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

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

Alternatives: 9

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

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

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]

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%

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

Alternative 2: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+18}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+90} \lor \neg \left(x \leq 3.5 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7.6e+18)
   (- 1.0 (/ y x))
   (if (<= x 2.1e-41)
     (+ (/ x y) -1.0)
     (if (or (<= x 3.3e+90) (not (<= x 3.5e+113)))
       (/ x (+ x y))
       (/ (- y) (+ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7.6e+18) {
		tmp = 1.0 - (y / x);
	} else if (x <= 2.1e-41) {
		tmp = (x / y) + -1.0;
	} else if ((x <= 3.3e+90) || !(x <= 3.5e+113)) {
		tmp = x / (x + y);
	} else {
		tmp = -y / (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 <= (-7.6d+18)) then
        tmp = 1.0d0 - (y / x)
    else if (x <= 2.1d-41) then
        tmp = (x / y) + (-1.0d0)
    else if ((x <= 3.3d+90) .or. (.not. (x <= 3.5d+113))) then
        tmp = x / (x + y)
    else
        tmp = -y / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -7.6e+18) {
		tmp = 1.0 - (y / x);
	} else if (x <= 2.1e-41) {
		tmp = (x / y) + -1.0;
	} else if ((x <= 3.3e+90) || !(x <= 3.5e+113)) {
		tmp = x / (x + y);
	} else {
		tmp = -y / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7.6e+18:
		tmp = 1.0 - (y / x)
	elif x <= 2.1e-41:
		tmp = (x / y) + -1.0
	elif (x <= 3.3e+90) or not (x <= 3.5e+113):
		tmp = x / (x + y)
	else:
		tmp = -y / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7.6e+18)
		tmp = Float64(1.0 - Float64(y / x));
	elseif (x <= 2.1e-41)
		tmp = Float64(Float64(x / y) + -1.0);
	elseif ((x <= 3.3e+90) || !(x <= 3.5e+113))
		tmp = Float64(x / Float64(x + y));
	else
		tmp = Float64(Float64(-y) / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7.6e+18)
		tmp = 1.0 - (y / x);
	elseif (x <= 2.1e-41)
		tmp = (x / y) + -1.0;
	elseif ((x <= 3.3e+90) || ~((x <= 3.5e+113)))
		tmp = x / (x + y);
	else
		tmp = -y / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7.6e+18], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e-41], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], If[Or[LessEqual[x, 3.3e+90], N[Not[LessEqual[x, 3.5e+113]], $MachinePrecision]], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.6e18

   1. Initial program 99.9%

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

      1. div-sub 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. frac-sub 30.9%

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

      2. associate-/r* 32.5%

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

      3. *-commutative 32.5%

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

   6. Applied egg-rr 32.5%

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

   7. Taylor expanded in x around inf 81.8%

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

   8. Taylor expanded in x around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. unsub-neg 82.1%

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

   10. Simplified 82.1%

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

   if -7.6e18 < x < 2.10000000000000013e-41

   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. Step-by-step derivation

      1. frac-sub 66.6%

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

      2. associate-/r* 67.1%

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

      3. *-commutative 67.1%

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

   6. Applied egg-rr 67.1%

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

   7. Taylor expanded in x around 0 76.9%

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

      1. neg-mul-1 76.9%

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

   9. Simplified 76.9%

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

   10. Taylor expanded in y around inf 77.0%

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

   if 2.10000000000000013e-41 < x < 3.30000000000000008e90 or 3.5000000000000001e113 < x

