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

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

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, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. clear-num 100.0%

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

   2. associate-/r/ 99.7%

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

4. Applied egg-rr 99.7%

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

   1. associate-*l/ 99.9%

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

   2. *-un-lft-identity 99.9%

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

   3. clear-num 100.0%

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

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x - y}}} \]
7. Add Preprocessing

Alternative 2: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8500000000 \lor \neg \left(x \leq 5.3 \cdot 10^{-12}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -8500000000.0) (not (<= x 5.3e-12)))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (* 2.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -8500000000.0) || !(x <= 5.3e-12)) {
		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 <= (-8500000000.0d0)) .or. (.not. (x <= 5.3d-12))) 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 <= -8500000000.0) || !(x <= 5.3e-12)) {
		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 <= -8500000000.0) or not (x <= 5.3e-12):
		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 <= -8500000000.0) || !(x <= 5.3e-12))
		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 <= -8500000000.0) || ~((x <= 5.3e-12)))
		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, -8500000000.0], N[Not[LessEqual[x, 5.3e-12]], $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 < -8.5e9 or 5.29999999999999963e-12 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.1%

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

   if -8.5e9 < x < 5.29999999999999963e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.4%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8500000000 \lor \neg \left(x \leq 5.3 \cdot 10^{-12}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7800000000 \lor \neg \left(x \leq 1.12 \cdot 10^{-10}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7800000000.0) (not (<= x 1.12e-10)))
   (+ 1.0 (* -2.0 (/ y x)))
   (/ (- x y) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7800000000.0) || !(x <= 1.12e-10)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (x - y) / 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 <= (-7800000000.0d0)) .or. (.not. (x <= 1.12d-10))) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = (x - y) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -7800000000.0) || !(x <= 1.12e-10)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (x - y) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7800000000.0) or not (x <= 1.12e-10):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = (x - y) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7800000000.0) || !(x <= 1.12e-10))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(x - y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -7800000000.0) || ~((x <= 1.12e-10)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = (x - y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7800000000.0], N[Not[LessEqual[x, 1.12e-10]], $MachinePrecision]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.8e9 or 1.12e-10 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.1%

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

   if -7.8e9 < x < 1.12e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7800000000 \lor \neg \left(x \leq 1.12 \cdot 10^{-10}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -310000000000 \lor \neg \left(x \leq 1.9 \cdot 10^{-36}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -310000000000.0) (not (<= x 1.9e-36))) (- 1.0 (/ y x)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -310000000000.0) || !(x <= 1.9e-36)) {
		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 <= (-310000000000.0d0)) .or. (.not. (x <= 1.9d-36))) 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 <= -310000000000.0) || !(x <= 1.9e-36)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -310000000000.0) or not (x <= 1.9e-36):
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -310000000000.0) || !(x <= 1.9e-36))
		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 <= -310000000000.0) || ~((x <= 1.9e-36)))
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -310000000000.0], N[Not[LessEqual[x, 1.9e-36]], $MachinePrecision]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e11 or 1.89999999999999985e-36 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 79.0%

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

   4. Taylor expanded in x around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. unsub-neg 78.9%

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

   6. Simplified 78.9%

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

   if -3.1e11 < x < 1.89999999999999985e-36

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -310000000000 \lor \neg \left(x \leq 1.9 \cdot 10^{-36}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -920000000000:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-13}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -920000000000.0)
   (/ x (+ x y))
   (if (<= x 2.75e-13) (/ (- x y) y) (/ x (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -920000000000.0) {
		tmp = x / (x + y);
	} else if (x <= 2.75e-13) {
		tmp = (x - y) / y;
	} 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 <= (-920000000000.0d0)) then
        tmp = x / (x + y)
    else if (x <= 2.75d-13) then
        tmp = (x - y) / y
    else
        tmp = x / (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -920000000000.0) {
		tmp = x / (x + y);
	} else if (x <= 2.75e-13) {
		tmp = (x - y) / y;
	} else {
		tmp = x / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -920000000000.0:
		tmp = x / (x + y)
	elif x <= 2.75e-13:
		tmp = (x - y) / y
	else:
		tmp = x / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -920000000000.0)
		tmp = Float64(x / Float64(x + y));
	elseif (x <= 2.75e-13)
		tmp = Float64(Float64(x - y) / y);
	else
		tmp = Float64(x / Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -920000000000.0)
		tmp = x / (x + y);
	elseif (x <= 2.75e-13)
		tmp = (x - y) / y;
	else
		tmp = x / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -920000000000.0], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.75e-13], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.2e11

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.2%

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

   if -9.2e11 < x < 2.74999999999999989e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.9%

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

   if 2.74999999999999989e-13 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.8%

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

      1. frac-2neg 78.8%

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

      2. div-inv 78.7%

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

      3. +-commutative 78.7%

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

      4. distribute-neg-in 78.7%

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

      5. add-sqr-sqrt 47.1%

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

      6. sqrt-unprod 72.9%

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

      7. sqr-neg 72.9%

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

      8. sqrt-unprod 32.1%

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

      9. add-sqr-sqrt 78.8%

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

   5. Applied egg-rr 78.8%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{y + \left(-x\right)}} \]
   6. Step-by-step derivation

      1. distribute-lft-neg-out 78.8%

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

      2. associate-*r/ 79.0%

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

      3. *-rgt-identity 79.0%

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

      4. distribute-neg-frac2 79.0%

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

      5. neg-sub0 79.0%

         \[\leadsto \frac{x}{\color{blue}{0 - \left(y + \left(-x\right)\right)}} \]

