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

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+68} \lor \neg \left(y \leq 5.7 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.1e+68) (not (<= y 5.7e+63)))
   (/ (- y) (+ x y))
   (+ 1.0 (* -2.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.1e+68) || !(y <= 5.7e+63)) {
		tmp = -y / (x + y);
	} else {
		tmp = 1.0 + (-2.0 * (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 <= (-2.1d+68)) .or. (.not. (y <= 5.7d+63))) then
        tmp = -y / (x + y)
    else
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.1e+68) || !(y <= 5.7e+63)) {
		tmp = -y / (x + y);
	} else {
		tmp = 1.0 + (-2.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.1e+68) or not (y <= 5.7e+63):
		tmp = -y / (x + y)
	else:
		tmp = 1.0 + (-2.0 * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.1e+68) || !(y <= 5.7e+63))
		tmp = Float64(Float64(-y) / Float64(x + y));
	else
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.1e+68) || ~((y <= 5.7e+63)))
		tmp = -y / (x + y);
	else
		tmp = 1.0 + (-2.0 * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.1e+68], N[Not[LessEqual[y, 5.7e+63]], $MachinePrecision]], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000001e68 or 5.7000000000000002e63 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.9%

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

      1. neg-mul-1 80.9%

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

   5. Simplified 80.9%

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

   if -2.10000000000000001e68 < y < 5.7000000000000002e63

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+68} \lor \neg \left(y \leq 5.7 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+62}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.8e+69)
   (/ (- y) (+ x y))
   (if (<= y 4.6e+62) (+ 1.0 (* -2.0 (/ y x))) (+ (* 2.0 (/ x y)) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.8e+69) {
		tmp = -y / (x + y);
	} else if (y <= 4.6e+62) {
		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 <= (-2.8d+69)) then
        tmp = -y / (x + y)
    else if (y <= 4.6d+62) 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 <= -2.8e+69) {
		tmp = -y / (x + y);
	} else if (y <= 4.6e+62) {
		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 <= -2.8e+69:
		tmp = -y / (x + y)
	elif y <= 4.6e+62:
		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 <= -2.8e+69)
		tmp = Float64(Float64(-y) / Float64(x + y));
	elseif (y <= 4.6e+62)
		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 <= -2.8e+69)
		tmp = -y / (x + y);
	elseif (y <= 4.6e+62)
		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, -2.8e+69], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+62], 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 < -2.79999999999999982e69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. neg-mul-1 80.1%

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

   5. Simplified 80.1%

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

   if -2.79999999999999982e69 < y < 4.59999999999999968e62

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.2%

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

   if 4.59999999999999968e62 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+62}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+72} \lor \neg \left(y \leq 8 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.3e+72) (not (<= y 8e+62))) (/ (- y) (+ x y)) (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e+72) || !(y <= 8e+62)) {
		tmp = -y / (x + y);
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.3d+72)) .or. (.not. (y <= 8d+62))) then
        tmp = -y / (x + y)
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e+72) || !(y <= 8e+62)) {
		tmp = -y / (x + y);
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.3e+72) or not (y <= 8e+62):
		tmp = -y / (x + y)
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.3e+72) || !(y <= 8e+62))
		tmp = Float64(Float64(-y) / Float64(x + y));
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.3e+72) || ~((y <= 8e+62)))
		tmp = -y / (x + y);
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.3e+72], N[Not[LessEqual[y, 8e+62]], $MachinePrecision]], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999991e72 or 8.00000000000000028e62 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.9%

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

      1. neg-mul-1 80.9%

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

   5. Simplified 80.9%

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

   if -1.29999999999999991e72 < y < 8.00000000000000028e62

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 83.3%

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

   4. Taylor expanded in y around 0 73.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+72} \lor \neg \left(y \leq 8 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+69} \lor \neg \left(y \leq 5.9 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9.8e+69) (not (<= y 5.9e+62))) (+ (/ x y) -1.0) (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9.8e+69) || !(y <= 5.9e+62)) {
		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 ((y <= (-9.8d+69)) .or. (.not. (y <= 5.9d+62))) 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 ((y <= -9.8e+69) || !(y <= 5.9e+62)) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9.8e+69) or not (y <= 5.9e+62):
		tmp = (x / y) + -1.0
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9.8e+69) || !(y <= 5.9e+62))
		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 ((y <= -9.8e+69) || ~((y <= 5.9e+62)))
		tmp = (x / y) + -1.0;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9.8e+69], N[Not[LessEqual[y, 5.9e+62]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.7999999999999999e69 or 5.9000000000000003e62 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.9%

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

      1. neg-mul-1 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in y around inf 80.7%

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

   if -9.7999999999999999e69 < y < 5.9000000000000003e62

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 83.3%

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

   4. Taylor expanded in y around 0 73.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+69} \lor \neg \left(y \leq 5.9 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+67} \lor \neg \left(y \leq 4.6 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.8e+67) (not (<= y 4.6e+62)))
   (+ (/ x y) -1.0)
   (- 1.0 (/ y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.8e+67) || !(y <= 4.6e+62)) {
		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 <= (-5.8d+67)) .or. (.not. (y <= 4.6d+62))) 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 <= -5.8e+67) || !(y <= 4.6e+62)) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.8e+67) or not (y <= 4.6e+62):
		tmp = (x / y) + -1.0
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.8e+67) || !(y <= 4.6e+62))
		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 <= -5.8e+67) || ~((y <= 4.6e+62)))
		tmp = (x / y) + -1.0;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.8e+67], N[Not[LessEqual[y, 4.6e+62]], $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 < -5.80000000000000047e67 or 4.59999999999999968e62 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.9%

