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

Percentage Accurate: 100.0% → 100.0%

Time: 9.1s

Alternatives: 7

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, 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. Final simplification 100.0%

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

Alternative 2: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-82} \lor \neg \left(x \leq 1.45 \cdot 10^{-22}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -9.4e-82) (not (<= x 1.45e-22)))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -9.4e-82) || !(x <= 1.45e-22)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-9.4d-82)) .or. (.not. (x <= 1.45d-22))) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = (x / y) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -9.4e-82) || !(x <= 1.45e-22)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -9.4e-82) or not (x <= 1.45e-22):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -9.4e-82) || !(x <= 1.45e-22))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(x / y) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -9.4e-82) || ~((x <= 1.45e-22)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -9.4e-82], N[Not[LessEqual[x, 1.45e-22]], $MachinePrecision]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4000000000000001e-82 or 1.4500000000000001e-22 < x

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in y around 0 77.4%

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

   if -9.4000000000000001e-82 < x < 1.4500000000000001e-22

   1. Initial program 100.0%

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

      1. div-sub 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. frac-sub 56.7%

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

      2. associate-/r* 57.5%

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

      3. *-commutative 57.5%

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

   5. Applied egg-rr 57.5%

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

   6. Taylor expanded in x around 0 80.9%

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

      1. neg-mul-1 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in y around inf 80.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{-82} \lor \neg \left(x \leq 1.45 \cdot 10^{-22}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]

Alternative 3: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.3 \cdot 10^{-82} \lor \neg \left(x \leq 1.55 \cdot 10^{-18}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7.3e-82) (not (<= x 1.55e-18))) (- 1.0 (/ y x)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7.3e-82) || !(x <= 1.55e-18)) {
		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 <= (-7.3d-82)) .or. (.not. (x <= 1.55d-18))) 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 <= -7.3e-82) || !(x <= 1.55e-18)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7.3e-82) or not (x <= 1.55e-18):
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7.3e-82) || !(x <= 1.55e-18))
		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 <= -7.3e-82) || ~((x <= 1.55e-18)))
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7.3e-82], N[Not[LessEqual[x, 1.55e-18]], $MachinePrecision]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -7.29999999999999948e-82 or 1.55000000000000003e-18 < x

   1. Initial program 100.0%

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

      1. div-sub 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. frac-sub 42.6%

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

      2. associate-/r* 44.1%

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

      3. *-commutative 44.1%

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

   5. Applied egg-rr 44.1%

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

   6. Taylor expanded in x around inf 76.9%

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

   7. Taylor expanded in x around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

   9. Simplified 76.9%

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

   if -7.29999999999999948e-82 < x < 1.55000000000000003e-18

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 79.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.3 \cdot 10^{-82} \lor \neg \left(x \leq 1.55 \cdot 10^{-18}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 73.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-81} \lor \neg \left(x \leq 8.8 \cdot 10^{-23}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1e-81) (not (<= x 8.8e-23))) (- 1.0 (/ y x)) (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1e-81) || !(x <= 8.8e-23)) {
		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 <= (-1d-81)) .or. (.not. (x <= 8.8d-23))) 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 <= -1e-81) || !(x <= 8.8e-23)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1e-81) or not (x <= 8.8e-23):
		tmp = 1.0 - (y / x)
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1e-81) || !(x <= 8.8e-23))
		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 <= -1e-81) || ~((x <= 8.8e-23)))
		tmp = 1.0 - (y / x);
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1e-81], N[Not[LessEqual[x, 8.8e-23]], $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 < -9.9999999999999996e-82 or 8.7999999999999998e-23 < x

