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

Percentage Accurate: 100.0% → 100.0%

Time: 8.5s

Alternatives: 8

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: 60.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-137}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-298}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-256}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 0.003:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.1e+64)
   1.0
   (if (<= y -3.8e-37)
     -1.0
     (if (<= y -4e-137)
       (* y -0.5)
       (if (<= y -5.5e-298)
         -1.0
         (if (<= y 1.25e-256)
           (* x 0.5)
           (if (<= y 4e-36)
             -1.0
             (if (<= y 0.003) (* y -0.5) (if (<= y 330.0) -1.0 1.0)))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1e+64) {
		tmp = 1.0;
	} else if (y <= -3.8e-37) {
		tmp = -1.0;
	} else if (y <= -4e-137) {
		tmp = y * -0.5;
	} else if (y <= -5.5e-298) {
		tmp = -1.0;
	} else if (y <= 1.25e-256) {
		tmp = x * 0.5;
	} else if (y <= 4e-36) {
		tmp = -1.0;
	} else if (y <= 0.003) {
		tmp = y * -0.5;
	} else if (y <= 330.0) {
		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 (y <= (-1.1d+64)) then
        tmp = 1.0d0
    else if (y <= (-3.8d-37)) then
        tmp = -1.0d0
    else if (y <= (-4d-137)) then
        tmp = y * (-0.5d0)
    else if (y <= (-5.5d-298)) then
        tmp = -1.0d0
    else if (y <= 1.25d-256) then
        tmp = x * 0.5d0
    else if (y <= 4d-36) then
        tmp = -1.0d0
    else if (y <= 0.003d0) then
        tmp = y * (-0.5d0)
    else if (y <= 330.0d0) 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 (y <= -1.1e+64) {
		tmp = 1.0;
	} else if (y <= -3.8e-37) {
		tmp = -1.0;
	} else if (y <= -4e-137) {
		tmp = y * -0.5;
	} else if (y <= -5.5e-298) {
		tmp = -1.0;
	} else if (y <= 1.25e-256) {
		tmp = x * 0.5;
	} else if (y <= 4e-36) {
		tmp = -1.0;
	} else if (y <= 0.003) {
		tmp = y * -0.5;
	} else if (y <= 330.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.1e+64:
		tmp = 1.0
	elif y <= -3.8e-37:
		tmp = -1.0
	elif y <= -4e-137:
		tmp = y * -0.5
	elif y <= -5.5e-298:
		tmp = -1.0
	elif y <= 1.25e-256:
		tmp = x * 0.5
	elif y <= 4e-36:
		tmp = -1.0
	elif y <= 0.003:
		tmp = y * -0.5
	elif y <= 330.0:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1e+64)
		tmp = 1.0;
	elseif (y <= -3.8e-37)
		tmp = -1.0;
	elseif (y <= -4e-137)
		tmp = Float64(y * -0.5);
	elseif (y <= -5.5e-298)
		tmp = -1.0;
	elseif (y <= 1.25e-256)
		tmp = Float64(x * 0.5);
	elseif (y <= 4e-36)
		tmp = -1.0;
	elseif (y <= 0.003)
		tmp = Float64(y * -0.5);
	elseif (y <= 330.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.1e+64)
		tmp = 1.0;
	elseif (y <= -3.8e-37)
		tmp = -1.0;
	elseif (y <= -4e-137)
		tmp = y * -0.5;
	elseif (y <= -5.5e-298)
		tmp = -1.0;
	elseif (y <= 1.25e-256)
		tmp = x * 0.5;
	elseif (y <= 4e-36)
		tmp = -1.0;
	elseif (y <= 0.003)
		tmp = y * -0.5;
	elseif (y <= 330.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1e+64], 1.0, If[LessEqual[y, -3.8e-37], -1.0, If[LessEqual[y, -4e-137], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -5.5e-298], -1.0, If[LessEqual[y, 1.25e-256], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 4e-36], -1.0, If[LessEqual[y, 0.003], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 330.0], -1.0, 1.0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.10000000000000001e64 or 330 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.8%

