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

Percentage Accurate: 100.0% → 100.0%

Time: 10.2s

Alternatives: 9

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. Final simplification 100.0%

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

Alternative 2: 60.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-285}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-229}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-154}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+73}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -9e+43)
     t_0
     (if (<= x 5e-285)
       (- 1.0 (/ x y))
       (if (<= x 5.7e-229)
         (* y -0.5)
         (if (<= x 3.1e-174)
           1.0
           (if (<= x 2.7e-154) (* y -0.5) (if (<= x 4.1e+73) 1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -9e+43) {
		tmp = t_0;
	} else if (x <= 5e-285) {
		tmp = 1.0 - (x / y);
	} else if (x <= 5.7e-229) {
		tmp = y * -0.5;
	} else if (x <= 3.1e-174) {
		tmp = 1.0;
	} else if (x <= 2.7e-154) {
		tmp = y * -0.5;
	} else if (x <= 4.1e+73) {
		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 <= (-9d+43)) then
        tmp = t_0
    else if (x <= 5d-285) then
        tmp = 1.0d0 - (x / y)
    else if (x <= 5.7d-229) then
        tmp = y * (-0.5d0)
    else if (x <= 3.1d-174) then
        tmp = 1.0d0
    else if (x <= 2.7d-154) then
        tmp = y * (-0.5d0)
    else if (x <= 4.1d+73) 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 <= -9e+43) {
		tmp = t_0;
	} else if (x <= 5e-285) {
		tmp = 1.0 - (x / y);
	} else if (x <= 5.7e-229) {
		tmp = y * -0.5;
	} else if (x <= 3.1e-174) {
		tmp = 1.0;
	} else if (x <= 2.7e-154) {
		tmp = y * -0.5;
	} else if (x <= 4.1e+73) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -9e+43:
		tmp = t_0
	elif x <= 5e-285:
		tmp = 1.0 - (x / y)
	elif x <= 5.7e-229:
		tmp = y * -0.5
	elif x <= 3.1e-174:
		tmp = 1.0
	elif x <= 2.7e-154:
		tmp = y * -0.5
	elif x <= 4.1e+73:
		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 <= -9e+43)
		tmp = t_0;
	elseif (x <= 5e-285)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= 5.7e-229)
		tmp = Float64(y * -0.5);
	elseif (x <= 3.1e-174)
		tmp = 1.0;
	elseif (x <= 2.7e-154)
		tmp = Float64(y * -0.5);
	elseif (x <= 4.1e+73)
		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 <= -9e+43)
		tmp = t_0;
	elseif (x <= 5e-285)
		tmp = 1.0 - (x / y);
	elseif (x <= 5.7e-229)
		tmp = y * -0.5;
	elseif (x <= 3.1e-174)
		tmp = 1.0;
	elseif (x <= 2.7e-154)
		tmp = y * -0.5;
	elseif (x <= 4.1e+73)
		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, -9e+43], t$95$0, If[LessEqual[x, 5e-285], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.7e-229], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 3.1e-174], 1.0, If[LessEqual[x, 2.7e-154], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 4.1e+73], 1.0, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9e43 or 4.0999999999999998e73 < x

   1. Initial program 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 86.7%

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

   6. Taylor expanded in x around 0 86.9%

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

   if -9e43 < x < 5.00000000000000018e-285

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 60.9%

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

   6. Taylor expanded in y around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   8. Simplified 61.1%

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

   if 5.00000000000000018e-285 < x < 5.70000000000000023e-229 or 3.0999999999999999e-174 < x < 2.69999999999999989e-154

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. distribute-neg-frac 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around 0 67.5%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 67.5%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

   if 5.70000000000000023e-229 < x < 3.0999999999999999e-174 or 2.69999999999999989e-154 < x < 4.0999999999999998e73

