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

Percentage Accurate: 100.0% → 100.0%

Time: 8.1s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -15500000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-144}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-263}:\\ \;\;\;\;\frac{y}{-2}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -15500000000.0)
     t_0
     (if (<= x -9.2e-144)
       (- 1.0 (/ x y))
       (if (<= x 5.1e-263) (/ y -2.0) (if (<= x 2.2e+42) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -15500000000.0) {
		tmp = t_0;
	} else if (x <= -9.2e-144) {
		tmp = 1.0 - (x / y);
	} else if (x <= 5.1e-263) {
		tmp = y / -2.0;
	} else if (x <= 2.2e+42) {
		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 = (y / x) + (-1.0d0)
    if (x <= (-15500000000.0d0)) then
        tmp = t_0
    else if (x <= (-9.2d-144)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= 5.1d-263) then
        tmp = y / (-2.0d0)
    else if (x <= 2.2d+42) 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 = (y / x) + -1.0;
	double tmp;
	if (x <= -15500000000.0) {
		tmp = t_0;
	} else if (x <= -9.2e-144) {
		tmp = 1.0 - (x / y);
	} else if (x <= 5.1e-263) {
		tmp = y / -2.0;
	} else if (x <= 2.2e+42) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -15500000000.0:
		tmp = t_0
	elif x <= -9.2e-144:
		tmp = 1.0 - (x / y)
	elif x <= 5.1e-263:
		tmp = y / -2.0
	elif x <= 2.2e+42:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	tmp = 0.0
	if (x <= -15500000000.0)
		tmp = t_0;
	elseif (x <= -9.2e-144)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= 5.1e-263)
		tmp = Float64(y / -2.0);
	elseif (x <= 2.2e+42)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	tmp = 0.0;
	if (x <= -15500000000.0)
		tmp = t_0;
	elseif (x <= -9.2e-144)
		tmp = 1.0 - (x / y);
	elseif (x <= 5.1e-263)
		tmp = y / -2.0;
	elseif (x <= 2.2e+42)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[x, -15500000000.0], t$95$0, If[LessEqual[x, -9.2e-144], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e-263], N[(y / -2.0), $MachinePrecision], If[LessEqual[x, 2.2e+42], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.55e10 or 2.2000000000000001e42 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in x around inf 83.3%

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

   if -1.55e10 < x < -9.2e-144

   1. Initial program 99.8%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.7%

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

   4. Taylor expanded in y around inf 55.7%

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

      1. neg-mul-1 55.7%

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

   6. Simplified 55.7%

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

   7. Taylor expanded in x around 0 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

   9. Simplified 55.7%

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

   if -9.2e-144 < x < 5.09999999999999971e-263

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 81.4%

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

      2. distribute-neg-frac2 81.4%

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

      3. mul-1-neg 81.4%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(2 - y\right)}} \]

      4. sub-neg 81.4%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 + \left(-y\right)\right)}} \]

      5. +-commutative 81.4%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(\left(-y\right) + 2\right)}} \]

      6. distribute-lft-in 81.4%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(-y\right) + -1 \cdot 2}} \]

      7. neg-mul-1 81.4%

         \[\leadsto \frac{y}{\color{blue}{\left(-\left(-y\right)\right)} + -1 \cdot 2} \]

      8. remove-double-neg 81.4%

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

      9. metadata-eval 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in y around 0 52.1%

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

   if 5.09999999999999971e-263 < x < 2.2000000000000001e42

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 54.4%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -15500000000:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-144}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-263}:\\ \;\;\;\;\frac{y}{-2}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-142}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-266}:\\ \;\;\;\;\frac{y}{-2}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -22000000000.0)
   -1.0
   (if (<= x -3.8e-142)
     (- 1.0 (/ x y))
     (if (<= x 3.05e-266) (/ y -2.0) (if (<= x 2.75e+49) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -22000000000.0) {
		tmp = -1.0;
	} else if (x <= -3.8e-142) {
		tmp = 1.0 - (x / y);
	} else if (x <= 3.05e-266) {
		tmp = y / -2.0;
	} else if (x <= 2.75e+49) {
		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 <= (-22000000000.0d0)) then
        tmp = -1.0d0
    else if (x <= (-3.8d-142)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= 3.05d-266) then
        tmp = y / (-2.0d0)
    else if (x <= 2.75d+49) 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 <= -22000000000.0) {
		tmp = -1.0;
	} else if (x <= -3.8e-142) {
		tmp = 1.0 - (x / y);
	} else if (x <= 3.05e-266) {
		tmp = y / -2.0;
	} else if (x <= 2.75e+49) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -22000000000.0:
		tmp = -1.0
	elif x <= -3.8e-142:
		tmp = 1.0 - (x / y)
	elif x <= 3.05e-266:
		tmp = y / -2.0
	elif x <= 2.75e+49:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -22000000000.0)
		tmp = -1.0;
	elseif (x <= -3.8e-142)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= 3.05e-266)
		tmp = Float64(y / -2.0);
	elseif (x <= 2.75e+49)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -22000000000.0)
		tmp = -1.0;
	elseif (x <= -3.8e-142)
		tmp = 1.0 - (x / y);
	elseif (x <= 3.05e-266)
		tmp = y / -2.0;
	elseif (x <= 2.75e+49)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -22000000000.0], -1.0, If[LessEqual[x, -3.8e-142], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.05e-266], N[(y / -2.0), $MachinePrecision], If[LessEqual[x, 2.75e+49], 1.0, -1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2e10 or 2.75000000000000021e49 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.3%