      6. +-commutative 79.0%

         \[\leadsto \frac{x}{0 - \color{blue}{\left(\left(-x\right) + y\right)}} \]

      7. associate--r+ 79.0%

         \[\leadsto \frac{x}{\color{blue}{\left(0 - \left(-x\right)\right) - y}} \]

      8. neg-sub0 79.0%

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

      9. remove-double-neg 79.0%

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

   7. Simplified 79.0%

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

Alternative 6: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36000000000:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-42}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -36000000000.0)
   (/ x (+ x y))
   (if (<= x 9.5e-42) -1.0 (/ x (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -36000000000.0) {
		tmp = x / (x + y);
	} else if (x <= 9.5e-42) {
		tmp = -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 <= (-36000000000.0d0)) then
        tmp = x / (x + y)
    else if (x <= 9.5d-42) then
        tmp = -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 <= -36000000000.0) {
		tmp = x / (x + y);
	} else if (x <= 9.5e-42) {
		tmp = -1.0;
	} else {
		tmp = x / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -36000000000.0:
		tmp = x / (x + y)
	elif x <= 9.5e-42:
		tmp = -1.0
	else:
		tmp = x / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -36000000000.0)
		tmp = Float64(x / Float64(x + y));
	elseif (x <= 9.5e-42)
		tmp = -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 <= -36000000000.0)
		tmp = x / (x + y);
	elseif (x <= 9.5e-42)
		tmp = -1.0;
	else
		tmp = x / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -36000000000.0], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e-42], -1.0, N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.6e10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.2%

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

   if -3.6e10 < x < 9.49999999999999948e-42

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.4%

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

   if 9.49999999999999948e-42 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.3%

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

      1. frac-2neg 77.3%

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

      2. div-inv 77.2%

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

      3. +-commutative 77.2%

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

      4. distribute-neg-in 77.2%

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

      5. add-sqr-sqrt 46.0%

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

      6. sqrt-unprod 71.8%

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

      7. sqr-neg 71.8%

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

      8. sqrt-unprod 31.9%

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

      9. add-sqr-sqrt 77.4%

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

   5. Applied egg-rr 77.4%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{y + \left(-x\right)}} \]
   6. Step-by-step derivation

      1. distribute-lft-neg-out 77.4%

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

      2. associate-*r/ 77.5%

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

      3. *-rgt-identity 77.5%

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

      4. distribute-neg-frac2 77.5%

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

      5. neg-sub0 77.5%

         \[\leadsto \frac{x}{\color{blue}{0 - \left(y + \left(-x\right)\right)}} \]

      6. +-commutative 77.5%

         \[\leadsto \frac{x}{0 - \color{blue}{\left(\left(-x\right) + y\right)}} \]

      7. associate--r+ 77.5%

         \[\leadsto \frac{x}{\color{blue}{\left(0 - \left(-x\right)\right) - y}} \]

      8. neg-sub0 77.5%

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

      9. remove-double-neg 77.5%

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

   7. Simplified 77.5%

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

Alternative 7: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -18000000000:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-28}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -18000000000.0)
   (/ x (+ x y))
   (if (<= x 2.5e-28) -1.0 (- 1.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -18000000000.0) {
		tmp = x / (x + y);
	} else if (x <= 2.5e-28) {
		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 <= (-18000000000.0d0)) then
        tmp = x / (x + y)
    else if (x <= 2.5d-28) 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 <= -18000000000.0) {
		tmp = x / (x + y);
	} else if (x <= 2.5e-28) {
		tmp = -1.0;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -18000000000.0:
		tmp = x / (x + y)
	elif x <= 2.5e-28:
		tmp = -1.0
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -18000000000.0)
		tmp = Float64(x / Float64(x + y));
	elseif (x <= 2.5e-28)
		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 <= -18000000000.0)
		tmp = x / (x + y);
	elseif (x <= 2.5e-28)
		tmp = -1.0;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -18000000000.0], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-28], -1.0, N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8e10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.2%

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

   if -1.8e10 < x < 2.5000000000000001e-28

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.4%

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

   if 2.5000000000000001e-28 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.3%

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

   4. Taylor expanded in x around inf 77.5%

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

      1. mul-1-neg 77.5%

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

      2. unsub-neg 77.5%

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

   6. Simplified 77.5%

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

Alternative 8: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -235000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-39}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -235000000000.0) 1.0 (if (<= x 4.6e-39) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -235000000000.0) {
		tmp = 1.0;
	} else if (x <= 4.6e-39) {
		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 <= (-235000000000.0d0)) then
        tmp = 1.0d0
    else if (x <= 4.6d-39) 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 <= -235000000000.0) {
		tmp = 1.0;
	} else if (x <= 4.6e-39) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -235000000000.0:
		tmp = 1.0
	elif x <= 4.6e-39:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -235000000000.0)
		tmp = 1.0;
	elseif (x <= 4.6e-39)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -235000000000.0)
		tmp = 1.0;
	elseif (x <= 4.6e-39)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -235000000000.0], 1.0, If[LessEqual[x, 4.6e-39], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.35e11 or 4.60000000000000016e-39 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.4%

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

   if -2.35e11 < x < 4.60000000000000016e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.4%

      \[\leadsto \color{blue}{-1} \]
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 99.9%

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

Alternative 10: 50.0% 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 99.9%

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

3. Taylor expanded in x around 0 49.0%

   \[\leadsto \color{blue}{-1} \]
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 2024172 
(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)))