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 59.5%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-285}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-229}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-154}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+73}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-287}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-228}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.34 \cdot 10^{-154}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e+43)
   -1.0
   (if (<= x 2.2e-287)
     1.0
     (if (<= x 1.1e-228)
       (* y -0.5)
       (if (<= x 3.1e-174)
         1.0
         (if (<= x 1.34e-154) (* y -0.5) (if (<= x 1.55e+68) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e+43) {
		tmp = -1.0;
	} else if (x <= 2.2e-287) {
		tmp = 1.0;
	} else if (x <= 1.1e-228) {
		tmp = y * -0.5;
	} else if (x <= 3.1e-174) {
		tmp = 1.0;
	} else if (x <= 1.34e-154) {
		tmp = y * -0.5;
	} else if (x <= 1.55e+68) {
		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 <= (-9d+43)) then
        tmp = -1.0d0
    else if (x <= 2.2d-287) then
        tmp = 1.0d0
    else if (x <= 1.1d-228) then
        tmp = y * (-0.5d0)
    else if (x <= 3.1d-174) then
        tmp = 1.0d0
    else if (x <= 1.34d-154) then
        tmp = y * (-0.5d0)
    else if (x <= 1.55d+68) 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 <= -9e+43) {
		tmp = -1.0;
	} else if (x <= 2.2e-287) {
		tmp = 1.0;
	} else if (x <= 1.1e-228) {
		tmp = y * -0.5;
	} else if (x <= 3.1e-174) {
		tmp = 1.0;
	} else if (x <= 1.34e-154) {
		tmp = y * -0.5;
	} else if (x <= 1.55e+68) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e+43:
		tmp = -1.0
	elif x <= 2.2e-287:
		tmp = 1.0
	elif x <= 1.1e-228:
		tmp = y * -0.5
	elif x <= 3.1e-174:
		tmp = 1.0
	elif x <= 1.34e-154:
		tmp = y * -0.5
	elif x <= 1.55e+68:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e+43)
		tmp = -1.0;
	elseif (x <= 2.2e-287)
		tmp = 1.0;
	elseif (x <= 1.1e-228)
		tmp = Float64(y * -0.5);
	elseif (x <= 3.1e-174)
		tmp = 1.0;
	elseif (x <= 1.34e-154)
		tmp = Float64(y * -0.5);
	elseif (x <= 1.55e+68)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9e+43)
		tmp = -1.0;
	elseif (x <= 2.2e-287)
		tmp = 1.0;
	elseif (x <= 1.1e-228)
		tmp = y * -0.5;
	elseif (x <= 3.1e-174)
		tmp = 1.0;
	elseif (x <= 1.34e-154)
		tmp = y * -0.5;
	elseif (x <= 1.55e+68)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e+43], -1.0, If[LessEqual[x, 2.2e-287], 1.0, If[LessEqual[x, 1.1e-228], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 3.1e-174], 1.0, If[LessEqual[x, 1.34e-154], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1.55e+68], 1.0, -1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e43 or 1.5499999999999999e68 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.6%

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

   if -9e43 < x < 2.2e-287 or 1.1e-228 < x < 3.0999999999999999e-174 or 1.34000000000000006e-154 < x < 1.5499999999999999e68

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 60.2%

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

   if 2.2e-287 < x < 1.1e-228 or 3.0999999999999999e-174 < x < 1.34000000000000006e-154