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

   if -2.2e10 < x < -3.79999999999999972e-142

   1. Initial program 99.8%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.7%

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

   4. Taylor expanded in y around inf 55.7%

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

      1. neg-mul-1 55.7%

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

   6. Simplified 55.7%

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

   7. Taylor expanded in x around 0 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

   9. Simplified 55.7%

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

   if -3.79999999999999972e-142 < x < 3.05e-266

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 81.4%

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

      2. distribute-neg-frac2 81.4%

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

      3. mul-1-neg 81.4%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(2 - y\right)}} \]

      4. sub-neg 81.4%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 + \left(-y\right)\right)}} \]

      5. +-commutative 81.4%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(\left(-y\right) + 2\right)}} \]

      6. distribute-lft-in 81.4%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(-y\right) + -1 \cdot 2}} \]

      7. neg-mul-1 81.4%

         \[\leadsto \frac{y}{\color{blue}{\left(-\left(-y\right)\right)} + -1 \cdot 2} \]

      8. remove-double-neg 81.4%

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

      9. metadata-eval 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in y around 0 52.1%

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

   if 3.05e-266 < x < 2.75000000000000021e49

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 54.3%

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

Alternative 4: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -13500000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-265}:\\ \;\;\;\;\frac{y}{-2}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -13500000000.0)
   -1.0
   (if (<= x -1.02e-143)
     1.0
     (if (<= x 8.2e-265) (/ y -2.0) (if (<= x 2.75e+49) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -13500000000.0) {
		tmp = -1.0;
	} else if (x <= -1.02e-143) {
		tmp = 1.0;
	} else if (x <= 8.2e-265) {
		tmp = y / -2.0;
	} else if (x <= 2.75e+49) {
		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 <= (-13500000000.0d0)) then
        tmp = -1.0d0
    else if (x <= (-1.02d-143)) then
        tmp = 1.0d0
    else if (x <= 8.2d-265) then
        tmp = y / (-2.0d0)
    else if (x <= 2.75d+49) 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 <= -13500000000.0) {
		tmp = -1.0;
	} else if (x <= -1.02e-143) {
		tmp = 1.0;
	} else if (x <= 8.2e-265) {
		tmp = y / -2.0;
	} else if (x <= 2.75e+49) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -13500000000.0:
		tmp = -1.0
	elif x <= -1.02e-143:
		tmp = 1.0
	elif x <= 8.2e-265:
		tmp = y / -2.0
	elif x <= 2.75e+49:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -13500000000.0)
		tmp = -1.0;
	elseif (x <= -1.02e-143)
		tmp = 1.0;
	elseif (x <= 8.2e-265)
		tmp = Float64(y / -2.0);
	elseif (x <= 2.75e+49)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -13500000000.0)
		tmp = -1.0;
	elseif (x <= -1.02e-143)
		tmp = 1.0;
	elseif (x <= 8.2e-265)
		tmp = y / -2.0;
	elseif (x <= 2.75e+49)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -13500000000.0], -1.0, If[LessEqual[x, -1.02e-143], 1.0, If[LessEqual[x, 8.2e-265], N[(y / -2.0), $MachinePrecision], If[LessEqual[x, 2.75e+49], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e10 or 2.75000000000000021e49 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.3%

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

   if -1.35e10 < x < -1.02e-143 or 8.2e-265 < x < 2.75000000000000021e49

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 54.6%

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

   if -1.02e-143 < x < 8.2e-265

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 81.4%

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

      2. distribute-neg-frac2 81.4%

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

      3. mul-1-neg 81.4%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(2 - y\right)}} \]

      4. sub-neg 81.4%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 + \left(-y\right)\right)}} \]

      5. +-commutative 81.4%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(\left(-y\right) + 2\right)}} \]