   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. Step-by-step derivation

      1. frac-sub 39.7%

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

      2. associate-/r* 41.1%

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

      3. *-commutative 41.1%

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

   6. Applied egg-rr 41.1%

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

   7. Taylor expanded in x around inf 86.9%

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

   if 3.30000000000000008e90 < x < 3.5000000000000001e113

   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. Step-by-step derivation

      1. frac-sub 44.4%

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

      2. associate-/r* 45.5%

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

      3. *-commutative 45.5%

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

   6. Applied egg-rr 45.5%

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

   7. Taylor expanded in x around 0 79.0%

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

      1. neg-mul-1 79.0%

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

   9. Simplified 79.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+18}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+90} \lor \neg \left(x \leq 3.5 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-40}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+90} \lor \neg \left(x \leq 3.5 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.4e+17)
   (- 1.0 (/ y x))
   (if (<= x 9e-40)
     (+ (* 2.0 (/ x y)) -1.0)
     (if (or (<= x 6.8e+90) (not (<= x 3.5e+113)))
       (/ x (+ x y))
       (/ (- y) (+ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.4e+17) {
		tmp = 1.0 - (y / x);
	} else if (x <= 9e-40) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else if ((x <= 6.8e+90) || !(x <= 3.5e+113)) {
		tmp = x / (x + y);
	} else {
		tmp = -y / (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 <= (-2.4d+17)) then
        tmp = 1.0d0 - (y / x)
    else if (x <= 9d-40) then
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    else if ((x <= 6.8d+90) .or. (.not. (x <= 3.5d+113))) then
        tmp = x / (x + y)
    else
        tmp = -y / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.4e+17) {
		tmp = 1.0 - (y / x);
	} else if (x <= 9e-40) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else if ((x <= 6.8e+90) || !(x <= 3.5e+113)) {
		tmp = x / (x + y);
	} else {
		tmp = -y / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.4e+17:
		tmp = 1.0 - (y / x)
	elif x <= 9e-40:
		tmp = (2.0 * (x / y)) + -1.0
	elif (x <= 6.8e+90) or not (x <= 3.5e+113):
		tmp = x / (x + y)
	else:
		tmp = -y / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.4e+17)
		tmp = Float64(1.0 - Float64(y / x));
	elseif (x <= 9e-40)
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	elseif ((x <= 6.8e+90) || !(x <= 3.5e+113))
		tmp = Float64(x / Float64(x + y));
	else
		tmp = Float64(Float64(-y) / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.4e+17)
		tmp = 1.0 - (y / x);
	elseif (x <= 9e-40)
		tmp = (2.0 * (x / y)) + -1.0;
	elseif ((x <= 6.8e+90) || ~((x <= 3.5e+113)))
		tmp = x / (x + y);
	else
		tmp = -y / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.4e+17], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-40], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], If[Or[LessEqual[x, 6.8e+90], N[Not[LessEqual[x, 3.5e+113]], $MachinePrecision]], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e17

   1. Initial program 99.9%

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

      1. div-sub 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. frac-sub 30.9%

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

      2. associate-/r* 32.5%

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

      3. *-commutative 32.5%

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

   6. Applied egg-rr 32.5%

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

   7. Taylor expanded in x around inf 81.8%

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

   8. Taylor expanded in x around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. unsub-neg 82.1%

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

   10. Simplified 82.1%

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

   if -2.4e17 < x < 9.0000000000000002e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.7%

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

   if 9.0000000000000002e-40 < x < 6.80000000000000036e90 or 3.5000000000000001e113 < x

   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. Step-by-step derivation

      1. frac-sub 39.7%

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

      2. associate-/r* 41.1%

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

      3. *-commutative 41.1%

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

   6. Applied egg-rr 41.1%

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

   7. Taylor expanded in x around inf 86.9%

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

   if 6.80000000000000036e90 < x < 3.5000000000000001e113

   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. Step-by-step derivation

      1. frac-sub 44.4%

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

      2. associate-/r* 45.5%

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

      3. *-commutative 45.5%

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

   6. Applied egg-rr 45.5%

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

   7. Taylor expanded in x around 0 79.0%

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

      1. neg-mul-1 79.0%

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

   9. Simplified 79.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-40}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+90} \lor \neg \left(x \leq 3.5 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{+16} \lor \neg \left(x \leq 1.55 \cdot 10^{-35}\right) \land \left(x \leq 6.8 \cdot 10^{+90} \lor \neg \left(x \leq 1.55 \cdot 10^{+95}\right)\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -6.7e+16)
         (and (not (<= x 1.55e-35)) (or (<= x 6.8e+90) (not (<= x 1.55e+95)))))
   (- 1.0 (/ y x))
   -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -6.7e+16) || (!(x <= 1.55e-35) && ((x <= 6.8e+90) || !(x <= 1.55e+95)))) {
		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 ((x <= (-6.7d+16)) .or. (.not. (x <= 1.55d-35)) .and. (x <= 6.8d+90) .or. (.not. (x <= 1.55d+95))) 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 ((x <= -6.7e+16) || (!(x <= 1.55e-35) && ((x <= 6.8e+90) || !(x <= 1.55e+95)))) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -6.7e+16) or (not (x <= 1.55e-35) and ((x <= 6.8e+90) or not (x <= 1.55e+95))):
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -6.7e+16) || (!(x <= 1.55e-35) && ((x <= 6.8e+90) || !(x <= 1.55e+95))))
		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 ((x <= -6.7e+16) || (~((x <= 1.55e-35)) && ((x <= 6.8e+90) || ~((x <= 1.55e+95)))))
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -6.7e+16], And[N[Not[LessEqual[x, 1.55e-35]], $MachinePrecision], Or[LessEqual[x, 6.8e+90], N[Not[LessEqual[x, 1.55e+95]], $MachinePrecision]]]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -6.7e16 or 1.55000000000000006e-35 < x < 6.80000000000000036e90 or 1.5500000000000001e95 < x

