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

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Alternatives: 11

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 99.9%

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

Alternative 2: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-57} \lor \neg \left(y \leq 2.2 \cdot 10^{+15}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.2e-57) (not (<= y 2.2e+15)))
   (+ (* 2.0 (/ x y)) -1.0)
   (+ 1.0 (* -2.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.2e-57) || !(y <= 2.2e+15)) {
		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 <= (-3.2d-57)) .or. (.not. (y <= 2.2d+15))) 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 <= -3.2e-57) || !(y <= 2.2e+15)) {
		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 <= -3.2e-57) or not (y <= 2.2e+15):
		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 <= -3.2e-57) || !(y <= 2.2e+15))
		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 <= -3.2e-57) || ~((y <= 2.2e+15)))
		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, -3.2e-57], N[Not[LessEqual[y, 2.2e+15]], $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 < -3.2000000000000001e-57 or 2.2e15 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.0%

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

   if -3.2000000000000001e-57 < y < 2.2e15

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-57} \lor \neg \left(y \leq 2.2 \cdot 10^{+15}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+16}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.4e-57)
   (/ (- x y) y)
   (if (<= y 8.5e+16) (+ 1.0 (* -2.0 (/ y x))) (/ y (- (- x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.4e-57) {
		tmp = (x - y) / y;
	} else if (y <= 8.5e+16) {
		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 <= (-3.4d-57)) then
        tmp = (x - y) / y
    else if (y <= 8.5d+16) 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 <= -3.4e-57) {
		tmp = (x - y) / y;
	} else if (y <= 8.5e+16) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = y / (-x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.4e-57:
		tmp = (x - y) / y
	elif y <= 8.5e+16:
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = y / (-x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.4e-57)
		tmp = Float64(Float64(x - y) / y);
	elseif (y <= 8.5e+16)
		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 <= -3.4e-57)
		tmp = (x - y) / y;
	elseif (y <= 8.5e+16)
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = y / (-x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.4e-57], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8.5e+16], 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 < -3.40000000000000016e-57

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 72.3%

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

   if -3.40000000000000016e-57 < y < 8.5e16

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.5%

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

   if 8.5e16 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.0%

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

      1. neg-mul-1 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-57}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+16}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -650000:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;y \leq 125000000:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -650000.0)
   (/ (- x y) y)
   (if (<= y 125000000.0) (/ x (+ x y)) (/ y (- (- x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -650000.0) {
		tmp = (x - y) / y;
	} else if (y <= 125000000.0) {
		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 <= (-650000.0d0)) then
        tmp = (x - y) / y
    else if (y <= 125000000.0d0) 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 <= -650000.0) {
		tmp = (x - y) / y;
	} else if (y <= 125000000.0) {
		tmp = x / (x + y);
	} else {
		tmp = y / (-x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -650000.0:
		tmp = (x - y) / y
	elif y <= 125000000.0:
		tmp = x / (x + y)
	else:
		tmp = y / (-x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -650000.0)
		tmp = Float64(Float64(x - y) / y);
	elseif (y <= 125000000.0)
		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 <= -650000.0)
		tmp = (x - y) / y;
	elseif (y <= 125000000.0)
		tmp = x / (x + y);
	else
		tmp = y / (-x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -650000.0], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 125000000.0], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], N[(y / N[((-x) - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.0%

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

   if -6.5e5 < y < 1.25e8

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 73.2%

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

   if 1.25e8 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.0%

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

      1. neg-mul-1 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -650000:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;y \leq 125000000:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11500 \lor \neg \left(y \leq 18000000\right):\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -11500.0) (not (<= y 18000000.0))) (/ (- x y) y) (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -11500.0) || !(y <= 18000000.0)) {
		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 <= (-11500.0d0)) .or. (.not. (y <= 18000000.0d0))) 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 <= -11500.0) || !(y <= 18000000.0)) {
		tmp = (x - y) / y;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -11500.0) or not (y <= 18000000.0):
		tmp = (x - y) / y
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -11500.0) || !(y <= 18000000.0))
		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 <= -11500.0) || ~((y <= 18000000.0)))
		tmp = (x - y) / y;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -11500.0], N[Not[LessEqual[y, 18000000.0]], $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 < -11500 or 1.8e7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.3%

