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

Percentage Accurate: 100.0% → 100.0%

Time: 6.6s

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: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ t_1 := 2 \cdot \frac{x}{y} + -1\\ \mathbf{if}\;x \leq -2100000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* -2.0 (/ y x)))) (t_1 (+ (* 2.0 (/ x y)) -1.0)))
   (if (<= x -2100000.0)
     t_0
     (if (<= x -1.5e-124)
       t_1
       (if (<= x -2.8e-137) 1.0 (if (<= x 5e+25) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double t_1 = (2.0 * (x / y)) + -1.0;
	double tmp;
	if (x <= -2100000.0) {
		tmp = t_0;
	} else if (x <= -1.5e-124) {
		tmp = t_1;
	} else if (x <= -2.8e-137) {
		tmp = 1.0;
	} else if (x <= 5e+25) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + ((-2.0d0) * (y / x))
    t_1 = (2.0d0 * (x / y)) + (-1.0d0)
    if (x <= (-2100000.0d0)) then
        tmp = t_0
    else if (x <= (-1.5d-124)) then
        tmp = t_1
    else if (x <= (-2.8d-137)) then
        tmp = 1.0d0
    else if (x <= 5d+25) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double t_1 = (2.0 * (x / y)) + -1.0;
	double tmp;
	if (x <= -2100000.0) {
		tmp = t_0;
	} else if (x <= -1.5e-124) {
		tmp = t_1;
	} else if (x <= -2.8e-137) {
		tmp = 1.0;
	} else if (x <= 5e+25) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (-2.0 * (y / x))
	t_1 = (2.0 * (x / y)) + -1.0
	tmp = 0
	if x <= -2100000.0:
		tmp = t_0
	elif x <= -1.5e-124:
		tmp = t_1
	elif x <= -2.8e-137:
		tmp = 1.0
	elif x <= 5e+25:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(-2.0 * Float64(y / x)))
	t_1 = Float64(Float64(2.0 * Float64(x / y)) + -1.0)
	tmp = 0.0
	if (x <= -2100000.0)
		tmp = t_0;
	elseif (x <= -1.5e-124)
		tmp = t_1;
	elseif (x <= -2.8e-137)
		tmp = 1.0;
	elseif (x <= 5e+25)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (-2.0 * (y / x));
	t_1 = (2.0 * (x / y)) + -1.0;
	tmp = 0.0;
	if (x <= -2100000.0)
		tmp = t_0;
	elseif (x <= -1.5e-124)
		tmp = t_1;
	elseif (x <= -2.8e-137)
		tmp = 1.0;
	elseif (x <= 5e+25)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[x, -2100000.0], t$95$0, If[LessEqual[x, -1.5e-124], t$95$1, If[LessEqual[x, -2.8e-137], 1.0, If[LessEqual[x, 5e+25], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e6 or 5.00000000000000024e25 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.8%

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

   if -2.1e6 < x < -1.5e-124 or -2.7999999999999999e-137 < x < 5.00000000000000024e25

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.9%

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

   if -1.5e-124 < x < -2.7999999999999999e-137

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2100000:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-124}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+25}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ t_1 := \frac{y}{\left(-x\right) - y}\\ \mathbf{if}\;x \leq -8500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* -2.0 (/ y x)))) (t_1 (/ y (- (- x) y))))
   (if (<= x -8500.0)
     t_0
     (if (<= x -1.5e-124)
       t_1
       (if (<= x -2.4e-137) 1.0 (if (<= x 4.2e+23) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double t_1 = y / (-x - y);
	double tmp;
	if (x <= -8500.0) {
		tmp = t_0;
	} else if (x <= -1.5e-124) {
		tmp = t_1;
	} else if (x <= -2.4e-137) {
		tmp = 1.0;
	} else if (x <= 4.2e+23) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + ((-2.0d0) * (y / x))
    t_1 = y / (-x - y)
    if (x <= (-8500.0d0)) then
        tmp = t_0
    else if (x <= (-1.5d-124)) then
        tmp = t_1
    else if (x <= (-2.4d-137)) then
        tmp = 1.0d0
    else if (x <= 4.2d+23) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double t_1 = y / (-x - y);
	double tmp;
	if (x <= -8500.0) {
		tmp = t_0;
	} else if (x <= -1.5e-124) {
		tmp = t_1;
	} else if (x <= -2.4e-137) {
		tmp = 1.0;
	} else if (x <= 4.2e+23) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (-2.0 * (y / x))
	t_1 = y / (-x - y)
	tmp = 0
	if x <= -8500.0:
		tmp = t_0
	elif x <= -1.5e-124:
		tmp = t_1
	elif x <= -2.4e-137:
		tmp = 1.0
	elif x <= 4.2e+23:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(-2.0 * Float64(y / x)))
	t_1 = Float64(y / Float64(Float64(-x) - y))
	tmp = 0.0
	if (x <= -8500.0)
		tmp = t_0;
	elseif (x <= -1.5e-124)
		tmp = t_1;
	elseif (x <= -2.4e-137)
		tmp = 1.0;
	elseif (x <= 4.2e+23)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (-2.0 * (y / x));
	t_1 = y / (-x - y);
	tmp = 0.0;
	if (x <= -8500.0)
		tmp = t_0;
	elseif (x <= -1.5e-124)
		tmp = t_1;
	elseif (x <= -2.4e-137)
		tmp = 1.0;
	elseif (x <= 4.2e+23)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[((-x) - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8500.0], t$95$0, If[LessEqual[x, -1.5e-124], t$95$1, If[LessEqual[x, -2.4e-137], 1.0, If[LessEqual[x, 4.2e+23], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8500 or 4.2000000000000003e23 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.8%