   1. Initial program 100.0%

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

      1. div-sub 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. frac-sub 43.4%

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

      2. associate-/r* 44.8%

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

      3. *-commutative 44.8%

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

   5. Applied egg-rr 44.8%

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

   6. Taylor expanded in x around inf 76.6%

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

   7. Taylor expanded in x around inf 76.6%

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

      1. mul-1-neg 76.6%

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

      2. unsub-neg 76.6%

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

   9. Simplified 76.6%

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

   if -9.9999999999999996e-82 < x < 8.7999999999999998e-23

   1. Initial program 100.0%

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

      1. div-sub 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. frac-sub 56.7%

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

      2. associate-/r* 57.5%

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

      3. *-commutative 57.5%

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

   5. Applied egg-rr 57.5%

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

   6. Taylor expanded in x around 0 80.9%

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

      1. neg-mul-1 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in y around inf 80.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-81} \lor \neg \left(x \leq 8.8 \cdot 10^{-23}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]

Alternative 5: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.2e-82)
   (/ x (+ x y))
   (if (<= x 5.8e-24) (+ (/ x y) -1.0) (- 1.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.2e-82) {
		tmp = x / (x + y);
	} else if (x <= 5.8e-24) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-9.2d-82)) then
        tmp = x / (x + y)
    else if (x <= 5.8d-24) then
        tmp = (x / y) + (-1.0d0)
    else
        tmp = 1.0d0 - (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.2e-82) {
		tmp = x / (x + y);
	} else if (x <= 5.8e-24) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.2e-82:
		tmp = x / (x + y)
	elif x <= 5.8e-24:
		tmp = (x / y) + -1.0
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.2e-82)
		tmp = Float64(x / Float64(x + y));
	elseif (x <= 5.8e-24)
		tmp = Float64(Float64(x / y) + -1.0);
	else
		tmp = Float64(1.0 - Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.2e-82)
		tmp = x / (x + y);
	elseif (x <= 5.8e-24)
		tmp = (x / y) + -1.0;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.2e-82], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-24], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.19999999999999988e-82

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

   3. Applied egg-rr 100.0%

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

      1. frac-sub 47.0%

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

      2. associate-/r* 48.3%

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

      3. *-commutative 48.3%

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

   5. Applied egg-rr 48.3%

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

   6. Taylor expanded in x around inf 82.4%

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

   if -9.19999999999999988e-82 < x < 5.7999999999999997e-24

   1. Initial program 100.0%

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

      1. div-sub 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. frac-sub 56.7%

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

      2. associate-/r* 57.5%

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

      3. *-commutative 57.5%

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

   5. Applied egg-rr 57.5%

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

   6. Taylor expanded in x around 0 80.9%

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

      1. neg-mul-1 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in y around inf 80.9%

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

   if 5.7999999999999997e-24 < x

   1. Initial program 100.0%

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

      1. div-sub 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. frac-sub 39.1%

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

      2. associate-/r* 40.6%

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

      3. *-commutative 40.6%

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

   5. Applied egg-rr 40.6%

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

   6. Taylor expanded in x around inf 69.6%

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

   7. Taylor expanded in x around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

   9. Simplified 69.7%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]

Alternative 6: 72.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-33}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e-81) 1.0 (if (<= x 2e-33) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e-81) {
		tmp = 1.0;
	} else if (x <= 2e-33) {
		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-81)) then
        tmp = 1.0d0
    else if (x <= 2d-33) 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-81) {
		tmp = 1.0;
	} else if (x <= 2e-33) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e-81:
		tmp = 1.0
	elif x <= 2e-33:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e-81)
		tmp = 1.0;
	elseif (x <= 2e-33)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e-81)
		tmp = 1.0;
	elseif (x <= 2e-33)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e-81], 1.0, If[LessEqual[x, 2e-33], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999996e-82 or 2.0000000000000001e-33 < x

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around inf 76.0%

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

   if -9.9999999999999996e-82 < x < 2.0000000000000001e-33

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 80.3%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-33}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 49.5% 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. Taylor expanded in x around 0 46.2%

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

3. Final simplification 46.2%

   \[\leadsto -1 \]

Developer target: 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 2023224 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))