      6. distribute-lft-in 81.4%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(-y\right) + -1 \cdot 2}} \]

      7. neg-mul-1 81.4%

         \[\leadsto \frac{y}{\color{blue}{\left(-\left(-y\right)\right)} + -1 \cdot 2} \]

      8. remove-double-neg 81.4%

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

      9. metadata-eval 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in y around 0 52.1%

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

Alternative 5: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -29000000000 \lor \neg \left(x \leq 2.6\right):\\ \;\;\;\;\frac{x}{2 - \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -29000000000.0) (not (<= x 2.6)))
   (/ x (- 2.0 (+ x y)))
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -29000000000.0) || !(x <= 2.6)) {
		tmp = x / (2.0 - (x + y));
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-29000000000.0d0)) .or. (.not. (x <= 2.6d0))) then
        tmp = x / (2.0d0 - (x + y))
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -29000000000.0) || !(x <= 2.6)) {
		tmp = x / (2.0 - (x + y));
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -29000000000.0) or not (x <= 2.6):
		tmp = x / (2.0 - (x + y))
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -29000000000.0) || !(x <= 2.6))
		tmp = Float64(x / Float64(2.0 - Float64(x + y)));
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -29000000000.0) || ~((x <= 2.6)))
		tmp = x / (2.0 - (x + y));
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -29000000000.0], N[Not[LessEqual[x, 2.6]], $MachinePrecision]], N[(x / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e10 or 2.60000000000000009 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.9%

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

   if -2.9e10 < x < 2.60000000000000009

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.2%

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

      2. distribute-neg-frac2 74.2%

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

      3. mul-1-neg 74.2%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(2 - y\right)}} \]

      4. sub-neg 74.2%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 + \left(-y\right)\right)}} \]

      5. +-commutative 74.2%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(\left(-y\right) + 2\right)}} \]

      6. distribute-lft-in 74.2%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(-y\right) + -1 \cdot 2}} \]

      7. neg-mul-1 74.2%

         \[\leadsto \frac{y}{\color{blue}{\left(-\left(-y\right)\right)} + -1 \cdot 2} \]

      8. remove-double-neg 74.2%

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

      9. metadata-eval 74.2%

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

   5. Simplified 74.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -29000000000 \lor \neg \left(x \leq 2.6\right):\\ \;\;\;\;\frac{x}{2 - \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -20500000000:\\ \;\;\;\;\frac{x}{2 - \left(x + y\right)}\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -20500000000.0)
   (/ x (- 2.0 (+ x y)))
   (if (<= x 0.6) (/ (- x y) (- 2.0 y)) (/ (- x y) (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -20500000000.0) {
		tmp = x / (2.0 - (x + y));
	} else if (x <= 0.6) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = (x - y) / (2.0 - 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 <= (-20500000000.0d0)) then
        tmp = x / (2.0d0 - (x + y))
    else if (x <= 0.6d0) then
        tmp = (x - y) / (2.0d0 - y)
    else
        tmp = (x - y) / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -20500000000.0) {
		tmp = x / (2.0 - (x + y));
	} else if (x <= 0.6) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = (x - y) / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -20500000000.0:
		tmp = x / (2.0 - (x + y))
	elif x <= 0.6:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = (x - y) / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -20500000000.0)
		tmp = Float64(x / Float64(2.0 - Float64(x + y)));
	elseif (x <= 0.6)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -20500000000.0)
		tmp = x / (2.0 - (x + y));
	elseif (x <= 0.6)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = (x - y) / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -20500000000.0], N[(x / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.6], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.05e10

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 85.6%

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

   if -2.05e10 < x < 0.599999999999999978

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

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

   if 0.599999999999999978 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.6%

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

Alternative 7: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.4e-5)
   (/ y (+ y -2.0))
   (if (<= y 3.2e+58) (/ (- x y) (- 2.0 x)) (- 1.0 (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.4e-5) {
		tmp = y / (y + -2.0);
	} else if (y <= 3.2e+58) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = 1.0 - (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 (y <= (-5.4d-5)) then
        tmp = y / (y + (-2.0d0))
    else if (y <= 3.2d+58) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.4e-5) {
		tmp = y / (y + -2.0);
	} else if (y <= 3.2e+58) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.4e-5:
		tmp = y / (y + -2.0)
	elif y <= 3.2e+58:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.4e-5)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (y <= 3.2e+58)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.4e-5)
		tmp = y / (y + -2.0);
	elseif (y <= 3.2e+58)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.4e-5], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+58], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3999999999999998e-5

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.4%

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

      2. distribute-neg-frac2 74.4%

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

      3. mul-1-neg 74.4%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(2 - y\right)}} \]