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

   if -8500 < x < -1.5e-124 or -2.4e-137 < x < 4.2000000000000003e23

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. frac-sub 61.3%

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

      3. *-un-lft-identity 61.3%

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

   6. Applied egg-rr 61.3%

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

      1. associate-*l/ 49.4%

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

      2. unpow2 49.4%

         \[\leadsto \frac{\left(x + y\right) - \frac{x + y}{x} \cdot y}{\frac{\color{blue}{{\left(x + y\right)}^{2}}}{x}} \]

      3. associate-/r/ 49.7%

         \[\leadsto \color{blue}{\frac{\left(x + y\right) - \frac{x + y}{x} \cdot y}{{\left(x + y\right)}^{2}} \cdot x} \]

      4. associate--l+ 49.7%

         \[\leadsto \frac{\color{blue}{x + \left(y - \frac{x + y}{x} \cdot y\right)}}{{\left(x + y\right)}^{2}} \cdot x \]

      5. associate-*l/ 49.7%

         \[\leadsto \frac{x + \left(y - \color{blue}{\frac{\left(x + y\right) \cdot y}{x}}\right)}{{\left(x + y\right)}^{2}} \cdot x \]

      6. associate-/l* 49.8%

         \[\leadsto \frac{x + \left(y - \color{blue}{\left(x + y\right) \cdot \frac{y}{x}}\right)}{{\left(x + y\right)}^{2}} \cdot x \]

   8. Simplified 49.8%

      \[\leadsto \color{blue}{\frac{x + \left(y - \left(x + y\right) \cdot \frac{y}{x}\right)}{{\left(x + y\right)}^{2}} \cdot x} \]
   9. Step-by-step derivation

      1. associate-*l/ 49.5%

         \[\leadsto \color{blue}{\frac{\left(x + \left(y - \left(x + y\right) \cdot \frac{y}{x}\right)\right) \cdot x}{{\left(x + y\right)}^{2}}} \]

