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

Percentage Accurate: 100.0% → 99.9%

Time: 5.8s

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: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y + x}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.22e+14)
   (/ x (+ y x))
   (if (<= x 2.8e-7) (+ (* 2.0 (/ x y)) -1.0) (- 1.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.22e+14) {
		tmp = x / (y + x);
	} else if (x <= 2.8e-7) {
		tmp = (2.0 * (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 <= (-1.22d+14)) then
        tmp = x / (y + x)
    else if (x <= 2.8d-7) then
        tmp = (2.0d0 * (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 <= -1.22e+14) {
		tmp = x / (y + x);
	} else if (x <= 2.8e-7) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.22e+14:
		tmp = x / (y + x)
	elif x <= 2.8e-7:
		tmp = (2.0 * (x / y)) + -1.0
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.22e+14)
		tmp = Float64(x / Float64(y + x));
	elseif (x <= 2.8e-7)
		tmp = Float64(Float64(2.0 * 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 <= -1.22e+14)
		tmp = x / (y + x);
	elseif (x <= 2.8e-7)
		tmp = (2.0 * (x / y)) + -1.0;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.22e+14], N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-7], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.22e14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.5%

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

   if -1.22e14 < x < 2.80000000000000019e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.1%

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

   if 2.80000000000000019e-7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.0%

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

   4. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. sub-neg 83.3%

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

   6. Simplified 83.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y + x}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -72000000000000 \lor \neg \left(x \leq 4.3 \cdot 10^{-7}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -72000000000000.0) (not (<= x 4.3e-7))) (- 1.0 (/ y x)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -72000000000000.0) || !(x <= 4.3e-7)) {
		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 <= (-72000000000000.0d0)) .or. (.not. (x <= 4.3d-7))) 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 <= -72000000000000.0) || !(x <= 4.3e-7)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -72000000000000.0) or not (x <= 4.3e-7):
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -72000000000000.0) || !(x <= 4.3e-7))
		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 <= -72000000000000.0) || ~((x <= 4.3e-7)))
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -72000000000000.0], N[Not[LessEqual[x, 4.3e-7]], $MachinePrecision]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -7.2e13 or 4.3000000000000001e-7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.8%

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

   4. Taylor expanded in x around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. sub-neg 82.8%

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

   6. Simplified 82.8%

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

   if -7.2e13 < x < 4.3000000000000001e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -72000000000000 \lor \neg \left(x \leq 4.3 \cdot 10^{-7}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -88000000000000:\\ \;\;\;\;\frac{x}{y + x}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-6}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -88000000000000.0)
   (/ x (+ y x))
   (if (<= x 1.02e-6) (/ (- x y) y) (- 1.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -88000000000000.0) {
		tmp = x / (y + x);
	} else if (x <= 1.02e-6) {
		tmp = (x - y) / y;
	} 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 <= (-88000000000000.0d0)) then
        tmp = x / (y + x)
    else if (x <= 1.02d-6) then
        tmp = (x - y) / y
    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 <= -88000000000000.0) {
		tmp = x / (y + x);
	} else if (x <= 1.02e-6) {
		tmp = (x - y) / y;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -88000000000000.0:
		tmp = x / (y + x)
	elif x <= 1.02e-6:
		tmp = (x - y) / y
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -88000000000000.0)
		tmp = Float64(x / Float64(y + x));
	elseif (x <= 1.02e-6)
		tmp = Float64(Float64(x - y) / y);
	else
		tmp = Float64(1.0 - Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -88000000000000.0)
		tmp = x / (y + x);
	elseif (x <= 1.02e-6)
		tmp = (x - y) / y;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -88000000000000.0], N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e-6], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.8e13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.5%

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

   if -8.8e13 < x < 1.02e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.0%

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

   if 1.02e-6 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.0%

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

   4. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. sub-neg 83.3%

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

   6. Simplified 83.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -88000000000000:\\ \;\;\;\;\frac{x}{y + x}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-6}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y + x}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.25e+14) (/ x (+ y x)) (if (<= x 9.2e-7) -1.0 (- 1.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.25e+14) {
		tmp = x / (y + x);
	} else if (x <= 9.2e-7) {
		tmp = -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 <= (-1.25d+14)) then
        tmp = x / (y + x)
    else if (x <= 9.2d-7) then
        tmp = -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 <= -1.25e+14) {
		tmp = x / (y + x);
	} else if (x <= 9.2e-7) {
		tmp = -1.0;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.25e+14:
		tmp = x / (y + x)
	elif x <= 9.2e-7:
		tmp = -1.0
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.25e+14)
		tmp = Float64(x / Float64(y + x));
	elseif (x <= 9.2e-7)
		tmp = -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 <= -1.25e+14)
		tmp = x / (y + x);
	elseif (x <= 9.2e-7)
		tmp = -1.0;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.25e+14], N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e-7], -1.0, N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.5%

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

   if -1.25e14 < x < 9.1999999999999998e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.3%

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

   if 9.1999999999999998e-7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.0%

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

   4. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. sub-neg 83.3%

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

   6. Simplified 83.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y + x}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-7}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+14) 1.0 (if (<= x 4e-7) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+14) {
		tmp = 1.0;
	} else if (x <= 4e-7) {
		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 <= (-1d+14)) then
        tmp = 1.0d0
    else if (x <= 4d-7) 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 <= -1e+14) {
		tmp = 1.0;
	} else if (x <= 4e-7) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+14:
		tmp = 1.0
	elif x <= 4e-7:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+14)
		tmp = 1.0;
	elseif (x <= 4e-7)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+14)
		tmp = 1.0;
	elseif (x <= 4e-7)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+14], 1.0, If[LessEqual[x, 4e-7], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1e14 or 3.9999999999999998e-7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.3%

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

   if -1e14 < x < 3.9999999999999998e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.3%

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

Alternative 7: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{x + y} \]
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. Final simplification 100.0%

   \[\leadsto \frac{x}{y + x} - \frac{y}{y + x} \]
6. 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: 49.0% 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 49.1%

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

Developer Target 1: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024137 
(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)))