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. distribute-neg-frac 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around 0 67.5%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 67.5%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-287}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-228}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.34 \cdot 10^{-154}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-281}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-229}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-174}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-154}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e+43)
   -1.0
   (if (<= x 2.5e-281)
     (- 1.0 (/ x y))
     (if (<= x 6.3e-229)
       (* y -0.5)
       (if (<= x 1.6e-174)
         1.0
         (if (<= x 1.25e-154) (* y -0.5) (if (<= x 4.2e+70) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e+43) {
		tmp = -1.0;
	} else if (x <= 2.5e-281) {
		tmp = 1.0 - (x / y);
	} else if (x <= 6.3e-229) {
		tmp = y * -0.5;
	} else if (x <= 1.6e-174) {
		tmp = 1.0;
	} else if (x <= 1.25e-154) {
		tmp = y * -0.5;
	} else if (x <= 4.2e+70) {
		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 <= (-9d+43)) then
        tmp = -1.0d0
    else if (x <= 2.5d-281) then
        tmp = 1.0d0 - (x / y)
    else if (x <= 6.3d-229) then
        tmp = y * (-0.5d0)
    else if (x <= 1.6d-174) then
        tmp = 1.0d0
    else if (x <= 1.25d-154) then
        tmp = y * (-0.5d0)
    else if (x <= 4.2d+70) 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 <= -9e+43) {
		tmp = -1.0;
	} else if (x <= 2.5e-281) {
		tmp = 1.0 - (x / y);
	} else if (x <= 6.3e-229) {
		tmp = y * -0.5;
	} else if (x <= 1.6e-174) {
		tmp = 1.0;
	} else if (x <= 1.25e-154) {
		tmp = y * -0.5;
	} else if (x <= 4.2e+70) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e+43:
		tmp = -1.0
	elif x <= 2.5e-281:
		tmp = 1.0 - (x / y)
	elif x <= 6.3e-229:
		tmp = y * -0.5
	elif x <= 1.6e-174:
		tmp = 1.0
	elif x <= 1.25e-154:
		tmp = y * -0.5
	elif x <= 4.2e+70:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e+43)
		tmp = -1.0;
	elseif (x <= 2.5e-281)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= 6.3e-229)
		tmp = Float64(y * -0.5);
	elseif (x <= 1.6e-174)
		tmp = 1.0;
	elseif (x <= 1.25e-154)
		tmp = Float64(y * -0.5);
	elseif (x <= 4.2e+70)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9e+43)
		tmp = -1.0;
	elseif (x <= 2.5e-281)
		tmp = 1.0 - (x / y);
	elseif (x <= 6.3e-229)
		tmp = y * -0.5;
	elseif (x <= 1.6e-174)
		tmp = 1.0;
	elseif (x <= 1.25e-154)
		tmp = y * -0.5;
	elseif (x <= 4.2e+70)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e+43], -1.0, If[LessEqual[x, 2.5e-281], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.3e-229], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1.6e-174], 1.0, If[LessEqual[x, 1.25e-154], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 4.2e+70], 1.0, -1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9e43 or 4.20000000000000015e70 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.6%

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

   if -9e43 < x < 2.4999999999999999e-281

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 60.9%

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

   6. Taylor expanded in y around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   8. Simplified 61.1%

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

   if 2.4999999999999999e-281 < x < 6.29999999999999987e-229 or 1.6e-174 < x < 1.25000000000000005e-154

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. distribute-neg-frac 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around 0 67.5%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 67.5%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

   if 6.29999999999999987e-229 < x < 1.6e-174 or 1.25000000000000005e-154 < x < 4.20000000000000015e70

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 59.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-281}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-229}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-174}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-154}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2700000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+70}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))))
   (if (<= x -9e+43)
     (+ (/ y x) -1.0)
     (if (<= x 4.7e-43)
       t_0
       (if (<= x 2700000.0)
         (/ x (- 2.0 x))
         (if (<= x 4.2e+70) t_0 (/ (- x y) (- x))))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (x <= -9e+43) {
		tmp = (y / x) + -1.0;
	} else if (x <= 4.7e-43) {
		tmp = t_0;
	} else if (x <= 2700000.0) {
		tmp = x / (2.0 - x);
	} else if (x <= 4.2e+70) {
		tmp = t_0;
	} else {
		tmp = (x - y) / -x;
	}
	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 / (y + (-2.0d0))
    if (x <= (-9d+43)) then
        tmp = (y / x) + (-1.0d0)
    else if (x <= 4.7d-43) then
        tmp = t_0
    else if (x <= 2700000.0d0) then
        tmp = x / (2.0d0 - x)
    else if (x <= 4.2d+70) then
        tmp = t_0
    else
        tmp = (x - y) / -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (x <= -9e+43) {
		tmp = (y / x) + -1.0;
	} else if (x <= 4.7e-43) {
		tmp = t_0;
	} else if (x <= 2700000.0) {
		tmp = x / (2.0 - x);
	} else if (x <= 4.2e+70) {
		tmp = t_0;
	} else {
		tmp = (x - y) / -x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	tmp = 0
	if x <= -9e+43:
		tmp = (y / x) + -1.0
	elif x <= 4.7e-43:
		tmp = t_0
	elif x <= 2700000.0:
		tmp = x / (2.0 - x)
	elif x <= 4.2e+70:
		tmp = t_0
	else:
		tmp = (x - y) / -x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	tmp = 0.0
	if (x <= -9e+43)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (x <= 4.7e-43)
		tmp = t_0;
	elseif (x <= 2700000.0)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 4.2e+70)
		tmp = t_0;
	else
		tmp = Float64(Float64(x - y) / Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	tmp = 0.0;
	if (x <= -9e+43)
		tmp = (y / x) + -1.0;
	elseif (x <= 4.7e-43)
		tmp = t_0;
	elseif (x <= 2700000.0)
		tmp = x / (2.0 - x);
	elseif (x <= 4.2e+70)
		tmp = t_0;
	else
		tmp = (x - y) / -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+43], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 4.7e-43], t$95$0, If[LessEqual[x, 2700000.0], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+70], t$95$0, N[(N[(x - y), $MachinePrecision] / (-x)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9e43

