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

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

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, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. div-sub 100.0%

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

   2. flip-+ 67.9%

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

   3. associate-/r/ 67.9%

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

   4. div-inv 67.7%

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

   5. prod-diff 67.7%

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

3. Applied egg-rr 67.7%

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

5. Simplified 62.9%

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

   1. associate-/l* 67.9%

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

   2. flip-+ 100.0%

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

   3. div-inv 99.9%

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

7. Applied egg-rr 99.9%

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

   1. un-div-inv 100.0%

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

   2. sub-div 100.0%

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

   3. clear-num 100.0%

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

   4. div-inv 99.7%

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

   5. associate-/r* 100.0%

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

9. Applied egg-rr 100.0%

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

10. Final simplification 100.0%

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

Alternative 2: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+58} \lor \neg \left(y \leq 0.00115\right) \land \left(y \leq 4.4 \cdot 10^{+207} \lor \neg \left(y \leq 2.55 \cdot 10^{+222}\right)\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.1e+58)
         (and (not (<= y 0.00115))
              (or (<= y 4.4e+207) (not (<= y 2.55e+222)))))
   (+ (* 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+58) || (!(y <= 0.00115) && ((y <= 4.4e+207) || !(y <= 2.55e+222)))) {
		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+58)) .or. (.not. (y <= 0.00115d0)) .and. (y <= 4.4d+207) .or. (.not. (y <= 2.55d+222))) 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+58) || (!(y <= 0.00115) && ((y <= 4.4e+207) || !(y <= 2.55e+222)))) {
		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+58) or (not (y <= 0.00115) and ((y <= 4.4e+207) or not (y <= 2.55e+222))):
		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+58) || (!(y <= 0.00115) && ((y <= 4.4e+207) || !(y <= 2.55e+222))))
		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+58) || (~((y <= 0.00115)) && ((y <= 4.4e+207) || ~((y <= 2.55e+222)))))
		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+58], And[N[Not[LessEqual[y, 0.00115]], $MachinePrecision], Or[LessEqual[y, 4.4e+207], N[Not[LessEqual[y, 2.55e+222]], $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 < -3.0999999999999999e58 or 0.00115 < y < 4.40000000000000017e207 or 2.55e222 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 79.3%

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

   if -3.0999999999999999e58 < y < 0.00115 or 4.40000000000000017e207 < y < 2.55e222

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in y around 0 80.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+58} \lor \neg \left(y \leq 0.00115\right) \land \left(y \leq 4.4 \cdot 10^{+207} \lor \neg \left(y \leq 2.55 \cdot 10^{+222}\right)\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]

Alternative 3: 72.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+58}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 0.0245 \lor \neg \left(y \leq 4.4 \cdot 10^{+207}\right) \land y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.5e+58)
   -1.0
   (if (or (<= y 0.0245) (and (not (<= y 4.4e+207)) (<= y 2.55e+222)))
     (+ 1.0 (* -2.0 (/ y x)))
     -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.5e+58) {
		tmp = -1.0;
	} else if ((y <= 0.0245) || (!(y <= 4.4e+207) && (y <= 2.55e+222))) {
		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 <= (-3.5d+58)) then
        tmp = -1.0d0
    else if ((y <= 0.0245d0) .or. (.not. (y <= 4.4d+207)) .and. (y <= 2.55d+222)) 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 <= -3.5e+58) {
		tmp = -1.0;
	} else if ((y <= 0.0245) || (!(y <= 4.4e+207) && (y <= 2.55e+222))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.5e+58:
		tmp = -1.0
	elif (y <= 0.0245) or (not (y <= 4.4e+207) and (y <= 2.55e+222)):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.5e+58)
		tmp = -1.0;
	elseif ((y <= 0.0245) || (!(y <= 4.4e+207) && (y <= 2.55e+222)))
		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 <= -3.5e+58)
		tmp = -1.0;
	elseif ((y <= 0.0245) || (~((y <= 4.4e+207)) && (y <= 2.55e+222)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.5e+58], -1.0, If[Or[LessEqual[y, 0.0245], And[N[Not[LessEqual[y, 4.4e+207]], $MachinePrecision], LessEqual[y, 2.55e+222]]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999997e58 or 0.024500000000000001 < y < 4.40000000000000017e207 or 2.55e222 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 78.5%

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

   if -3.4999999999999997e58 < y < 0.024500000000000001 or 4.40000000000000017e207 < y < 2.55e222

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in y around 0 80.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+58}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 0.0245 \lor \neg \left(y \leq 4.4 \cdot 10^{+207}\right) \land y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 71.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+58}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.9e+58)
   -1.0
   (if (<= y 1.4e+16)
     1.0
     (if (<= y 4.4e+207) -1.0 (if (<= y 2.55e+222) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.9e+58) {
		tmp = -1.0;
	} else if (y <= 1.4e+16) {
		tmp = 1.0;
	} else if (y <= 4.4e+207) {
		tmp = -1.0;
	} else if (y <= 2.55e+222) {
		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 <= (-4.9d+58)) then
        tmp = -1.0d0
    else if (y <= 1.4d+16) then
        tmp = 1.0d0
    else if (y <= 4.4d+207) then
        tmp = -1.0d0
    else if (y <= 2.55d+222) 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 <= -4.9e+58) {
		tmp = -1.0;
	} else if (y <= 1.4e+16) {
		tmp = 1.0;
	} else if (y <= 4.4e+207) {
		tmp = -1.0;
	} else if (y <= 2.55e+222) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.9e+58:
		tmp = -1.0
	elif y <= 1.4e+16:
		tmp = 1.0
	elif y <= 4.4e+207:
		tmp = -1.0
	elif y <= 2.55e+222:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.9e+58)
		tmp = -1.0;
	elseif (y <= 1.4e+16)
		tmp = 1.0;
	elseif (y <= 4.4e+207)
		tmp = -1.0;
	elseif (y <= 2.55e+222)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.9e+58)
		tmp = -1.0;
	elseif (y <= 1.4e+16)
		tmp = 1.0;
	elseif (y <= 4.4e+207)
		tmp = -1.0;
	elseif (y <= 2.55e+222)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.9e+58], -1.0, If[LessEqual[y, 1.4e+16], 1.0, If[LessEqual[y, 4.4e+207], -1.0, If[LessEqual[y, 2.55e+222], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.90000000000000018e58 or 1.4e16 < y < 4.40000000000000017e207 or 2.55e222 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 79.4%

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

   if -4.90000000000000018e58 < y < 1.4e16 or 4.40000000000000017e207 < y < 2.55e222

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around inf 78.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+58}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 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 100.0%

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

   1. div-sub 100.0%

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

   2. div-inv 99.9%

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

   3. fma-neg 99.9%

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

3. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{1}{x + y}, -\frac{y}{x + y}\right)} \]
4. Step-by-step derivation

   1. fma-udef 99.9%

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

   2. distribute-neg-frac 99.9%

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

   3. div-inv 99.7%

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

   4. distribute-rgt-in 99.7%

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

   5. sub-neg 99.7%

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

   6. *-commutative 99.7%

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

   7. div-inv 100.0%

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

   8. clear-num 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

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. Final simplification 100.0%

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

Alternative 7: 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. Taylor expanded in x around 0 47.6%

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

3. Final simplification 47.6%

   \[\leadsto -1 \]

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 2023200 
(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)))