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

   if -1.10000000000000001e64 < y < -3.8000000000000004e-37 or -3.99999999999999991e-137 < y < -5.4999999999999996e-298 or 1.25e-256 < y < 3.9999999999999998e-36 or 0.0030000000000000001 < y < 330

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.9%

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

   if -3.8000000000000004e-37 < y < -3.99999999999999991e-137 or 3.9999999999999998e-36 < y < 0.0030000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 61.5%

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

      1. mul-1-neg 61.5%

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

      2. distribute-neg-frac 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in y around 0 57.7%

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

      1. *-commutative 57.7%

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

   8. Simplified 57.7%

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

   if -5.4999999999999996e-298 < y < 1.25e-256

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.2%

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

   4. Taylor expanded in x around 0 77.3%

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

      1. *-commutative 77.3%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   6. Simplified 77.3%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-137}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-298}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-256}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 0.003:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.013:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -1.45e+64)
     1.0
     (if (<= y 3.8e-38)
       t_0
       (if (<= y 0.013) (* y -0.5) (if (<= y 330.0) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -1.45e+64) {
		tmp = 1.0;
	} else if (y <= 3.8e-38) {
		tmp = t_0;
	} else if (y <= 0.013) {
		tmp = y * -0.5;
	} else if (y <= 330.0) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-1.45d+64)) then
        tmp = 1.0d0
    else if (y <= 3.8d-38) then
        tmp = t_0
    else if (y <= 0.013d0) then
        tmp = y * (-0.5d0)
    else if (y <= 330.0d0) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -1.45e+64) {
		tmp = 1.0;
	} else if (y <= 3.8e-38) {
		tmp = t_0;
	} else if (y <= 0.013) {
		tmp = y * -0.5;
	} else if (y <= 330.0) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -1.45e+64:
		tmp = 1.0
	elif y <= 3.8e-38:
		tmp = t_0
	elif y <= 0.013:
		tmp = y * -0.5
	elif y <= 330.0:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -1.45e+64)
		tmp = 1.0;
	elseif (y <= 3.8e-38)
		tmp = t_0;
	elseif (y <= 0.013)
		tmp = Float64(y * -0.5);
	elseif (y <= 330.0)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -1.45e+64)
		tmp = 1.0;
	elseif (y <= 3.8e-38)
		tmp = t_0;
	elseif (y <= 0.013)
		tmp = y * -0.5;
	elseif (y <= 330.0)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+64], 1.0, If[LessEqual[y, 3.8e-38], t$95$0, If[LessEqual[y, 0.013], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 330.0], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.44999999999999997e64 or 330 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.8%

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

   if -1.44999999999999997e64 < y < 3.8e-38 or 0.0129999999999999994 < y < 330

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.4%

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

   if 3.8e-38 < y < 0.0129999999999999994

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.7%

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

      1. mul-1-neg 88.7%

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

      2. distribute-neg-frac 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in y around 0 74.3%

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

      1. *-commutative 74.3%

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

   8. Simplified 74.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 0.013:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-296}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-253}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.12e+64)
   1.0
   (if (<= y -1.9e-296)
     -1.0
     (if (<= y 1.7e-253) (* x 0.5) (if (<= y 330.0) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.12e+64) {
		tmp = 1.0;
	} else if (y <= -1.9e-296) {
		tmp = -1.0;
	} else if (y <= 1.7e-253) {
		tmp = x * 0.5;
	} else if (y <= 330.0) {
		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 (y <= (-1.12d+64)) then
        tmp = 1.0d0
    else if (y <= (-1.9d-296)) then
        tmp = -1.0d0
    else if (y <= 1.7d-253) then
        tmp = x * 0.5d0
    else if (y <= 330.0d0) 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 (y <= -1.12e+64) {
		tmp = 1.0;
	} else if (y <= -1.9e-296) {
		tmp = -1.0;
	} else if (y <= 1.7e-253) {
		tmp = x * 0.5;
	} else if (y <= 330.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.12e+64:
		tmp = 1.0
	elif y <= -1.9e-296:
		tmp = -1.0
	elif y <= 1.7e-253:
		tmp = x * 0.5
	elif y <= 330.0:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.12e+64)
		tmp = 1.0;
	elseif (y <= -1.9e-296)
		tmp = -1.0;
	elseif (y <= 1.7e-253)
		tmp = Float64(x * 0.5);
	elseif (y <= 330.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.12e+64)
		tmp = 1.0;
	elseif (y <= -1.9e-296)
		tmp = -1.0;
	elseif (y <= 1.7e-253)
		tmp = x * 0.5;
	elseif (y <= 330.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.12e+64], 1.0, If[LessEqual[y, -1.9e-296], -1.0, If[LessEqual[y, 1.7e-253], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 330.0], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999995e64 or 330 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.8%