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 82.3%

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

   6. Taylor expanded in x around 0 82.5%

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

   if -9e43 < x < 4.7000000000000001e-43 or 2.7e6 < x < 4.20000000000000015e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-neg-frac 82.6%

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

   5. Simplified 82.6%

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

      1. expm1-log1p-u 82.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-y}{2 - y}\right)\right)} \]

      2. expm1-udef 57.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-y}{2 - y}\right)} - 1} \]

      3. add-sqr-sqrt 30.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{2 - y}\right)} - 1 \]

      4. sqrt-unprod 17.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{2 - y}\right)} - 1 \]

      5. sqr-neg 17.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{y \cdot y}}}{2 - y}\right)} - 1 \]

      6. sqrt-unprod 1.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{2 - y}\right)} - 1 \]

      7. add-sqr-sqrt 3.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{y}}{2 - y}\right)} - 1 \]

      8. frac-2neg 3.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-y}{-\left(2 - y\right)}}\right)} - 1 \]

      9. add-sqr-sqrt 1.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{-\left(2 - y\right)}\right)} - 1 \]

      10. sqrt-unprod 15.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{-\left(2 - y\right)}\right)} - 1 \]

      11. sqr-neg 15.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{y \cdot y}}}{-\left(2 - y\right)}\right)} - 1 \]

      12. sqrt-unprod 26.6%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{-\left(2 - y\right)}\right)} - 1 \]

      13. add-sqr-sqrt 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{y}}{-\left(2 - y\right)}\right)} - 1 \]

      14. sub-neg 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{-\color{blue}{\left(2 + \left(-y\right)\right)}}\right)} - 1 \]

      15. distribute-neg-in 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\left(-2\right) + \left(-\left(-y\right)\right)}}\right)} - 1 \]

      16. metadata-eval 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{-2} + \left(-\left(-y\right)\right)}\right)} - 1 \]

      17. remove-double-neg 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{-2 + \color{blue}{y}}\right)} - 1 \]

   7. Applied egg-rr 57.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{-2 + y}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 82.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{-2 + y}\right)\right)} \]

      2. expm1-log1p 82.6%

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

      3. +-commutative 82.6%

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

   9. Simplified 82.6%

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

   if 4.7000000000000001e-43 < x < 2.7e6

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 66.5%

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

   if 4.20000000000000015e70 < x

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf 90.3%

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

      1. expm1-log1p-u 88.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-1}{x} \cdot \left(x - y\right)\right)\right)} \]

      2. expm1-udef 88.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-1}{x} \cdot \left(x - y\right)\right)} - 1} \]

      3. *-commutative 88.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(x - y\right) \cdot \frac{-1}{x}}\right)} - 1 \]

      4. frac-2neg 88.8%

         \[\leadsto e^{\mathsf{log1p}\left(\left(x - y\right) \cdot \color{blue}{\frac{--1}{-x}}\right)} - 1 \]

      5. metadata-eval 88.8%

         \[\leadsto e^{\mathsf{log1p}\left(\left(x - y\right) \cdot \frac{\color{blue}{1}}{-x}\right)} - 1 \]