   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. Step-by-step derivation

      1. frac-sub 36.0%

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

      2. associate-/r* 37.6%

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

      3. *-commutative 37.6%

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

   6. Applied egg-rr 37.6%

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

   7. Taylor expanded in x around inf 83.4%

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

   8. Taylor expanded in x around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. unsub-neg 83.5%

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

   10. Simplified 83.5%

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

   if -6.7e16 < x < 1.55000000000000006e-35 or 6.80000000000000036e90 < x < 1.5500000000000001e95

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{+16} \lor \neg \left(x \leq 1.55 \cdot 10^{-35}\right) \land \left(x \leq 6.8 \cdot 10^{+90} \lor \neg \left(x \leq 1.55 \cdot 10^{+95}\right)\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{x}\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+90} \lor \neg \left(x \leq 1.55 \cdot 10^{+95}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y x))))
   (if (<= x -1.02e+17)
     t_0
     (if (<= x 2.8e-37)
       (+ (/ x y) -1.0)
       (if (or (<= x 8.5e+90) (not (<= x 1.55e+95))) t_0 -1.0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (y / x);
	double tmp;
	if (x <= -1.02e+17) {
		tmp = t_0;
	} else if (x <= 2.8e-37) {
		tmp = (x / y) + -1.0;
	} else if ((x <= 8.5e+90) || !(x <= 1.55e+95)) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / x)
    if (x <= (-1.02d+17)) then
        tmp = t_0
    else if (x <= 2.8d-37) then
        tmp = (x / y) + (-1.0d0)
    else if ((x <= 8.5d+90) .or. (.not. (x <= 1.55d+95))) then
        tmp = t_0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (y / x);
	double tmp;
	if (x <= -1.02e+17) {
		tmp = t_0;
	} else if (x <= 2.8e-37) {
		tmp = (x / y) + -1.0;
	} else if ((x <= 8.5e+90) || !(x <= 1.55e+95)) {
		tmp = t_0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (y / x)
	tmp = 0
	if x <= -1.02e+17:
		tmp = t_0
	elif x <= 2.8e-37:
		tmp = (x / y) + -1.0
	elif (x <= 8.5e+90) or not (x <= 1.55e+95):
		tmp = t_0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(y / x))
	tmp = 0.0
	if (x <= -1.02e+17)
		tmp = t_0;
	elseif (x <= 2.8e-37)
		tmp = Float64(Float64(x / y) + -1.0);
	elseif ((x <= 8.5e+90) || !(x <= 1.55e+95))
		tmp = t_0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (y / x);
	tmp = 0.0;
	if (x <= -1.02e+17)
		tmp = t_0;
	elseif (x <= 2.8e-37)
		tmp = (x / y) + -1.0;
	elseif ((x <= 8.5e+90) || ~((x <= 1.55e+95)))
		tmp = t_0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e+17], t$95$0, If[LessEqual[x, 2.8e-37], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], If[Or[LessEqual[x, 8.5e+90], N[Not[LessEqual[x, 1.55e+95]], $MachinePrecision]], t$95$0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02e17 or 2.8000000000000001e-37 < x < 8.5000000000000002e90 or 1.5500000000000001e95 < x

