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

Percentage Accurate: 100.0% → 100.0%

Time: 7.2s

Alternatives: 7

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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + y}\\ t_1 := \frac{y}{x + y}\\ \frac{\frac{x}{\frac{x + y}{t_0}} - t_1 \cdot t_1}{t_1 + t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ x y))) (t_1 (/ y (+ x y))))
   (/ (- (/ x (/ (+ x y) t_0)) (* t_1 t_1)) (+ t_1 t_0))))

C

double code(double x, double y) {
	double t_0 = x / (x + y);
	double t_1 = y / (x + y);
	return ((x / ((x + y) / t_0)) - (t_1 * t_1)) / (t_1 + t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    t_0 = x / (x + y)
    t_1 = y / (x + y)
    code = ((x / ((x + y) / t_0)) - (t_1 * t_1)) / (t_1 + t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (x + y);
	double t_1 = y / (x + y);
	return ((x / ((x + y) / t_0)) - (t_1 * t_1)) / (t_1 + t_0);
}

Python

def code(x, y):
	t_0 = x / (x + y)
	t_1 = y / (x + y)
	return ((x / ((x + y) / t_0)) - (t_1 * t_1)) / (t_1 + t_0)

Julia

function code(x, y)
	t_0 = Float64(x / Float64(x + y))
	t_1 = Float64(y / Float64(x + y))
	return Float64(Float64(Float64(x / Float64(Float64(x + y) / t_0)) - Float64(t_1 * t_1)) / Float64(t_1 + t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = x / (x + y);
	t_1 = y / (x + y);
	tmp = ((x / ((x + y) / t_0)) - (t_1 * t_1)) / (t_1 + t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(x / N[(N[(x + y), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 100.0%

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

   1. add-cbrt-cube 100.0%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{x - y}{x + y} \cdot \frac{x - y}{x + y}\right) \cdot \frac{x - y}{x + y}}} \]

   2. pow3 100.0%

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{x - y}{x + y}\right)}^{3}}} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{x - y}{x + y}\right)}^{3}}} \]
5. Step-by-step derivation

   1. rem-cbrt-cube 100.0%

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

   2. div-sub 100.0%

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

   3. flip-- 100.0%

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

6. Applied egg-rr 100.0%

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

   1. associate-*l/ 100.0%

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

   2. associate-/l* 100.0%

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

   3. +-commutative 100.0%

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

   4. +-commutative 100.0%

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

8. Applied egg-rr 100.0%

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

9. Final simplification 100.0%

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

Alternative 2: 100.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + y}\\ t_1 := \frac{y}{x + y}\\ \frac{t_0 \cdot t_0 - t_1 \cdot t_1}{t_1 + t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ x y))) (t_1 (/ y (+ x y))))
   (/ (- (* t_0 t_0) (* t_1 t_1)) (+ t_1 t_0))))

C

double code(double x, double y) {
	double t_0 = x / (x + y);
	double t_1 = y / (x + y);
	return ((t_0 * t_0) - (t_1 * t_1)) / (t_1 + t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    t_0 = x / (x + y)
    t_1 = y / (x + y)
    code = ((t_0 * t_0) - (t_1 * t_1)) / (t_1 + t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (x + y);
	double t_1 = y / (x + y);
	return ((t_0 * t_0) - (t_1 * t_1)) / (t_1 + t_0);
}

Python

def code(x, y):
	t_0 = x / (x + y)
	t_1 = y / (x + y)
	return ((t_0 * t_0) - (t_1 * t_1)) / (t_1 + t_0)

Julia

function code(x, y)
	t_0 = Float64(x / Float64(x + y))
	t_1 = Float64(y / Float64(x + y))
	return Float64(Float64(Float64(t_0 * t_0) - Float64(t_1 * t_1)) / Float64(t_1 + t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = x / (x + y);
	t_1 = y / (x + y);
	tmp = ((t_0 * t_0) - (t_1 * t_1)) / (t_1 + t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 100.0%

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

   1. add-cbrt-cube 100.0%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{x - y}{x + y} \cdot \frac{x - y}{x + y}\right) \cdot \frac{x - y}{x + y}}} \]

   2. pow3 100.0%

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{x - y}{x + y}\right)}^{3}}} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{x - y}{x + y}\right)}^{3}}} \]
5. Step-by-step derivation

   1. rem-cbrt-cube 100.0%

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

   2. div-sub 100.0%

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

   3. flip-- 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 3: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-16} \lor \neg \left(y \leq 2.75 \cdot 10^{+37}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.1e-16) (not (<= y 2.75e+37)))
   (+ (* 2.0 (/ x y)) -1.0)
   (+ 1.0 (* -2.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.1e-16) || !(y <= 2.75e+37)) {
		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 <= (-3.1d-16)) .or. (.not. (y <= 2.75d+37))) 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 <= -3.1e-16) || !(y <= 2.75e+37)) {
		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 <= -3.1e-16) or not (y <= 2.75e+37):
		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 <= -3.1e-16) || !(y <= 2.75e+37))
		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 <= -3.1e-16) || ~((y <= 2.75e+37)))
		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, -3.1e-16], N[Not[LessEqual[y, 2.75e+37]], $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 < -3.1000000000000001e-16 or 2.75000000000000008e37 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.1%

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

   if -3.1000000000000001e-16 < y < 2.75000000000000008e37

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.9%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-16} \lor \neg \left(y \leq 2.75 \cdot 10^{+37}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-16}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+38}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.4e-16) -1.0 (if (<= y 2.25e+38) (+ 1.0 (* -2.0 (/ y x))) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.4e-16) {
		tmp = -1.0;
	} else if (y <= 2.25e+38) {
		tmp = 1.0 + (-2.0 * (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 <= (-1.4d-16)) then
        tmp = -1.0d0
    else if (y <= 2.25d+38) then
        tmp = 1.0d0 + ((-2.0d0) * (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 <= -1.4e-16) {
		tmp = -1.0;
	} else if (y <= 2.25e+38) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.4e-16:
		tmp = -1.0
	elif y <= 2.25e+38:
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.4e-16)
		tmp = -1.0;
	elseif (y <= 2.25e+38)
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.4e-16)
		tmp = -1.0;
	elseif (y <= 2.25e+38)
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.4e-16], -1.0, If[LessEqual[y, 2.25e+38], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e-16 or 2.2499999999999999e38 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.3%

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

   if -1.4000000000000001e-16 < y < 2.2499999999999999e38

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-16}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+38}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-16}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e-16) -1.0 (if (<= y 8.4e+30) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e-16) {
		tmp = -1.0;
	} else if (y <= 8.4e+30) {
		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 <= (-1.8d-16)) then
        tmp = -1.0d0
    else if (y <= 8.4d+30) 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 <= -1.8e-16) {
		tmp = -1.0;
	} else if (y <= 8.4e+30) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.8e-16:
		tmp = -1.0
	elif y <= 8.4e+30:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e-16)
		tmp = -1.0;
	elseif (y <= 8.4e+30)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.8e-16)
		tmp = -1.0;
	elseif (y <= 8.4e+30)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e-16], -1.0, If[LessEqual[y, 8.4e+30], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999991e-16 or 8.4000000000000001e30 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.9%

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

   if -1.79999999999999991e-16 < y < 8.4000000000000001e30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-16}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 7: 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 100.0%

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

3. Taylor expanded in x around 0 50.1%

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

4. Final simplification 50.1%

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

Developer target: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024019 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

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