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

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

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: 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: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+61}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x} \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.2e+61)
   (- 1.0 (/ y x))
   (if (<= x 3.6e+100) (+ (* 2.0 (/ x y)) -1.0) (+ 1.0 (* (/ y x) -2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.2e+61) {
		tmp = 1.0 - (y / x);
	} else if (x <= 3.6e+100) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0 + ((y / x) * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-8.2d+61)) then
        tmp = 1.0d0 - (y / x)
    else if (x <= 3.6d+100) then
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    else
        tmp = 1.0d0 + ((y / x) * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -8.2e+61) {
		tmp = 1.0 - (y / x);
	} else if (x <= 3.6e+100) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0 + ((y / x) * -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.2e+61:
		tmp = 1.0 - (y / x)
	elif x <= 3.6e+100:
		tmp = (2.0 * (x / y)) + -1.0
	else:
		tmp = 1.0 + ((y / x) * -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.2e+61)
		tmp = Float64(1.0 - Float64(y / x));
	elseif (x <= 3.6e+100)
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	else
		tmp = Float64(1.0 + Float64(Float64(y / x) * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8.2e+61)
		tmp = 1.0 - (y / x);
	elseif (x <= 3.6e+100)
		tmp = (2.0 * (x / y)) + -1.0;
	else
		tmp = 1.0 + ((y / x) * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.2e+61], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+100], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(1.0 + N[(N[(y / x), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.19999999999999944e61

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.5%

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

      1. div-sub 87.5%

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

      2. *-inverses 87.5%

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

      3. sub-neg 87.5%

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

   5. Applied egg-rr 87.5%

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

   6. Taylor expanded in y around 0 87.5%

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

      1. neg-mul-1 87.5%

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

      2. sub-neg 87.5%

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

   8. Simplified 87.5%

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

   if -8.19999999999999944e61 < x < 3.6e100

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.9%

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

   if 3.6e100 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+61}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x} \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+63}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+107}:\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x} \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.2e+63)
   (- 1.0 (/ y x))
   (if (<= x 3.6e+107) (/ (- y) (+ x y)) (+ 1.0 (* (/ y x) -2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.2e+63) {
		tmp = 1.0 - (y / x);
	} else if (x <= 3.6e+107) {
		tmp = -y / (x + y);
	} else {
		tmp = 1.0 + ((y / x) * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.2d+63)) then
        tmp = 1.0d0 - (y / x)
    else if (x <= 3.6d+107) then
        tmp = -y / (x + y)
    else
        tmp = 1.0d0 + ((y / x) * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.2e+63) {
		tmp = 1.0 - (y / x);
	} else if (x <= 3.6e+107) {
		tmp = -y / (x + y);
	} else {
		tmp = 1.0 + ((y / x) * -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.2e+63:
		tmp = 1.0 - (y / x)
	elif x <= 3.6e+107:
		tmp = -y / (x + y)
	else:
		tmp = 1.0 + ((y / x) * -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.2e+63)
		tmp = Float64(1.0 - Float64(y / x));
	elseif (x <= 3.6e+107)
		tmp = Float64(Float64(-y) / Float64(x + y));
	else
		tmp = Float64(1.0 + Float64(Float64(y / x) * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.2e+63)
		tmp = 1.0 - (y / x);
	elseif (x <= 3.6e+107)
		tmp = -y / (x + y);
	else
		tmp = 1.0 + ((y / x) * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.2e+63], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+107], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y / x), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1999999999999999e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.5%

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

      1. div-sub 87.5%

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

      2. *-inverses 87.5%

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

      3. sub-neg 87.5%

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

   5. Applied egg-rr 87.5%

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

   6. Taylor expanded in y around 0 87.5%

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

      1. neg-mul-1 87.5%

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

      2. sub-neg 87.5%

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

   8. Simplified 87.5%

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

   if -2.1999999999999999e63 < x < 3.5999999999999998e107

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. neg-mul-1 74.6%

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

   5. Simplified 74.6%

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

   if 3.5999999999999998e107 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 85.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+63}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+107}:\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x} \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+61} \lor \neg \left(x \leq 2.8 \cdot 10^{+99}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -8.5e+61) (not (<= x 2.8e+99)))
   (- 1.0 (/ y x))
   (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -8.5e+61) || !(x <= 2.8e+99)) {
		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 <= (-8.5d+61)) .or. (.not. (x <= 2.8d+99))) 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 <= -8.5e+61) || !(x <= 2.8e+99)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -8.5e+61) or not (x <= 2.8e+99):
		tmp = 1.0 - (y / x)
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -8.5e+61) || !(x <= 2.8e+99))
		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 <= -8.5e+61) || ~((x <= 2.8e+99)))
		tmp = 1.0 - (y / x);
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -8.5e+61], N[Not[LessEqual[x, 2.8e+99]], $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 < -8.50000000000000035e61 or 2.8e99 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.5%