      2. unpow2 49.5%

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

      3. associate-/r* 50.6%

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

      4. *-commutative 50.6%

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

      5. associate-+r- 50.6%

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

      6. *-un-lft-identity 50.6%

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

      7. *-commutative 50.6%

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

      8. distribute-rgt-out-- 50.6%

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

   10. Applied egg-rr 50.6%

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

   11. Taylor expanded in x around 0 77.3%

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

       1. mul-1-neg 77.3%

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

   13. Simplified 77.3%

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

   if -1.5e-124 < x < -2.4e-137

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8500:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-124}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + y}\\ t_1 := \frac{y}{\left(-x\right) - y}\\ \mathbf{if}\;x \leq -740000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ x y))) (t_1 (/ y (- (- x) y))))
   (if (<= x -740000.0)
     t_0
     (if (<= x -1.5e-124)
       t_1
       (if (<= x -2.8e-137) 1.0 (if (<= x 4.4e+39) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = x / (x + y);
	double t_1 = y / (-x - y);
	double tmp;
	if (x <= -740000.0) {
		tmp = t_0;
	} else if (x <= -1.5e-124) {
		tmp = t_1;
	} else if (x <= -2.8e-137) {
		tmp = 1.0;
	} else if (x <= 4.4e+39) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (x + y)
    t_1 = y / (-x - y)
    if (x <= (-740000.0d0)) then
        tmp = t_0
    else if (x <= (-1.5d-124)) then
        tmp = t_1
    else if (x <= (-2.8d-137)) then
        tmp = 1.0d0
    else if (x <= 4.4d+39) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (x + y);
	double t_1 = y / (-x - y);
	double tmp;
	if (x <= -740000.0) {
		tmp = t_0;
	} else if (x <= -1.5e-124) {
		tmp = t_1;
	} else if (x <= -2.8e-137) {
		tmp = 1.0;
	} else if (x <= 4.4e+39) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (x + y)
	t_1 = y / (-x - y)
	tmp = 0
	if x <= -740000.0:
		tmp = t_0
	elif x <= -1.5e-124:
		tmp = t_1
	elif x <= -2.8e-137:
		tmp = 1.0
	elif x <= 4.4e+39:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(x + y))
	t_1 = Float64(y / Float64(Float64(-x) - y))
	tmp = 0.0
	if (x <= -740000.0)
		tmp = t_0;
	elseif (x <= -1.5e-124)
		tmp = t_1;
	elseif (x <= -2.8e-137)
		tmp = 1.0;
	elseif (x <= 4.4e+39)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (x + y);
	t_1 = y / (-x - y);
	tmp = 0.0;
	if (x <= -740000.0)
		tmp = t_0;
	elseif (x <= -1.5e-124)
		tmp = t_1;
	elseif (x <= -2.8e-137)
		tmp = 1.0;
	elseif (x <= 4.4e+39)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[((-x) - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -740000.0], t$95$0, If[LessEqual[x, -1.5e-124], t$95$1, If[LessEqual[x, -2.8e-137], 1.0, If[LessEqual[x, 4.4e+39], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.4e5 or 4.4000000000000003e39 < x

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. frac-sub 92.3%

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

      3. *-un-lft-identity 92.3%

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

   6. Applied egg-rr 92.3%

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

      1. associate-*l/ 30.9%

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

      2. unpow2 30.9%

         \[\leadsto \frac{\left(x + y\right) - \frac{x + y}{x} \cdot y}{\frac{\color{blue}{{\left(x + y\right)}^{2}}}{x}} \]

      3. associate-/r/ 30.9%

         \[\leadsto \color{blue}{\frac{\left(x + y\right) - \frac{x + y}{x} \cdot y}{{\left(x + y\right)}^{2}} \cdot x} \]

      4. associate--l+ 30.9%

         \[\leadsto \frac{\color{blue}{x + \left(y - \frac{x + y}{x} \cdot y\right)}}{{\left(x + y\right)}^{2}} \cdot x \]

      5. associate-*l/ 29.9%

         \[\leadsto \frac{x + \left(y - \color{blue}{\frac{\left(x + y\right) \cdot y}{x}}\right)}{{\left(x + y\right)}^{2}} \cdot x \]

      6. associate-/l* 30.9%

         \[\leadsto \frac{x + \left(y - \color{blue}{\left(x + y\right) \cdot \frac{y}{x}}\right)}{{\left(x + y\right)}^{2}} \cdot x \]

   8. Simplified 30.9%

      \[\leadsto \color{blue}{\frac{x + \left(y - \left(x + y\right) \cdot \frac{y}{x}\right)}{{\left(x + y\right)}^{2}} \cdot x} \]
   9. Step-by-step derivation

      1. associate-*l/ 29.0%

         \[\leadsto \color{blue}{\frac{\left(x + \left(y - \left(x + y\right) \cdot \frac{y}{x}\right)\right) \cdot x}{{\left(x + y\right)}^{2}}} \]

      2. unpow2 29.0%

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

      3. associate-/r* 31.1%

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

      4. *-commutative 31.1%

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

      5. associate-+r- 31.1%

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

      6. *-un-lft-identity 31.1%

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

      7. *-commutative 31.1%

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

      8. distribute-rgt-out-- 31.2%

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

   10. Applied egg-rr 31.2%

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

   11. Taylor expanded in x around inf 82.6%

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

   if -7.4e5 < x < -1.5e-124 or -2.7999999999999999e-137 < x < 4.4000000000000003e39

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. frac-sub 61.9%

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

      3. *-un-lft-identity 61.9%

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

   6. Applied egg-rr 61.9%

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

      1. associate-*l/ 50.2%

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

      2. unpow2 50.2%

         \[\leadsto \frac{\left(x + y\right) - \frac{x + y}{x} \cdot y}{\frac{\color{blue}{{\left(x + y\right)}^{2}}}{x}} \]

