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

Percentage Accurate: 100.0% → 99.9%

Time: 5.6s

Alternatives: 10

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: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{y + \left(x + y \cdot -2\right)}{y + x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ y (+ x (* y -2.0))) (+ y x)))

C

double code(double x, double y) {
	return (y + (x + (y * -2.0))) / (y + x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + (x + (y * (-2.0d0)))) / (y + x)
end function

Java

public static double code(double x, double y) {
	return (y + (x + (y * -2.0))) / (y + x);
}

Python

def code(x, y):
	return (y + (x + (y * -2.0))) / (y + x)

Julia

function code(x, y)
	return Float64(Float64(y + Float64(x + Float64(y * -2.0))) / Float64(y + x))
end

MATLAB

function tmp = code(x, y)
	tmp = (y + (x + (y * -2.0))) / (y + x);
end

Wolfram

code[x_, y_] := N[(N[(y + N[(x + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. *-un-lft-identity 100.0%

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

   2. *-un-lft-identity 100.0%

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

   3. prod-diff 100.0%

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

   4. *-commutative 100.0%

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

   5. *-un-lft-identity 100.0%

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

   6. fma-neg 100.0%

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

   7. *-un-lft-identity 100.0%

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

   8. *-commutative 100.0%

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

   9. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

   \[\leadsto \frac{\color{blue}{\left(x - y\right) + \mathsf{fma}\left(-y, 1, y\right)}}{x + y} \]
5. Step-by-step derivation

   1. fma-undefine 100.0%

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

   2. *-rgt-identity 100.0%

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

   3. associate-+r+ 100.0%

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

   4. +-commutative 100.0%

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

   5. sub-neg 100.0%

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

   6. associate-+l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. neg-mul-1 100.0%

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

   9. distribute-rgt-out 100.0%

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

   10. metadata-eval 100.0%

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

6. Simplified 100.0%

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

7. Final simplification 100.0%

   \[\leadsto \frac{y + \left(x + y \cdot -2\right)}{y + x} \]
8. Add Preprocessing

Alternative 2: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\left(-y\right) - x}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+20}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.5e-6)
   (/ y (- (- y) x))
   (if (<= y 2.8e+20) (+ 1.0 (* -2.0 (/ y x))) (+ (* 2.0 (/ x y)) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.5e-6) {
		tmp = y / (-y - x);
	} else if (y <= 2.8e+20) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (2.0 * (x / y)) + -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 (y <= (-6.5d-6)) then
        tmp = y / (-y - x)
    else if (y <= 2.8d+20) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.5e-6) {
		tmp = y / (-y - x);
	} else if (y <= 2.8e+20) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (2.0 * (x / y)) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.5e-6:
		tmp = y / (-y - x)
	elif y <= 2.8e+20:
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = (2.0 * (x / y)) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.5e-6)
		tmp = Float64(y / Float64(Float64(-y) - x));
	elseif (y <= 2.8e+20)
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.5e-6)
		tmp = y / (-y - x);
	elseif (y <= 2.8e+20)
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = (2.0 * (x / y)) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.5e-6], N[(y / N[((-y) - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+20], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4999999999999996e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.0%

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

      1. neg-mul-1 83.0%

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

   5. Simplified 83.0%

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

   if -6.4999999999999996e-6 < y < 2.8e20

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.9%

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

   if 2.8e20 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\left(-y\right) - x}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+20}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{\left(-y\right) - x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.2e-9)
   (/ y (- (- y) x))
   (if (<= y 1.7e+20) (+ 1.0 (* -2.0 (/ y x))) (+ (/ x y) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.2e-9) {
		tmp = y / (-y - x);
	} else if (y <= 1.7e+20) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (x / y) + -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 (y <= (-3.2d-9)) then
        tmp = y / (-y - x)
    else if (y <= 1.7d+20) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = (x / y) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.2e-9) {
		tmp = y / (-y - x);
	} else if (y <= 1.7e+20) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.2e-9:
		tmp = y / (-y - x)
	elif y <= 1.7e+20:
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.2e-9)
		tmp = Float64(y / Float64(Float64(-y) - x));
	elseif (y <= 1.7e+20)
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(x / y) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.2e-9)
		tmp = y / (-y - x);
	elseif (y <= 1.7e+20)
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.2e-9], N[(y / N[((-y) - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+20], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.20000000000000012e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.0%

