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

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

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, 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 99.9%

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

Alternative 2: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+50} \lor \neg \left(y \leq 5.3 \cdot 10^{+16}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.9e+50) (not (<= y 5.3e+16)))
   (+ (* 2.0 (/ x y)) -1.0)
   (+ 1.0 (* -2.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.9e+50) || !(y <= 5.3e+16)) {
		tmp = (2.0 * (x / y)) + -1.0;
	} 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 <= (-2.9d+50)) .or. (.not. (y <= 5.3d+16))) then
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    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 <= -2.9e+50) || !(y <= 5.3e+16)) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0 + (-2.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.9e+50) or not (y <= 5.3e+16):
		tmp = (2.0 * (x / y)) + -1.0
	else:
		tmp = 1.0 + (-2.0 * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.9e+50) || !(y <= 5.3e+16))
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	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 <= -2.9e+50) || ~((y <= 5.3e+16)))
		tmp = (2.0 * (x / y)) + -1.0;
	else
		tmp = 1.0 + (-2.0 * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.9e+50], N[Not[LessEqual[y, 5.3e+16]], $MachinePrecision]], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e50 or 5.3e16 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.8%

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

   if -2.9e50 < y < 5.3e16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.3%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+50} \lor \neg \left(y \leq 5.3 \cdot 10^{+16}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+50}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.75e+50)
   (/ (- x y) y)
   (if (<= y 4.5e+55) (+ 1.0 (* -2.0 (/ y x))) (/ y (- (- x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.75e+50) {
		tmp = (x - y) / y;
	} else if (y <= 4.5e+55) {
		tmp = 1.0 + (-2.0 * (y / x));
	} 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 (y <= (-1.75d+50)) then
        tmp = (x - y) / y
    else if (y <= 4.5d+55) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = y / (-x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.75e+50) {
		tmp = (x - y) / y;
	} else if (y <= 4.5e+55) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = y / (-x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.75e+50:
		tmp = (x - y) / y
	elif y <= 4.5e+55:
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = y / (-x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.75e+50)
		tmp = Float64(Float64(x - y) / y);
	elseif (y <= 4.5e+55)
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(y / Float64(Float64(-x) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.75e+50)
		tmp = (x - y) / y;
	elseif (y <= 4.5e+55)
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = y / (-x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.75e+50], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 4.5e+55], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[((-x) - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75000000000000003e50

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.9%

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

   if -1.75000000000000003e50 < y < 4.49999999999999998e55

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 72.9%

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

   if 4.49999999999999998e55 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.0%

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

      1. neg-mul-1 79.0%

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

   5. Simplified 79.0%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+50}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.1e+49)
   (/ (- x y) y)
   (if (<= y 4.7e+17) (/ x (+ x y)) (/ y (- (- x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1e+49) {
		tmp = (x - y) / y;
	} else if (y <= 4.7e+17) {
		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 (y <= (-1.1d+49)) then
        tmp = (x - y) / y
    else if (y <= 4.7d+17) 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 (y <= -1.1e+49) {
		tmp = (x - y) / y;
	} else if (y <= 4.7e+17) {
		tmp = x / (x + y);
	} else {
		tmp = y / (-x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.1e+49:
		tmp = (x - y) / y
	elif y <= 4.7e+17:
		tmp = x / (x + y)
	else:
		tmp = y / (-x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1e+49)
		tmp = Float64(Float64(x - y) / y);
	elseif (y <= 4.7e+17)
		tmp = Float64(x / Float64(x + y));
	else
		tmp = Float64(y / Float64(Float64(-x) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.1e+49)
		tmp = (x - y) / y;
	elseif (y <= 4.7e+17)
		tmp = x / (x + y);
	else
		tmp = y / (-x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1e+49], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 4.7e+17], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], N[(y / N[((-x) - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e49