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

      1. div-sub 84.5%

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

      2. *-inverses 84.5%

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

      3. sub-neg 84.5%

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

   5. Applied egg-rr 84.5%

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

   6. Taylor expanded in y around 0 84.5%

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

      1. neg-mul-1 84.5%

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

      2. sub-neg 84.5%

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

   8. Simplified 84.5%

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

   if -8.50000000000000035e61 < x < 2.8e99

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.1%

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

      1. neg-mul-1 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in y around inf 75.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+61} \lor \neg \left(x \leq 2.8 \cdot 10^{+99}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+61} \lor \neg \left(x \leq 3.2 \cdot 10^{+107}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.5e+61) (not (<= x 3.2e+107))) (- 1.0 (/ y x)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.5e+61) || !(x <= 3.2e+107)) {
		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 <= (-4.5d+61)) .or. (.not. (x <= 3.2d+107))) 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 <= -4.5e+61) || !(x <= 3.2e+107)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.5e+61) or not (x <= 3.2e+107):
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.5e+61) || !(x <= 3.2e+107))
		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 <= -4.5e+61) || ~((x <= 3.2e+107)))
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.5e+61], N[Not[LessEqual[x, 3.2e+107]], $MachinePrecision]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e61 or 3.20000000000000029e107 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. div-sub 86.0%

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

      2. *-inverses 86.0%

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

      3. sub-neg 86.0%

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

   5. Applied egg-rr 86.0%

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

   6. Taylor expanded in y around 0 86.0%

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

      1. neg-mul-1 86.0%

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

      2. sub-neg 86.0%

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

   8. Simplified 86.0%

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

   if -4.5e61 < x < 3.20000000000000029e107

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 73.9%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+61} \lor \neg \left(x \leq 3.2 \cdot 10^{+107}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+65}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 10^{+100}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2e+65)
   (- 1.0 (/ y x))
   (if (<= x 1e+100) (+ (/ x y) -1.0) (/ x (+ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e+65) {
		tmp = 1.0 - (y / x);
	} else if (x <= 1e+100) {
		tmp = (x / y) + -1.0;
	} 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 (x <= (-2d+65)) then
        tmp = 1.0d0 - (y / x)
    else if (x <= 1d+100) then
        tmp = (x / y) + (-1.0d0)
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2e+65) {
		tmp = 1.0 - (y / x);
	} else if (x <= 1e+100) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e+65:
		tmp = 1.0 - (y / x)
	elif x <= 1e+100:
		tmp = (x / y) + -1.0
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e+65)
		tmp = Float64(1.0 - Float64(y / x));
	elseif (x <= 1e+100)
		tmp = Float64(Float64(x / y) + -1.0);
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e+65)
		tmp = 1.0 - (y / x);
	elseif (x <= 1e+100)
		tmp = (x / y) + -1.0;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e+65], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+100], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e65

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.5%

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

      1. div-sub 87.5%

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

      2. *-inverses 87.5%

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

      3. sub-neg 87.5%

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

   5. Applied egg-rr 87.5%

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

   6. Taylor expanded in y around 0 87.5%

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

      1. neg-mul-1 87.5%

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

      2. sub-neg 87.5%

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

   8. Simplified 87.5%

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

   if -2e65 < x < 1.00000000000000002e100

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.1%

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

      1. neg-mul-1 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in y around inf 75.2%

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

   if 1.00000000000000002e100 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.1%

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

   4. Taylor expanded in y around 0 81.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+65}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 10^{+100}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+105}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.4e+61) 1.0 (if (<= x 2e+105) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.4e+61) {
		tmp = 1.0;
	} else if (x <= 2e+105) {
		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 <= (-4.4d+61)) then
        tmp = 1.0d0
    else if (x <= 2d+105) 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 <= -4.4e+61) {
		tmp = 1.0;
	} else if (x <= 2e+105) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.4e+61:
		tmp = 1.0
	elif x <= 2e+105:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.4e+61)
		tmp = 1.0;
	elseif (x <= 2e+105)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.4e+61)
		tmp = 1.0;
	elseif (x <= 2e+105)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.4e+61], 1.0, If[LessEqual[x, 2e+105], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4000000000000001e61 or 1.9999999999999999e105 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.8%

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

   if -4.4000000000000001e61 < x < 1.9999999999999999e105

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.2%

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

Alternative 8: 100.0% accurate, 1.0× speedup

Math

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

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 9: 49.7% 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 52.9%

   \[\leadsto \color{blue}{-1} \]
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 2024135 
(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)))