      3. associate-/r/ 50.5%

         \[\leadsto \color{blue}{\frac{\left(x + y\right) - \frac{x + y}{x} \cdot y}{{\left(x + y\right)}^{2}} \cdot x} \]

      4. associate--l+ 50.5%

         \[\leadsto \frac{\color{blue}{x + \left(y - \frac{x + y}{x} \cdot y\right)}}{{\left(x + y\right)}^{2}} \cdot x \]

      5. associate-*l/ 50.5%

         \[\leadsto \frac{x + \left(y - \color{blue}{\frac{\left(x + y\right) \cdot y}{x}}\right)}{{\left(x + y\right)}^{2}} \cdot x \]

      6. associate-/l* 50.5%

         \[\leadsto \frac{x + \left(y - \color{blue}{\left(x + y\right) \cdot \frac{y}{x}}\right)}{{\left(x + y\right)}^{2}} \cdot x \]

   8. Simplified 50.5%

      \[\leadsto \color{blue}{\frac{x + \left(y - \left(x + y\right) \cdot \frac{y}{x}\right)}{{\left(x + y\right)}^{2}} \cdot x} \]
   9. Step-by-step derivation

      1. associate-*l/ 50.2%

         \[\leadsto \color{blue}{\frac{\left(x + \left(y - \left(x + y\right) \cdot \frac{y}{x}\right)\right) \cdot x}{{\left(x + y\right)}^{2}}} \]

      2. unpow2 50.2%

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

      3. associate-/r* 51.4%

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

      4. *-commutative 51.4%

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

      5. associate-+r- 51.4%

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

      6. *-un-lft-identity 51.4%

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

      7. *-commutative 51.4%

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

      8. distribute-rgt-out-- 51.4%

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

   10. Applied egg-rr 51.4%

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

   11. Taylor expanded in x around 0 76.9%

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

       1. mul-1-neg 76.9%

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

   13. Simplified 76.9%

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

   if -1.5e-124 < x < -2.7999999999999999e-137

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -740000:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-124}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + y}\\ \mathbf{if}\;x \leq -95000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-124}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ x y))))
   (if (<= x -95000.0)
     t_0
     (if (<= x -1.5e-124)
       -1.0
       (if (<= x -2.8e-137) 1.0 (if (<= x 2.1e+30) -1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = x / (x + y);
	double tmp;
	if (x <= -95000.0) {
		tmp = t_0;
	} else if (x <= -1.5e-124) {
		tmp = -1.0;
	} else if (x <= -2.8e-137) {
		tmp = 1.0;
	} else if (x <= 2.1e+30) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (x + y)
    if (x <= (-95000.0d0)) then
        tmp = t_0
    else if (x <= (-1.5d-124)) then
        tmp = -1.0d0
    else if (x <= (-2.8d-137)) then
        tmp = 1.0d0
    else if (x <= 2.1d+30) then
        tmp = -1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (x + y);
	double tmp;
	if (x <= -95000.0) {
		tmp = t_0;
	} else if (x <= -1.5e-124) {
		tmp = -1.0;
	} else if (x <= -2.8e-137) {
		tmp = 1.0;
	} else if (x <= 2.1e+30) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (x + y)
	tmp = 0
	if x <= -95000.0:
		tmp = t_0
	elif x <= -1.5e-124:
		tmp = -1.0
	elif x <= -2.8e-137:
		tmp = 1.0
	elif x <= 2.1e+30:
		tmp = -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(x + y))
	tmp = 0.0
	if (x <= -95000.0)
		tmp = t_0;
	elseif (x <= -1.5e-124)
		tmp = -1.0;
	elseif (x <= -2.8e-137)
		tmp = 1.0;
	elseif (x <= 2.1e+30)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (x + y);
	tmp = 0.0;
	if (x <= -95000.0)
		tmp = t_0;
	elseif (x <= -1.5e-124)
		tmp = -1.0;
	elseif (x <= -2.8e-137)
		tmp = 1.0;
	elseif (x <= 2.1e+30)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -95000.0], t$95$0, If[LessEqual[x, -1.5e-124], -1.0, If[LessEqual[x, -2.8e-137], 1.0, If[LessEqual[x, 2.1e+30], -1.0, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -95000 or 2.1e30 < x