      6. un-div-inv 89.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x - y}{-x}}\right)} - 1 \]

   7. Applied egg-rr 89.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x - y}{-x}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 89.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{-x}\right)\right)} \]

      2. expm1-log1p 90.6%

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

   9. Simplified 90.6%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 2700000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -2000000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-12}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -2000000000000.0)
     t_0
     (if (<= y 1.35e-92)
       t_1
       (if (<= y 6.2e-12) (* y -0.5) (if (<= y 5.8e+117) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -2000000000000.0) {
		tmp = t_0;
	} else if (y <= 1.35e-92) {
		tmp = t_1;
	} else if (y <= 6.2e-12) {
		tmp = y * -0.5;
	} else if (y <= 5.8e+117) {
		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 - (x / y)
    t_1 = x / (2.0d0 - x)
    if (y <= (-2000000000000.0d0)) then
        tmp = t_0
    else if (y <= 1.35d-92) then
        tmp = t_1
    else if (y <= 6.2d-12) then
        tmp = y * (-0.5d0)
    else if (y <= 5.8d+117) 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 - (x / y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -2000000000000.0) {
		tmp = t_0;
	} else if (y <= 1.35e-92) {
		tmp = t_1;
	} else if (y <= 6.2e-12) {
		tmp = y * -0.5;
	} else if (y <= 5.8e+117) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	t_1 = x / (2.0 - x)
	tmp = 0
	if y <= -2000000000000.0:
		tmp = t_0
	elif y <= 1.35e-92:
		tmp = t_1
	elif y <= 6.2e-12:
		tmp = y * -0.5
	elif y <= 5.8e+117:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	t_1 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -2000000000000.0)
		tmp = t_0;
	elseif (y <= 1.35e-92)
		tmp = t_1;
	elseif (y <= 6.2e-12)
		tmp = Float64(y * -0.5);
	elseif (y <= 5.8e+117)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	t_1 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -2000000000000.0)
		tmp = t_0;
	elseif (y <= 1.35e-92)
		tmp = t_1;
	elseif (y <= 6.2e-12)
		tmp = y * -0.5;
	elseif (y <= 5.8e+117)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2000000000000.0], t$95$0, If[LessEqual[y, 1.35e-92], t$95$1, If[LessEqual[y, 6.2e-12], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 5.8e+117], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2e12 or 5.80000000000000055e117 < y

   1. Initial program 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 77.7%

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

   6. Taylor expanded in y around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. unsub-neg 77.9%

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

   8. Simplified 77.9%

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

   if -2e12 < y < 1.34999999999999998e-92 or 6.2000000000000002e-12 < y < 5.80000000000000055e117

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.0%

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

   if 1.34999999999999998e-92 < y < 6.2000000000000002e-12

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. distribute-neg-frac 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in y around 0 61.3%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 61.3%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2000000000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-12}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ t_1 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.32:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)) (t_1 (/ y (+ y -2.0))))
   (if (<= x -9e+43)
     t_0
     (if (<= x 2.4e-42)
       t_1
       (if (<= x 0.32) (/ x (- 2.0 x)) (if (<= x 1.05e+68) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double t_1 = y / (y + -2.0);
	double tmp;
	if (x <= -9e+43) {
		tmp = t_0;
	} else if (x <= 2.4e-42) {
		tmp = t_1;
	} else if (x <= 0.32) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.05e+68) {
		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 = (y / x) + (-1.0d0)
    t_1 = y / (y + (-2.0d0))
    if (x <= (-9d+43)) then
        tmp = t_0
    else if (x <= 2.4d-42) then
        tmp = t_1
    else if (x <= 0.32d0) then
        tmp = x / (2.0d0 - x)
    else if (x <= 1.05d+68) 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 = (y / x) + -1.0;
	double t_1 = y / (y + -2.0);
	double tmp;
	if (x <= -9e+43) {
		tmp = t_0;
	} else if (x <= 2.4e-42) {
		tmp = t_1;
	} else if (x <= 0.32) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.05e+68) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	t_1 = y / (y + -2.0)
	tmp = 0
	if x <= -9e+43:
		tmp = t_0
	elif x <= 2.4e-42:
		tmp = t_1
	elif x <= 0.32:
		tmp = x / (2.0 - x)
	elif x <= 1.05e+68:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	t_1 = Float64(y / Float64(y + -2.0))
	tmp = 0.0
	if (x <= -9e+43)
		tmp = t_0;
	elseif (x <= 2.4e-42)
		tmp = t_1;
	elseif (x <= 0.32)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 1.05e+68)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	t_1 = y / (y + -2.0);
	tmp = 0.0;
	if (x <= -9e+43)
		tmp = t_0;
	elseif (x <= 2.4e-42)
		tmp = t_1;
	elseif (x <= 0.32)
		tmp = x / (2.0 - x);
	elseif (x <= 1.05e+68)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+43], t$95$0, If[LessEqual[x, 2.4e-42], t$95$1, If[LessEqual[x, 0.32], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+68], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e43 or 1.05e68 < x

