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

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 10

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 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. Add Preprocessing

Alternative 2: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+42} \lor \neg \left(x \leq 9.5 \cdot 10^{-51}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.5e+42) (not (<= x 9.5e-51)))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (* 2.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.5e+42) || !(x <= 9.5e-51)) {
		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 <= (-2.5d+42)) .or. (.not. (x <= 9.5d-51))) 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 <= -2.5e+42) || !(x <= 9.5e-51)) {
		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 <= -2.5e+42) or not (x <= 9.5e-51):
		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 <= -2.5e+42) || !(x <= 9.5e-51))
		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 <= -2.5e+42) || ~((x <= 9.5e-51)))
		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, -2.5e+42], N[Not[LessEqual[x, 9.5e-51]], $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 < -2.50000000000000003e42 or 9.4999999999999998e-51 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.6%

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

   if -2.50000000000000003e42 < x < 9.4999999999999998e-51

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.4%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+42} \lor \neg \left(x \leq 9.5 \cdot 10^{-51}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+42} \lor \neg \left(x \leq 4.2 \cdot 10^{-46}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.5e+42) (not (<= x 4.2e-46)))
   (+ 1.0 (* -2.0 (/ y x)))
   (/ (- y) (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.5e+42) || !(x <= 4.2e-46)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -y / (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 <= (-2.5d+42)) .or. (.not. (x <= 4.2d-46))) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = -y / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.5e+42) || !(x <= 4.2e-46)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -y / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.5e+42) or not (x <= 4.2e-46):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -y / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.5e+42) || !(x <= 4.2e-46))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(-y) / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.5e+42) || ~((x <= 4.2e-46)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -y / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.5e+42], N[Not[LessEqual[x, 4.2e-46]], $MachinePrecision]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.50000000000000003e42 or 4.19999999999999975e-46 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.0%

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

   if -2.50000000000000003e42 < x < 4.19999999999999975e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.8%

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

      1. neg-mul-1 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+42} \lor \neg \left(x \leq 4.2 \cdot 10^{-46}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+42} \lor \neg \left(x \leq 4.5 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.6e+42) (not (<= x 4.5e-46)))
   (/ x (+ x y))
   (/ (- y) (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.6e+42) || !(x <= 4.5e-46)) {
		tmp = x / (x + y);
	} else {
		tmp = -y / (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 <= (-2.6d+42)) .or. (.not. (x <= 4.5d-46))) then
        tmp = x / (x + y)
    else
        tmp = -y / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.6e+42) || !(x <= 4.5e-46)) {
		tmp = x / (x + y);
	} else {
		tmp = -y / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.6e+42) or not (x <= 4.5e-46):
		tmp = x / (x + y)
	else:
		tmp = -y / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.6e+42) || !(x <= 4.5e-46))
		tmp = Float64(x / Float64(x + y));
	else
		tmp = Float64(Float64(-y) / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.6e+42) || ~((x <= 4.5e-46)))
		tmp = x / (x + y);
	else
		tmp = -y / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.6e+42], N[Not[LessEqual[x, 4.5e-46]], $MachinePrecision]], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e42 or 4.50000000000000001e-46 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.9%

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

   if -2.5999999999999999e42 < x < 4.50000000000000001e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.8%

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

      1. neg-mul-1 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+42} \lor \neg \left(x \leq 4.5 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+42} \lor \neg \left(x \leq 3.2 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.65e+42) (not (<= x 3.2e-50)))
   (/ x (+ x y))
   (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.65e+42) || !(x <= 3.2e-50)) {
		tmp = x / (x + y);
	} 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 <= (-2.65d+42)) .or. (.not. (x <= 3.2d-50))) then
        tmp = x / (x + y)
    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 <= -2.65e+42) || !(x <= 3.2e-50)) {
		tmp = x / (x + y);
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.65e+42) or not (x <= 3.2e-50):
		tmp = x / (x + y)
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.65e+42) || !(x <= 3.2e-50))
		tmp = Float64(x / Float64(x + y));
	else
		tmp = Float64(Float64(x / y) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.65e+42) || ~((x <= 3.2e-50)))
		tmp = x / (x + y);
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.65e+42], N[Not[LessEqual[x, 3.2e-50]], $MachinePrecision]], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.65000000000000014e42 or 3.2e-50 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.5%

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

   if -2.65000000000000014e42 < x < 3.2e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.2%

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

      1. neg-mul-1 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in y around inf 79.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+42} \lor \neg \left(x \leq 3.2 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+42} \lor \neg \left(x \leq 9.2 \cdot 10^{-48}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.6e+42) (not (<= x 9.2e-48)))
   (- 1.0 (/ y x))
   (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.6e+42) || !(x <= 9.2e-48)) {
		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 <= (-2.6d+42)) .or. (.not. (x <= 9.2d-48))) 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 <= -2.6e+42) || !(x <= 9.2e-48)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.6e+42) or not (x <= 9.2e-48):
		tmp = 1.0 - (y / x)
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.6e+42) || !(x <= 9.2e-48))
		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 <= -2.6e+42) || ~((x <= 9.2e-48)))
		tmp = 1.0 - (y / x);
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.6e+42], N[Not[LessEqual[x, 9.2e-48]], $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 < -2.5999999999999999e42 or 9.2000000000000003e-48 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.5%

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

   4. Taylor expanded in x around inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

   6. Simplified 76.5%

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

   if -2.5999999999999999e42 < x < 9.2000000000000003e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.2%

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

      1. neg-mul-1 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in y around inf 79.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+42} \lor \neg \left(x \leq 9.2 \cdot 10^{-48}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+42} \lor \neg \left(x \leq 1.15 \cdot 10^{-48}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.65e+42) (not (<= x 1.15e-48))) (- 1.0 (/ y x)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.65e+42) || !(x <= 1.15e-48)) {
		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 <= (-2.65d+42)) .or. (.not. (x <= 1.15d-48))) 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 <= -2.65e+42) || !(x <= 1.15e-48)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.65e+42) or not (x <= 1.15e-48):
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.65e+42) || !(x <= 1.15e-48))
		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 <= -2.65e+42) || ~((x <= 1.15e-48)))
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.65e+42], N[Not[LessEqual[x, 1.15e-48]], $MachinePrecision]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -2.65000000000000014e42 or 1.15e-48 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.5%

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

   4. Taylor expanded in x around inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

   6. Simplified 76.5%

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

   if -2.65000000000000014e42 < x < 1.15e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+42} \lor \neg \left(x \leq 1.15 \cdot 10^{-48}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-72}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.5e+42) 1.0 (if (<= x 3.5e-72) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+42) {
		tmp = 1.0;
	} else if (x <= 3.5e-72) {
		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 <= (-2.5d+42)) then
        tmp = 1.0d0
    else if (x <= 3.5d-72) 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 <= -2.5e+42) {
		tmp = 1.0;
	} else if (x <= 3.5e-72) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.5e+42:
		tmp = 1.0
	elif x <= 3.5e-72:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.5e+42)
		tmp = 1.0;
	elseif (x <= 3.5e-72)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.5e+42)
		tmp = 1.0;
	elseif (x <= 3.5e-72)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.5e+42], 1.0, If[LessEqual[x, 3.5e-72], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.50000000000000003e42 or 3.5e-72 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.5%

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

   if -2.50000000000000003e42 < x < 3.5e-72

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.0%

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

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 10: 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 50.0%

   \[\leadsto \color{blue}{-1} \]
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 2024130 
(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)))