   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. Step-by-step derivation

      1. frac-sub 36.0%

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

      2. associate-/r* 37.6%

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

      3. *-commutative 37.6%

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

   6. Applied egg-rr 37.6%

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

   7. Taylor expanded in x around inf 83.4%

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

   8. Taylor expanded in x around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. unsub-neg 83.5%

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

   10. Simplified 83.5%

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

   if -1.02e17 < x < 2.8000000000000001e-37

   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. Step-by-step derivation

      1. frac-sub 66.6%

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

      2. associate-/r* 67.1%

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

      3. *-commutative 67.1%

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

   6. Applied egg-rr 67.1%

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

   7. Taylor expanded in x around 0 76.9%

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

      1. neg-mul-1 76.9%

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

   9. Simplified 76.9%

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

   10. Taylor expanded in y around inf 77.0%

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

   if 8.5000000000000002e90 < x < 1.5500000000000001e95

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+17}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+90} \lor \neg \left(x \leq 1.55 \cdot 10^{+95}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+17}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-35} \lor \neg \left(x \leq 8.5 \cdot 10^{+90}\right) \land x \leq 1.95 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.35e+17)
   (- 1.0 (/ y x))
   (if (or (<= x 3.2e-35) (and (not (<= x 8.5e+90)) (<= x 1.95e+115)))
     (+ (/ x y) -1.0)
     (/ x (+ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.35e+17) {
		tmp = 1.0 - (y / x);
	} else if ((x <= 3.2e-35) || (!(x <= 8.5e+90) && (x <= 1.95e+115))) {
		tmp = (x / y) + -1.0;
	} 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 <= (-1.35d+17)) then
        tmp = 1.0d0 - (y / x)
    else if ((x <= 3.2d-35) .or. (.not. (x <= 8.5d+90)) .and. (x <= 1.95d+115)) then
        tmp = (x / y) + (-1.0d0)
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.35e+17) {
		tmp = 1.0 - (y / x);
	} else if ((x <= 3.2e-35) || (!(x <= 8.5e+90) && (x <= 1.95e+115))) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.35e+17:
		tmp = 1.0 - (y / x)
	elif (x <= 3.2e-35) or (not (x <= 8.5e+90) and (x <= 1.95e+115)):
		tmp = (x / y) + -1.0
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.35e+17)
		tmp = Float64(1.0 - Float64(y / x));
	elseif ((x <= 3.2e-35) || (!(x <= 8.5e+90) && (x <= 1.95e+115)))
		tmp = Float64(Float64(x / y) + -1.0);
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.35e+17)
		tmp = 1.0 - (y / x);
	elseif ((x <= 3.2e-35) || (~((x <= 8.5e+90)) && (x <= 1.95e+115)))
		tmp = (x / y) + -1.0;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.35e+17], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.2e-35], And[N[Not[LessEqual[x, 8.5e+90]], $MachinePrecision], LessEqual[x, 1.95e+115]]], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e17

   1. Initial program 99.9%

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

      1. div-sub 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. frac-sub 30.9%

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

      2. associate-/r* 32.5%

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

      3. *-commutative 32.5%

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

   6. Applied egg-rr 32.5%

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

   7. Taylor expanded in x around inf 81.8%

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

   8. Taylor expanded in x around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. unsub-neg 82.1%

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

   10. Simplified 82.1%

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

   if -1.35e17 < x < 3.1999999999999998e-35 or 8.5000000000000002e90 < x < 1.95000000000000003e115

   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. Step-by-step derivation

      1. frac-sub 65.2%

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

      2. associate-/r* 65.7%

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

      3. *-commutative 65.7%

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

   6. Applied egg-rr 65.7%

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

   7. Taylor expanded in x around 0 77.1%

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

      1. neg-mul-1 77.1%

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

   9. Simplified 77.1%

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

   10. Taylor expanded in y around inf 77.1%

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

   if 3.1999999999999998e-35 < x < 8.5000000000000002e90 or 1.95000000000000003e115 < x

   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. Step-by-step derivation

      1. frac-sub 39.7%

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

      2. associate-/r* 41.1%

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

      3. *-commutative 41.1%

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

   6. Applied egg-rr 41.1%

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

   7. Taylor expanded in x around inf 86.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+17}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-35} \lor \neg \left(x \leq 8.5 \cdot 10^{+90}\right) \land x \leq 1.95 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-40}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+95}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e-39)
   1.0
   (if (<= x 1e-40)
     -1.0
     (if (<= x 8.5e+90) 1.0 (if (<= x 1.55e+95) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e-39) {
		tmp = 1.0;
	} else if (x <= 1e-40) {
		tmp = -1.0;
	} else if (x <= 8.5e+90) {
		tmp = 1.0;
	} else if (x <= 1.55e+95) {
		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 <= (-5d-39)) then
        tmp = 1.0d0
    else if (x <= 1d-40) then
        tmp = -1.0d0
    else if (x <= 8.5d+90) then
        tmp = 1.0d0
    else if (x <= 1.55d+95) 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 <= -5e-39) {
		tmp = 1.0;
	} else if (x <= 1e-40) {
		tmp = -1.0;
	} else if (x <= 8.5e+90) {
		tmp = 1.0;
	} else if (x <= 1.55e+95) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e-39:
		tmp = 1.0
	elif x <= 1e-40:
		tmp = -1.0
	elif x <= 8.5e+90:
		tmp = 1.0
	elif x <= 1.55e+95:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e-39)
		tmp = 1.0;
	elseif (x <= 1e-40)
		tmp = -1.0;
	elseif (x <= 8.5e+90)
		tmp = 1.0;
	elseif (x <= 1.55e+95)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e-39)
		tmp = 1.0;
	elseif (x <= 1e-40)
		tmp = -1.0;
	elseif (x <= 8.5e+90)
		tmp = 1.0;
	elseif (x <= 1.55e+95)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e-39], 1.0, If[LessEqual[x, 1e-40], -1.0, If[LessEqual[x, 8.5e+90], 1.0, If[LessEqual[x, 1.55e+95], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9999999999999998e-39 or 9.9999999999999993e-41 < x < 8.5000000000000002e90 or 1.5500000000000001e95 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.1%

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

   if -4.9999999999999998e-39 < x < 9.9999999999999993e-41 or 8.5000000000000002e90 < x < 1.5500000000000001e95

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.9%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-40}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+95}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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. Final simplification 100.0%

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

Alternative 9: 48.8% 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 48.3%

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

4. Final simplification 48.3%

   \[\leadsto -1 \]
5. Add Preprocessing

Developer target: 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 2024027 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

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