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

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 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: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+21} \lor \neg \left(y \leq 2.6 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.15e+21) (not (<= y 2.6e-11)))
   (/ (- y) (+ x y))
   (+ 1.0 (* -2.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.15e+21) || !(y <= 2.6e-11)) {
		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 <= (-1.15d+21)) .or. (.not. (y <= 2.6d-11))) 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 <= -1.15e+21) || !(y <= 2.6e-11)) {
		tmp = -y / (x + y);
	} else {
		tmp = 1.0 + (-2.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.15e+21) or not (y <= 2.6e-11):
		tmp = -y / (x + y)
	else:
		tmp = 1.0 + (-2.0 * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.15e+21) || !(y <= 2.6e-11))
		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 <= -1.15e+21) || ~((y <= 2.6e-11)))
		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, -1.15e+21], N[Not[LessEqual[y, 2.6e-11]], $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 < -1.15e21 or 2.6000000000000001e-11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.2%

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

      1. neg-mul-1 85.2%

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

   5. Simplified 85.2%

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

   if -1.15e21 < y < 2.6000000000000001e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+21} \lor \neg \left(y \leq 2.6 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-14}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.8e+26)
   (/ (- y) (+ x y))
   (if (<= y 4.6e-14) (+ 1.0 (* -2.0 (/ y x))) (+ (* 2.0 (/ x y)) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.8e+26) {
		tmp = -y / (x + y);
	} else if (y <= 4.6e-14) {
		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 <= (-8.8d+26)) then
        tmp = -y / (x + y)
    else if (y <= 4.6d-14) 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 <= -8.8e+26) {
		tmp = -y / (x + y);
	} else if (y <= 4.6e-14) {
		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 <= -8.8e+26:
		tmp = -y / (x + y)
	elif y <= 4.6e-14:
		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 <= -8.8e+26)
		tmp = Float64(Float64(-y) / Float64(x + y));
	elseif (y <= 4.6e-14)
		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 <= -8.8e+26)
		tmp = -y / (x + y);
	elseif (y <= 4.6e-14)
		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, -8.8e+26], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-14], 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 < -8.80000000000000028e26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.9%

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

      1. neg-mul-1 86.9%

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

   5. Simplified 86.9%

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

   if -8.80000000000000028e26 < y < 4.59999999999999996e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

   if 4.59999999999999996e-14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-14}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+24} \lor \neg \left(y \leq 10500\right):\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.9e+24) (not (<= y 10500.0)))
   (/ (- y) (+ x y))
   (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.9e+24) || !(y <= 10500.0)) {
		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 <= (-2.9d+24)) .or. (.not. (y <= 10500.0d0))) 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 <= -2.9e+24) || !(y <= 10500.0)) {
		tmp = -y / (x + y);
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.9e+24) or not (y <= 10500.0):
		tmp = -y / (x + y)
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.9e+24) || !(y <= 10500.0))
		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 <= -2.9e+24) || ~((y <= 10500.0)))
		tmp = -y / (x + y);
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.9e+24], N[Not[LessEqual[y, 10500.0]], $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 < -2.89999999999999979e24 or 10500 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. neg-mul-1 85.8%

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

   5. Simplified 85.8%

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

   if -2.89999999999999979e24 < y < 10500

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+24} \lor \neg \left(y \leq 10500\right):\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+27} \lor \neg \left(y \leq 330000000\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.12e+27) (not (<= y 330000000.0)))
   (+ (/ x y) -1.0)
   (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.12e+27) || !(y <= 330000000.0)) {
		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 <= (-1.12d+27)) .or. (.not. (y <= 330000000.0d0))) 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 <= -1.12e+27) || !(y <= 330000000.0)) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.12e+27) or not (y <= 330000000.0):
		tmp = (x / y) + -1.0
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.12e+27) || !(y <= 330000000.0))
		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 <= -1.12e+27) || ~((y <= 330000000.0)))
		tmp = (x / y) + -1.0;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.12e+27], N[Not[LessEqual[y, 330000000.0]], $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 < -1.12e27 or 3.3e8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.3%

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

      1. neg-mul-1 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around inf 86.0%

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

   if -1.12e27 < y < 3.3e8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+27} \lor \neg \left(y \leq 330000000\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+21} \lor \neg \left(y \leq 7 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.25e+21) (not (<= y 7e-15))) (+ (/ x y) -1.0) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.25e+21) || !(y <= 7e-15)) {
		tmp = (x / y) + -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 <= (-1.25d+21)) .or. (.not. (y <= 7d-15))) then
        tmp = (x / y) + (-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 <= -1.25e+21) || !(y <= 7e-15)) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.25e+21) or not (y <= 7e-15):
		tmp = (x / y) + -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.25e+21) || !(y <= 7e-15))
		tmp = Float64(Float64(x / y) + -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.25e+21) || ~((y <= 7e-15)))
		tmp = (x / y) + -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.25e+21], N[Not[LessEqual[y, 7e-15]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e21 or 7.0000000000000001e-15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.2%

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

      1. neg-mul-1 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in y around inf 84.9%

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

   if -1.25e21 < y < 7.0000000000000001e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+21} \lor \neg \left(y \leq 7 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+28}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 100000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+28) -1.0 (if (<= y 100000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+28) {
		tmp = -1.0;
	} else if (y <= 100000.0) {
		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 <= (-5d+28)) then
        tmp = -1.0d0
    else if (y <= 100000.0d0) 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 <= -5e+28) {
		tmp = -1.0;
	} else if (y <= 100000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+28:
		tmp = -1.0
	elif y <= 100000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+28)
		tmp = -1.0;
	elseif (y <= 100000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+28)
		tmp = -1.0;
	elseif (y <= 100000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+28], -1.0, If[LessEqual[y, 100000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999957e28 or 1e5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.2%

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

   if -4.99999999999999957e28 < y < 1e5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.5%

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

Alternative 8: 49.5% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 56.1%

   \[\leadsto \color{blue}{-1} \]
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 2024177 
(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)))