= -2.75e+29)
		tmp = t_0;
	elseif (x <= 6200000000000.0)
		tmp = Float64(-1.0 + Float64(x / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (x + y);
	tmp = 0.0;
	if (x <= -2.75e+29)
		tmp = t_0;
	elseif (x <= 6200000000000.0)
		tmp = -1.0 + (x / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.75e+29], t$95$0, If[LessEqual[x, 6200000000000.0], N[(-1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.75e29 or 6.2e12 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(x, y\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 80.7%

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

   if -2.75e29 < x < 6.2e12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{y}\right) \]
   4. Step-by-step derivation

   5. Simplified 77.4%

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

      1. div-sub N/A

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

      2. *-inverses N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x}{y}\right), \color{blue}{1}\right) \]

      4. /-lowering-/.f64 77.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, y\right), 1\right) \]

   7. Applied egg-rr 77.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 6200000000000:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 12000000000000:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.2e+34) 1.0 (if (<= x 12000000000000.0) (+ -1.0 (/ x y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.2e+34) {
		tmp = 1.0;
	} else if (x <= 12000000000000.0) {
		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 <= (-2.2d+34)) then
        tmp = 1.0d0
    else if (x <= 12000000000000.0d0) 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 <= -2.2e+34) {
		tmp = 1.0;
	} else if (x <= 12000000000000.0) {
		tmp = -1.0 + (x / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.2e+34:
		tmp = 1.0
	elif x <= 12000000000000.0:
		tmp = -1.0 + (x / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.2e+34)
		tmp = 1.0;
	elseif (x <= 12000000000000.0)
		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 <= -2.2e+34)
		tmp = 1.0;
	elseif (x <= 12000000000000.0)
		tmp = -1.0 + (x / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.2e+34], 1.0, If[LessEqual[x, 12000000000000.0], N[(-1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000002e34 or 1.2e13 < x

   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 80.1%

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

   if -2.2000000000000002e34 < x < 1.2e13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{y}\right) \]
   4. Step-by-step derivation

   5. Simplified 77.4%

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

      1. div-sub N/A

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

      2. *-inverses N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x}{y}\right), \color{blue}{1}\right) \]

      4. /-lowering-/.f64 77.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, y\right), 1\right) \]

   7. Applied egg-rr 77.4%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 12000000000000:\\ \;\;\;\;-1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+32}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 28000000000000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+32) 1.0 (if (<= x 28000000000000.0) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+32) {
		tmp = 1.0;
	} else if (x <= 28000000000000.0) {
		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 <= (-1d+32)) then
        tmp = 1.0d0
    else if (x <= 28000000000000.0d0) 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 <= -1e+32) {
		tmp = 1.0;
	} else if (x <= 28000000000000.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+32:
		tmp = 1.0
	elif x <= 28000000000000.0:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+32)
		tmp = 1.0;
	elseif (x <= 28000000000000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+32)
		tmp = 1.0;
	elseif (x <= 28000000000000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+32], 1.0, If[LessEqual[x, 28000000000000.0], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000005e32 or 2.8e13 < x

   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 80.1%

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

   if -1.00000000000000005e32 < x < 2.8e13

   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 76.8%

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

Alternative 7: 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 8: 49.5% accurate, 7.0× 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 50.2%

   \[\leadsto \color{blue}{-1} \]
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 2024161 
(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)))