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.9%

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

   if -1.1e49 < y < 4.7e17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.7%

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

   if 4.7e17 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 73.6%

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

      1. neg-mul-1 73.6%

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

   5. Simplified 73.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+49} \lor \neg \left(y \leq 1.45 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.5e+49) (not (<= y 1.45e+17))) (/ (- x y) y) (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.5e+49) || !(y <= 1.45e+17)) {
		tmp = (x - y) / 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 <= (-1.5d+49)) .or. (.not. (y <= 1.45d+17))) then
        tmp = (x - y) / 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 <= -1.5e+49) || !(y <= 1.45e+17)) {
		tmp = (x - y) / y;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.5e+49) or not (y <= 1.45e+17):
		tmp = (x - y) / y
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.5e+49) || !(y <= 1.45e+17))
		tmp = Float64(Float64(x - y) / y);
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.5e+49) || ~((y <= 1.45e+17)))
		tmp = (x - y) / y;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.5e+49], N[Not[LessEqual[y, 1.45e+17]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5000000000000001e49 or 1.45e17 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.8%

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

   if -1.5000000000000001e49 < y < 1.45e17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+49} \lor \neg \left(y \leq 1.45 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+51}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.4e+51) -1.0 (if (<= y 4.6e+55) (/ x (+ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.4e+51) {
		tmp = -1.0;
	} else if (y <= 4.6e+55) {
		tmp = x / (x + y);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.4d+51)) then
        tmp = -1.0d0
    else if (y <= 4.6d+55) then
        tmp = x / (x + y)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.4e+51) {
		tmp = -1.0;
	} else if (y <= 4.6e+55) {
		tmp = x / (x + y);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.4e+51:
		tmp = -1.0
	elif y <= 4.6e+55:
		tmp = x / (x + y)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.4e+51)
		tmp = -1.0;
	elseif (y <= 4.6e+55)
		tmp = Float64(x / Float64(x + y));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.4e+51)
		tmp = -1.0;
	elseif (y <= 4.6e+55)
		tmp = x / (x + y);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.4e+51], -1.0, If[LessEqual[y, 4.6e+55], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000002e51 or 4.59999999999999975e55 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.5%

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

   if -1.40000000000000002e51 < y < 4.59999999999999975e55

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 72.1%

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

Alternative 7: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+50}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+54}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2e+50) -1.0 (if (<= y 4.1e+54) (- 1.0 (/ y x)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2e+50) {
		tmp = -1.0;
	} else if (y <= 4.1e+54) {
		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 <= (-2d+50)) then
        tmp = -1.0d0
    else if (y <= 4.1d+54) 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 <= -2e+50) {
		tmp = -1.0;
	} else if (y <= 4.1e+54) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2e+50:
		tmp = -1.0
	elif y <= 4.1e+54:
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2e+50)
		tmp = -1.0;
	elseif (y <= 4.1e+54)
		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 <= -2e+50)
		tmp = -1.0;
	elseif (y <= 4.1e+54)
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2e+50], -1.0, If[LessEqual[y, 4.1e+54], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0000000000000002e50 or 4.09999999999999967e54 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.5%

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

   if -2.0000000000000002e50 < y < 4.09999999999999967e54

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 72.1%

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

   4. Taylor expanded in x around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

   6. Simplified 72.0%

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

Alternative 8: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+49}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 200000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6e+49) -1.0 (if (<= y 200000000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6e+49) {
		tmp = -1.0;
	} else if (y <= 200000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-6d+49)) then
        tmp = -1.0d0
    else if (y <= 200000000000.0d0) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6e+49) {
		tmp = -1.0;
	} else if (y <= 200000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6e+49:
		tmp = -1.0
	elif y <= 200000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6e+49)
		tmp = -1.0;
	elseif (y <= 200000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6e+49)
		tmp = -1.0;
	elseif (y <= 200000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6e+49], -1.0, If[LessEqual[y, 200000000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6.0000000000000005e49 or 2e11 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.1%

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

   if -6.0000000000000005e49 < y < 2e11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.8%

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

Alternative 9: 49.7% 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 99.9%

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

3. Taylor expanded in x around 0 50.5%

   \[\leadsto \color{blue}{-1} \]
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 2024165 
(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)))