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

Percentage Accurate: 100.0% → 99.9%

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: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{y + \left(x + y \cdot -2\right)}{y + x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ y (+ x (* y -2.0))) (+ y x)))

C

double code(double x, double y) {
	return (y + (x + (y * -2.0))) / (y + x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + (x + (y * (-2.0d0)))) / (y + x)
end function

Java

public static double code(double x, double y) {
	return (y + (x + (y * -2.0))) / (y + x);
}

Python

def code(x, y):
	return (y + (x + (y * -2.0))) / (y + x)

Julia

function code(x, y)
	return Float64(Float64(y + Float64(x + Float64(y * -2.0))) / Float64(y + x))
end

MATLAB

function tmp = code(x, y)
	tmp = (y + (x + (y * -2.0))) / (y + x);
end

Wolfram

code[x_, y_] := N[(N[(y + N[(x + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. *-un-lft-identity 100.0%

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

   2. *-un-lft-identity 100.0%

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

   3. prod-diff 100.0%

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

   4. *-commutative 100.0%

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

   5. *-un-lft-identity 100.0%

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

   6. fma-neg 100.0%

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

   7. *-un-lft-identity 100.0%

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

   8. *-commutative 100.0%

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

   9. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

   1. fma-undefine 100.0%

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

   2. *-rgt-identity 100.0%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. sub-neg 99.9%

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

   6. associate-+l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. neg-mul-1 100.0%

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

   9. distribute-rgt-out 100.0%

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

   10. metadata-eval 100.0%

       \[\leadsto \frac{y + \left(x + y \cdot \color{blue}{-2}\right)}{x + y} \]

6. Simplified 100.0%

   \[\leadsto \frac{\color{blue}{y + \left(x + y \cdot -2\right)}}{x + y} \]

7. Final simplification 100.0%

   \[\leadsto \frac{y + \left(x + y \cdot -2\right)}{y + x} \]
8. Add Preprocessing

Alternative 2: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-73} \lor \neg \left(x \leq 8.6 \cdot 10^{+35}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -9e-73) (not (<= x 8.6e+35)))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (* 2.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -9e-73) || !(x <= 8.6e+35)) {
		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 ((x <= (-9d-73)) .or. (.not. (x <= 8.6d+35))) 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 ((x <= -9e-73) || !(x <= 8.6e+35)) {
		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 (x <= -9e-73) or not (x <= 8.6e+35):
		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 ((x <= -9e-73) || !(x <= 8.6e+35))
		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 ((x <= -9e-73) || ~((x <= 8.6e+35)))
		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[Or[LessEqual[x, -9e-73], N[Not[LessEqual[x, 8.6e+35]], $MachinePrecision]], 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 2 regimes

2. if x < -9e-73 or 8.5999999999999995e35 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.2%

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

   if -9e-73 < x < 8.5999999999999995e35

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.8%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-73} \lor \neg \left(x \leq 8.6 \cdot 10^{+35}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-73} \lor \neg \left(x \leq 5.2 \cdot 10^{-47}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -9.5e-73) (not (<= x 5.2e-47)))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -9.5e-73) || !(x <= 5.2e-47)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (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 ((x <= (-9.5d-73)) .or. (.not. (x <= 5.2d-47))) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = (x / y) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -9.5e-73) || !(x <= 5.2e-47)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -9.5e-73) or not (x <= 5.2e-47):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -9.5e-73) || !(x <= 5.2e-47))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(x / y) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -9.5e-73) || ~((x <= 5.2e-47)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -9.5e-73], N[Not[LessEqual[x, 5.2e-47]], $MachinePrecision]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000005e-73 or 5.2e-47 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.5%

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

   if -9.50000000000000005e-73 < x < 5.2e-47

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.6%

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

      1. neg-mul-1 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around inf 80.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-73} \lor \neg \left(x \leq 5.2 \cdot 10^{-47}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-73} \lor \neg \left(x \leq 1.45 \cdot 10^{+38}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.35e-73) (not (<= x 1.45e+38)))
   (- 1.0 (/ y x))
   (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.35e-73) || !(x <= 1.45e+38)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = (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 ((x <= (-1.35d-73)) .or. (.not. (x <= 1.45d+38))) then
        tmp = 1.0d0 - (y / x)
    else
        tmp = (x / y) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.35e-73) || !(x <= 1.45e+38)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.35e-73) or not (x <= 1.45e+38):
		tmp = 1.0 - (y / x)
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.35e-73) || !(x <= 1.45e+38))
		tmp = Float64(1.0 - Float64(y / x));
	else
		tmp = Float64(Float64(x / y) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.35e-73) || ~((x <= 1.45e+38)))
		tmp = 1.0 - (y / x);
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.35e-73], N[Not[LessEqual[x, 1.45e+38]], $MachinePrecision]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.34999999999999997e-73 or 1.45000000000000003e38 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.7%