      4. sub-neg 74.4%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 + \left(-y\right)\right)}} \]

      5. +-commutative 74.4%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(\left(-y\right) + 2\right)}} \]

      6. distribute-lft-in 74.4%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(-y\right) + -1 \cdot 2}} \]

      7. neg-mul-1 74.4%

         \[\leadsto \frac{y}{\color{blue}{\left(-\left(-y\right)\right)} + -1 \cdot 2} \]

      8. remove-double-neg 74.4%

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

      9. metadata-eval 74.4%

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

   5. Simplified 74.4%

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

   if -5.3999999999999998e-5 < y < 3.20000000000000015e58

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 94.8%

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

   if 3.20000000000000015e58 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.4%

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

   4. Taylor expanded in y around inf 77.7%

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

      1. neg-mul-1 77.7%

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

   6. Simplified 77.7%

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

   7. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   9. Simplified 77.7%

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

Alternative 8: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7800000000 \lor \neg \left(x \leq 3.2\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7800000000.0) (not (<= x 3.2)))
   (/ x (- 2.0 x))
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7800000000.0) || !(x <= 3.2)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-7800000000.0d0)) .or. (.not. (x <= 3.2d0))) then
        tmp = x / (2.0d0 - x)
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -7800000000.0) || !(x <= 3.2)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7800000000.0) or not (x <= 3.2):
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7800000000.0) || !(x <= 3.2))
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -7800000000.0) || ~((x <= 3.2)))
		tmp = x / (2.0 - x);
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7800000000.0], N[Not[LessEqual[x, 3.2]], $MachinePrecision]], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.8e9 or 3.2000000000000002 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.5%

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

   if -7.8e9 < x < 3.2000000000000002

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.2%

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

      2. distribute-neg-frac2 74.2%

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

      3. mul-1-neg 74.2%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(2 - y\right)}} \]

      4. sub-neg 74.2%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(2 + \left(-y\right)\right)}} \]

      5. +-commutative 74.2%

         \[\leadsto \frac{y}{-1 \cdot \color{blue}{\left(\left(-y\right) + 2\right)}} \]

      6. distribute-lft-in 74.2%

         \[\leadsto \frac{y}{\color{blue}{-1 \cdot \left(-y\right) + -1 \cdot 2}} \]

      7. neg-mul-1 74.2%

         \[\leadsto \frac{y}{\color{blue}{\left(-\left(-y\right)\right)} + -1 \cdot 2} \]

      8. remove-double-neg 74.2%

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

      9. metadata-eval 74.2%

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

   5. Simplified 74.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7800000000 \lor \neg \left(x \leq 3.2\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+23} \lor \neg \left(y \leq 2.8 \cdot 10^{+56}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9e+23) (not (<= y 2.8e+56))) (- 1.0 (/ x y)) (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9e+23) || !(y <= 2.8e+56)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-9d+23)) .or. (.not. (y <= 2.8d+56))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -9e+23) || !(y <= 2.8e+56)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9e+23) or not (y <= 2.8e+56):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9e+23) || !(y <= 2.8e+56))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -9e+23) || ~((y <= 2.8e+56)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9e+23], N[Not[LessEqual[y, 2.8e+56]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999958e23 or 2.80000000000000008e56 < y

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.1%

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

   4. Taylor expanded in y around inf 77.5%

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

      1. neg-mul-1 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in x around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. unsub-neg 77.5%

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

   9. Simplified 77.5%

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

   if -8.99999999999999958e23 < y < 2.80000000000000008e56

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+23} \lor \neg \left(y \leq 2.8 \cdot 10^{+56}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -10200000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -10200000000.0) -1.0 (if (<= x 5e+49) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -10200000000.0) {
		tmp = -1.0;
	} else if (x <= 5e+49) {
		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 <= (-10200000000.0d0)) then
        tmp = -1.0d0
    else if (x <= 5d+49) 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 <= -10200000000.0) {
		tmp = -1.0;
	} else if (x <= 5e+49) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -10200000000.0:
		tmp = -1.0
	elif x <= 5e+49:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -10200000000.0)
		tmp = -1.0;
	elseif (x <= 5e+49)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -10200000000.0)
		tmp = -1.0;
	elseif (x <= 5e+49)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -10200000000.0], -1.0, If[LessEqual[x, 5e+49], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e10 or 5.0000000000000004e49 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.3%

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

   if -1.02e10 < x < 5.0000000000000004e49

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 47.8%

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

Alternative 11: 38.6% accurate, 9.0× 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%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 39.3%

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

Developer Target 1: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t\_0} - \frac{y}{t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024172 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y)))))

  (/ (- x y) (- 2.0 (+ x y))))