   1. Initial program 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 86.7%

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

   6. Taylor expanded in x around 0 86.9%

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

   if -9e43 < x < 2.40000000000000003e-42 or 0.320000000000000007 < x < 1.05e68

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-neg-frac 82.6%

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

   5. Simplified 82.6%

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

      1. expm1-log1p-u 82.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-y}{2 - y}\right)\right)} \]

      2. expm1-udef 57.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-y}{2 - y}\right)} - 1} \]

      3. add-sqr-sqrt 30.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{2 - y}\right)} - 1 \]

      4. sqrt-unprod 17.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{2 - y}\right)} - 1 \]

      5. sqr-neg 17.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{y \cdot y}}}{2 - y}\right)} - 1 \]

      6. sqrt-unprod 1.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{2 - y}\right)} - 1 \]

      7. add-sqr-sqrt 3.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{y}}{2 - y}\right)} - 1 \]

      8. frac-2neg 3.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-y}{-\left(2 - y\right)}}\right)} - 1 \]

      9. add-sqr-sqrt 1.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{-\left(2 - y\right)}\right)} - 1 \]

      10. sqrt-unprod 15.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{-\left(2 - y\right)}\right)} - 1 \]

      11. sqr-neg 15.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{y \cdot y}}}{-\left(2 - y\right)}\right)} - 1 \]

      12. sqrt-unprod 26.6%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{-\left(2 - y\right)}\right)} - 1 \]

      13. add-sqr-sqrt 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{y}}{-\left(2 - y\right)}\right)} - 1 \]

      14. sub-neg 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{-\color{blue}{\left(2 + \left(-y\right)\right)}}\right)} - 1 \]

      15. distribute-neg-in 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\left(-2\right) + \left(-\left(-y\right)\right)}}\right)} - 1 \]

      16. metadata-eval 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{-2} + \left(-\left(-y\right)\right)}\right)} - 1 \]

      17. remove-double-neg 57.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{-2 + \color{blue}{y}}\right)} - 1 \]

   7. Applied egg-rr 57.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{-2 + y}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 82.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{-2 + y}\right)\right)} \]

      2. expm1-log1p 82.6%

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

      3. +-commutative 82.6%

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

   9. Simplified 82.6%

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

   if 2.40000000000000003e-42 < x < 0.320000000000000007

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 66.5%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 0.32:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e+43) -1.0 (if (<= x 2e+68) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e+43) {
		tmp = -1.0;
	} else if (x <= 2e+68) {
		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 <= (-9d+43)) then
        tmp = -1.0d0
    else if (x <= 2d+68) 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 <= -9e+43) {
		tmp = -1.0;
	} else if (x <= 2e+68) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e+43:
		tmp = -1.0
	elif x <= 2e+68:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e+43)
		tmp = -1.0;
	elseif (x <= 2e+68)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9e+43)
		tmp = -1.0;
	elseif (x <= 2e+68)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e+43], -1.0, If[LessEqual[x, 2e+68], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9e43 or 1.99999999999999991e68 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.6%

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

   if -9e43 < x < 1.99999999999999991e68

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 54.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.2% 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 40.6%

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

4. Final simplification 40.6%

   \[\leadsto -1 \]
5. Add Preprocessing

Developer target: 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 2024011 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

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