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

   4. Taylor expanded in x around inf 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

   6. Simplified 79.0%

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

   if -1.34999999999999997e-73 < x < 1.45000000000000003e38

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. neg-mul-1 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y around inf 75.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-73} \lor \neg \left(x \leq 1.45 \cdot 10^{+38}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-73} \lor \neg \left(x \leq 8.5 \cdot 10^{-49}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.6e-73) (not (<= x 8.5e-49))) (- 1.0 (/ y x)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.6e-73) || !(x <= 8.5e-49)) {
		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 ((x <= (-5.6d-73)) .or. (.not. (x <= 8.5d-49))) 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 ((x <= -5.6e-73) || !(x <= 8.5e-49)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.6e-73) or not (x <= 8.5e-49):
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.6e-73) || !(x <= 8.5e-49))
		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 ((x <= -5.6e-73) || ~((x <= 8.5e-49)))
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.6e-73], N[Not[LessEqual[x, 8.5e-49]], $MachinePrecision]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -5.60000000000000023e-73 or 8.50000000000000069e-49 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.0%

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

   4. Taylor expanded in x around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unsub-neg 75.2%

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

   6. Simplified 75.2%

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

   if -5.60000000000000023e-73 < x < 8.50000000000000069e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-73} \lor \neg \left(x \leq 8.5 \cdot 10^{-49}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e-73)
   (/ (- x y) x)
   (if (<= x 5.5e+35) (+ (/ x y) -1.0) (- 1.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e-73) {
		tmp = (x - y) / x;
	} else if (x <= 5.5e+35) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = 1.0 - (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 (x <= (-9.5d-73)) then
        tmp = (x - y) / x
    else if (x <= 5.5d+35) then
        tmp = (x / y) + (-1.0d0)
    else
        tmp = 1.0d0 - (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.5e-73) {
		tmp = (x - y) / x;
	} else if (x <= 5.5e+35) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e-73:
		tmp = (x - y) / x
	elif x <= 5.5e+35:
		tmp = (x / y) + -1.0
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e-73)
		tmp = Float64(Float64(x - y) / x);
	elseif (x <= 5.5e+35)
		tmp = Float64(Float64(x / y) + -1.0);
	else
		tmp = Float64(1.0 - Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e-73)
		tmp = (x - y) / x;
	elseif (x <= 5.5e+35)
		tmp = (x / y) + -1.0;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e-73], N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 5.5e+35], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000005e-73

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.8%

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

   4. Taylor expanded in x around inf 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

   6. Simplified 79.2%

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

   7. Taylor expanded in x around 0 79.2%

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

   if -9.50000000000000005e-73 < x < 5.50000000000000001e35

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. neg-mul-1 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y around inf 75.3%

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

   if 5.50000000000000001e35 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.5%

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

   4. Taylor expanded in x around inf 78.8%

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

      1. mul-1-neg 78.8%

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

      2. unsub-neg 78.8%

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

   6. Simplified 78.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+35}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.35e-73) 1.0 (if (<= x 9e+35) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.35e-73) {
		tmp = 1.0;
	} else if (x <= 9e+35) {
		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 (x <= (-1.35d-73)) then
        tmp = 1.0d0
    else if (x <= 9d+35) 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 (x <= -1.35e-73) {
		tmp = 1.0;
	} else if (x <= 9e+35) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.35e-73:
		tmp = 1.0
	elif x <= 9e+35:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.35e-73)
		tmp = 1.0;
	elseif (x <= 9e+35)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.35e-73)
		tmp = 1.0;
	elseif (x <= 9e+35)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.35e-73], 1.0, If[LessEqual[x, 9e+35], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.34999999999999997e-73 or 8.9999999999999993e35 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.3%

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

   if -1.34999999999999997e-73 < x < 8.9999999999999993e35

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.5%

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

Alternative 8: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 9: 49.9% 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 45.7%

   \[\leadsto \color{blue}{-1} \]
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 2024123 
(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)))