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. frac-sub 92.4%

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

      3. *-un-lft-identity 92.4%

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

   6. Applied egg-rr 92.4%

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

      1. associate-*l/ 32.1%

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

      2. unpow2 32.1%

         \[\leadsto \frac{\left(x + y\right) - \frac{x + y}{x} \cdot y}{\frac{\color{blue}{{\left(x + y\right)}^{2}}}{x}} \]

      3. associate-/r/ 32.0%

         \[\leadsto \color{blue}{\frac{\left(x + y\right) - \frac{x + y}{x} \cdot y}{{\left(x + y\right)}^{2}} \cdot x} \]

      4. associate--l+ 32.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - \frac{x + y}{x} \cdot y\right)}}{{\left(x + y\right)}^{2}} \cdot x \]

      5. associate-*l/ 31.1%

         \[\leadsto \frac{x + \left(y - \color{blue}{\frac{\left(x + y\right) \cdot y}{x}}\right)}{{\left(x + y\right)}^{2}} \cdot x \]

      6. associate-/l* 32.0%

         \[\leadsto \frac{x + \left(y - \color{blue}{\left(x + y\right) \cdot \frac{y}{x}}\right)}{{\left(x + y\right)}^{2}} \cdot x \]

   8. Simplified 32.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - \left(x + y\right) \cdot \frac{y}{x}\right)}{{\left(x + y\right)}^{2}} \cdot x} \]
   9. Step-by-step derivation

      1. associate-*l/ 30.2%

         \[\leadsto \color{blue}{\frac{\left(x + \left(y - \left(x + y\right) \cdot \frac{y}{x}\right)\right) \cdot x}{{\left(x + y\right)}^{2}}} \]

      2. unpow2 30.2%

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

      3. associate-/r* 32.3%

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

      4. *-commutative 32.3%

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

      5. associate-+r- 32.3%

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

      6. *-un-lft-identity 32.3%

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

      7. *-commutative 32.3%

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

      8. distribute-rgt-out-- 32.3%

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

   10. Applied egg-rr 32.3%

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

   11. Taylor expanded in x around inf 82.1%

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

   if -95000 < x < -1.5e-124 or -2.7999999999999999e-137 < x < 2.1e30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 76.7%

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

   if -1.5e-124 < x < -2.7999999999999999e-137

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

Alternative 6: 72.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -10000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-124}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-137}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -10000.0)
   1.0
   (if (<= x -1.56e-124)
     -1.0
     (if (<= x -2.8e-137) 1.0 (if (<= x 2.8e+29) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -10000.0) {
		tmp = 1.0;
	} else if (x <= -1.56e-124) {
		tmp = -1.0;
	} else if (x <= -2.8e-137) {
		tmp = 1.0;
	} else if (x <= 2.8e+29) {
		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 <= (-10000.0d0)) then
        tmp = 1.0d0
    else if (x <= (-1.56d-124)) then
        tmp = -1.0d0
    else if (x <= (-2.8d-137)) then
        tmp = 1.0d0
    else if (x <= 2.8d+29) 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 <= -10000.0) {
		tmp = 1.0;
	} else if (x <= -1.56e-124) {
		tmp = -1.0;
	} else if (x <= -2.8e-137) {
		tmp = 1.0;
	} else if (x <= 2.8e+29) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -10000.0:
		tmp = 1.0
	elif x <= -1.56e-124:
		tmp = -1.0
	elif x <= -2.8e-137:
		tmp = 1.0
	elif x <= 2.8e+29:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -10000.0)
		tmp = 1.0;
	elseif (x <= -1.56e-124)
		tmp = -1.0;
	elseif (x <= -2.8e-137)
		tmp = 1.0;
	elseif (x <= 2.8e+29)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -10000.0)
		tmp = 1.0;
	elseif (x <= -1.56e-124)
		tmp = -1.0;
	elseif (x <= -2.8e-137)
		tmp = 1.0;
	elseif (x <= 2.8e+29)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -10000.0], 1.0, If[LessEqual[x, -1.56e-124], -1.0, If[LessEqual[x, -2.8e-137], 1.0, If[LessEqual[x, 2.8e+29], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1e4 or -1.55999999999999993e-124 < x < -2.7999999999999999e-137 or 2.8e29 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.3%

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

   if -1e4 < x < -1.55999999999999993e-124 or -2.7999999999999999e-137 < x < 2.8e29

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 76.7%

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

Alternative 7: 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. 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. Step-by-step derivation

   1. sub-div 99.9%

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

   2. 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 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: 49.6% 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 47.8%

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

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 2024106 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :alt
  (- (/ x (+ x y)) (/ y (+ x y)))

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