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

   if -11500 < y < 1.8e7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 73.2%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11500 \lor \neg \left(y \leq 18000000\right):\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -95000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3600000000000:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -95000.0) -1.0 (if (<= y 3600000000000.0) (/ x (+ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -95000.0) {
		tmp = -1.0;
	} else if (y <= 3600000000000.0) {
		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 <= (-95000.0d0)) then
        tmp = -1.0d0
    else if (y <= 3600000000000.0d0) 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 <= -95000.0) {
		tmp = -1.0;
	} else if (y <= 3600000000000.0) {
		tmp = x / (x + y);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -95000.0:
		tmp = -1.0
	elif y <= 3600000000000.0:
		tmp = x / (x + y)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -95000.0)
		tmp = -1.0;
	elseif (y <= 3600000000000.0)
		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 <= -95000.0)
		tmp = -1.0;
	elseif (y <= 3600000000000.0)
		tmp = x / (x + y);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -95000.0], -1.0, If[LessEqual[y, 3600000000000.0], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -95000 or 3.6e12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.6%

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

   if -95000 < y < 3.6e12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 73.2%

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

Alternative 7: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-8}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 80000000000:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.1e-8) -1.0 (if (<= y 80000000000.0) (- 1.0 (/ y x)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1e-8) {
		tmp = -1.0;
	} else if (y <= 80000000000.0) {
		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 <= (-1.1d-8)) then
        tmp = -1.0d0
    else if (y <= 80000000000.0d0) 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 <= -1.1e-8) {
		tmp = -1.0;
	} else if (y <= 80000000000.0) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.1e-8:
		tmp = -1.0
	elif y <= 80000000000.0:
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1e-8)
		tmp = -1.0;
	elseif (y <= 80000000000.0)
		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 <= -1.1e-8)
		tmp = -1.0;
	elseif (y <= 80000000000.0)
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1e-8], -1.0, If[LessEqual[y, 80000000000.0], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0999999999999999e-8 or 8e10 < 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 -1.0999999999999999e-8 < y < 8e10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 73.5%

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

   4. Taylor expanded in x around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-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: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3200000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3200000.0) -1.0 (if (<= y 8000000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3200000.0) {
		tmp = -1.0;
	} else if (y <= 8000000000.0) {
		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 <= (-3200000.0d0)) then
        tmp = -1.0d0
    else if (y <= 8000000000.0d0) 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 <= -3200000.0) {
		tmp = -1.0;
	} else if (y <= 8000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3200000.0:
		tmp = -1.0
	elif y <= 8000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3200000.0)
		tmp = -1.0;
	elseif (y <= 8000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3200000.0)
		tmp = -1.0;
	elseif (y <= 8000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3200000.0], -1.0, If[LessEqual[y, 8000000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e6 or 8e9 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.6%

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

   if -3.2e6 < y < 8e9

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 72.4%

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

Alternative 9: 100.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{x + y}{x - y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0 / ((x + y) / (x - y))

Julia

function code(x, y)
	return Float64(1.0 / Float64(Float64(x + y) / Float64(x - y)))
end

MATLAB

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

Wolfram

code[x_, y_] := N[(1.0 / N[(N[(x + y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. clear-num 99.9%

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

   2. associate-/r/ 99.8%

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

4. Applied egg-rr 99.8%

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

   1. associate-*l/ 99.9%

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

   2. *-un-lft-identity 99.9%

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

   3. clear-num 99.9%

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

6. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x - y}}} \]
7. Add Preprocessing

Alternative 10: 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 11: 48.9% 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 50.6%

   \[\leadsto \color{blue}{-1} \]
4. Add Preprocessing

Developer Target 1: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024180 
(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)))