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

      1. neg-mul-1 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in y around inf 80.7%

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

   if -5.80000000000000047e67 < y < 4.59999999999999968e62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.3%

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

   4. Taylor expanded in x around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. mul-1-neg 73.3%

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

      3. remove-double-neg 73.3%

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

      4. distribute-neg-in 73.3%

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

      5. distribute-neg-frac 73.3%

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

      6. neg-sub0 73.3%

         \[\leadsto \color{blue}{0 - \frac{y + \left(-x\right)}{x}} \]

      7. sub-neg 73.3%

         \[\leadsto 0 - \frac{\color{blue}{y - x}}{x} \]

      8. div-sub 73.4%

         \[\leadsto 0 - \color{blue}{\left(\frac{y}{x} - \frac{x}{x}\right)} \]

      9. *-rgt-identity 73.4%

         \[\leadsto 0 - \left(\frac{y}{x} - \frac{\color{blue}{x \cdot 1}}{x}\right) \]

      10. associate-*r/ 73.2%

          \[\leadsto 0 - \left(\frac{y}{x} - \color{blue}{x \cdot \frac{1}{x}}\right) \]

      11. rgt-mult-inverse 73.4%

          \[\leadsto 0 - \left(\frac{y}{x} - \color{blue}{1}\right) \]

      12. associate-+l- 73.4%

          \[\leadsto \color{blue}{\left(0 - \frac{y}{x}\right) + 1} \]

      13. neg-sub0 73.4%

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

      14. +-commutative 73.4%

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

      15. sub-neg 73.4%

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

   6. Simplified 73.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+67} \lor \neg \left(y \leq 4.6 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.1e+70) -1.0 (if (<= y 2.6e+63) (- 1.0 (/ y x)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.1e+70) {
		tmp = -1.0;
	} else if (y <= 2.6e+63) {
		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 <= (-5.1d+70)) then
        tmp = -1.0d0
    else if (y <= 2.6d+63) 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 <= -5.1e+70) {
		tmp = -1.0;
	} else if (y <= 2.6e+63) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.1e+70:
		tmp = -1.0
	elif y <= 2.6e+63:
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.1e+70)
		tmp = -1.0;
	elseif (y <= 2.6e+63)
		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 <= -5.1e+70)
		tmp = -1.0;
	elseif (y <= 2.6e+63)
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.1e+70], -1.0, If[LessEqual[y, 2.6e+63], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.10000000000000014e70 or 2.6000000000000001e63 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.3%

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

   if -5.10000000000000014e70 < y < 2.6000000000000001e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.3%

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

   4. Taylor expanded in x around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. mul-1-neg 73.3%

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

      3. remove-double-neg 73.3%

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

      4. distribute-neg-in 73.3%

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

      5. distribute-neg-frac 73.3%

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

      6. neg-sub0 73.3%

         \[\leadsto \color{blue}{0 - \frac{y + \left(-x\right)}{x}} \]

      7. sub-neg 73.3%

         \[\leadsto 0 - \frac{\color{blue}{y - x}}{x} \]

      8. div-sub 73.4%

         \[\leadsto 0 - \color{blue}{\left(\frac{y}{x} - \frac{x}{x}\right)} \]

      9. *-rgt-identity 73.4%

         \[\leadsto 0 - \left(\frac{y}{x} - \frac{\color{blue}{x \cdot 1}}{x}\right) \]

      10. associate-*r/ 73.2%

          \[\leadsto 0 - \left(\frac{y}{x} - \color{blue}{x \cdot \frac{1}{x}}\right) \]

      11. rgt-mult-inverse 73.4%

          \[\leadsto 0 - \left(\frac{y}{x} - \color{blue}{1}\right) \]

      12. associate-+l- 73.4%

          \[\leadsto \color{blue}{\left(0 - \frac{y}{x}\right) + 1} \]

      13. neg-sub0 73.4%

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

      14. +-commutative 73.4%

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

      15. sub-neg 73.4%

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

   6. Simplified 73.4%

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

Alternative 8: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+67}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+67) -1.0 (if (<= y 1.5e+64) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+67) {
		tmp = -1.0;
	} else if (y <= 1.5e+64) {
		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 <= (-5d+67)) then
        tmp = -1.0d0
    else if (y <= 1.5d+64) 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 <= -5e+67) {
		tmp = -1.0;
	} else if (y <= 1.5e+64) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+67:
		tmp = -1.0
	elif y <= 1.5e+64:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+67)
		tmp = -1.0;
	elseif (y <= 1.5e+64)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+67)
		tmp = -1.0;
	elseif (y <= 1.5e+64)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+67], -1.0, If[LessEqual[y, 1.5e+64], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999976e67 or 1.5000000000000001e64 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.3%

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

   if -4.99999999999999976e67 < y < 1.5000000000000001e64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.8%

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

Alternative 9: 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 48.5%

   \[\leadsto \color{blue}{-1} \]
4. 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 2024110 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :alt
  (- (/ x (+ x y)) (/ y (+ x y)))

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