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

      1. neg-mul-1 83.0%

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

   5. Simplified 83.0%

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

   if -3.20000000000000012e-9 < y < 1.7e20

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.9%

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

   if 1.7e20 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.4%

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

      1. neg-mul-1 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in y around inf 75.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{\left(-y\right) - x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0004 \lor \neg \left(y \leq 1.05 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.0004) (not (<= y 1.05e+23)))
   (+ (/ x y) -1.0)
   (- 1.0 (/ y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.0004) || !(y <= 1.05e+23)) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-0.0004d0)) .or. (.not. (y <= 1.05d+23))) then
        tmp = (x / y) + (-1.0d0)
    else
        tmp = 1.0d0 - (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -0.0004) || !(y <= 1.05e+23)) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.0004) or not (y <= 1.05e+23):
		tmp = (x / y) + -1.0
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.0004) || !(y <= 1.05e+23))
		tmp = Float64(Float64(x / y) + -1.0);
	else
		tmp = Float64(1.0 - Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.0004) || ~((y <= 1.05e+23)))
		tmp = (x / y) + -1.0;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.0004], N[Not[LessEqual[y, 1.05e+23]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000019e-4 or 1.0500000000000001e23 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.5%

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

      1. neg-mul-1 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in y around inf 79.4%

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

   if -4.00000000000000019e-4 < y < 1.0500000000000001e23

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.4%

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

   4. Taylor expanded in x around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   6. Simplified 78.4%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0004 \lor \neg \left(y \leq 1.05 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\left(-y\right) - x}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.2e-6)
   (/ y (- (- y) x))
   (if (<= y 2.05e+20) (- 1.0 (/ y x)) (+ (/ x y) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.2e-6) {
		tmp = y / (-y - x);
	} else if (y <= 2.05e+20) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = (x / y) + -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 (y <= (-6.2d-6)) then
        tmp = y / (-y - x)
    else if (y <= 2.05d+20) then
        tmp = 1.0d0 - (y / x)
    else
        tmp = (x / y) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.2e-6) {
		tmp = y / (-y - x);
	} else if (y <= 2.05e+20) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.2e-6:
		tmp = y / (-y - x)
	elif y <= 2.05e+20:
		tmp = 1.0 - (y / x)
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.2e-6)
		tmp = Float64(y / Float64(Float64(-y) - x));
	elseif (y <= 2.05e+20)
		tmp = Float64(1.0 - Float64(y / x));
	else
		tmp = Float64(Float64(x / y) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.2e-6)
		tmp = y / (-y - x);
	elseif (y <= 2.05e+20)
		tmp = 1.0 - (y / x);
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.2e-6], N[(y / N[((-y) - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+20], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999999e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.0%

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

      1. neg-mul-1 83.0%

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

   5. Simplified 83.0%

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

   if -6.1999999999999999e-6 < y < 2.05e20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.4%

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

   4. Taylor expanded in x around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   6. Simplified 78.4%

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

   if 2.05e20 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.4%

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

      1. neg-mul-1 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in y around inf 75.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\left(-y\right) - x}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-6}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+20}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3e-6) -1.0 (if (<= y 1.55e+20) (- 1.0 (/ y x)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3e-6) {
		tmp = -1.0;
	} else if (y <= 1.55e+20) {
		tmp = 1.0 - (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 (y <= (-3d-6)) then
        tmp = -1.0d0
    else if (y <= 1.55d+20) then
        tmp = 1.0d0 - (y / x)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3e-6) {
		tmp = -1.0;
	} else if (y <= 1.55e+20) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3e-6:
		tmp = -1.0
	elif y <= 1.55e+20:
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3e-6)
		tmp = -1.0;
	elseif (y <= 1.55e+20)
		tmp = Float64(1.0 - Float64(y / x));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3e-6)
		tmp = -1.0;
	elseif (y <= 1.55e+20)
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3e-6], -1.0, If[LessEqual[y, 1.55e+20], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0000000000000001e-6 or 1.55e20 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.9%

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

   if -3.0000000000000001e-6 < y < 1.55e20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.4%

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

   4. Taylor expanded in x around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   6. Simplified 78.4%

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

Alternative 7: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0005:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.0005) -1.0 (if (<= y 1e+20) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.0005) {
		tmp = -1.0;
	} else if (y <= 1e+20) {
		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 (y <= (-0.0005d0)) then
        tmp = -1.0d0
    else if (y <= 1d+20) 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 (y <= -0.0005) {
		tmp = -1.0;
	} else if (y <= 1e+20) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.0005:
		tmp = -1.0
	elif y <= 1e+20:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.0005)
		tmp = -1.0;
	elseif (y <= 1e+20)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.0005)
		tmp = -1.0;
	elseif (y <= 1e+20)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.0005], -1.0, If[LessEqual[y, 1e+20], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000001e-4 or 1e20 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.9%

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

   if -5.0000000000000001e-4 < y < 1e20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.8%

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

Alternative 8: 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. div-sub 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 9: 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 10: 49.3% 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 50.6%

   \[\leadsto \color{blue}{-1} \]
4. 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 2024133 
(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)))