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

   if -1.11999999999999995e64 < y < -1.9000000000000001e-296 or 1.69999999999999993e-253 < y < 330

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 52.9%

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

   if -1.9000000000000001e-296 < y < 1.69999999999999993e-253

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.2%

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

   4. Taylor expanded in x around 0 77.3%

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

      1. *-commutative 77.3%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   6. Simplified 77.3%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-296}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-253}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.1e+64) 1.0 (if (<= y 4e-36) (/ x (- 2.0 x)) (/ y (+ y -2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1e+64) {
		tmp = 1.0;
	} else if (y <= 4e-36) {
		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 (y <= (-1.1d+64)) then
        tmp = 1.0d0
    else if (y <= 4d-36) 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 (y <= -1.1e+64) {
		tmp = 1.0;
	} else if (y <= 4e-36) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.1e+64:
		tmp = 1.0
	elif y <= 4e-36:
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1e+64)
		tmp = 1.0;
	elseif (y <= 4e-36)
		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 (y <= -1.1e+64)
		tmp = 1.0;
	elseif (y <= 4e-36)
		tmp = x / (2.0 - x);
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1e+64], 1.0, If[LessEqual[y, 4e-36], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.10000000000000001e64

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.7%

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

   if -1.10000000000000001e64 < y < 3.9999999999999998e-36

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.1%

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

   if 3.9999999999999998e-36 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. distribute-neg-frac 78.7%

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

   5. Simplified 78.7%

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

      1. expm1-log1p-u 78.4%

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

      2. expm1-udef 71.2%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 4.8%

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

      5. sqr-neg 4.8%

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

      6. sqrt-unprod 13.4%

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

      7. add-sqr-sqrt 16.4%

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

      8. frac-2neg 16.4%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 32.6%

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

      11. sqr-neg 32.6%

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

      12. sqrt-unprod 71.0%

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

      13. add-sqr-sqrt 71.2%

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

      14. sub-neg 71.2%

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

      15. distribute-neg-in 71.2%

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

      16. metadata-eval 71.2%

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

      17. remove-double-neg 71.2%

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

   7. Applied egg-rr 71.2%

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

      1. expm1-def 78.4%

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

      2. expm1-log1p 78.7%

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

      3. +-commutative 78.7%

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

   9. Simplified 78.7%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;1 + \frac{2 + x \cdot -2}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.1e+64)
   (+ 1.0 (/ (+ 2.0 (* x -2.0)) y))
   (if (<= y 8.8e-39) (/ x (- 2.0 x)) (/ y (+ y -2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1e+64) {
		tmp = 1.0 + ((2.0 + (x * -2.0)) / y);
	} else if (y <= 8.8e-39) {
		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 (y <= (-1.1d+64)) then
        tmp = 1.0d0 + ((2.0d0 + (x * (-2.0d0))) / y)
    else if (y <= 8.8d-39) 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 (y <= -1.1e+64) {
		tmp = 1.0 + ((2.0 + (x * -2.0)) / y);
	} else if (y <= 8.8e-39) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.1e+64:
		tmp = 1.0 + ((2.0 + (x * -2.0)) / y)
	elif y <= 8.8e-39:
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1e+64)
		tmp = Float64(1.0 + Float64(Float64(2.0 + Float64(x * -2.0)) / y));
	elseif (y <= 8.8e-39)
		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 (y <= -1.1e+64)
		tmp = 1.0 + ((2.0 + (x * -2.0)) / y);
	elseif (y <= 8.8e-39)
		tmp = x / (2.0 - x);
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1e+64], N[(1.0 + N[(N[(2.0 + N[(x * -2.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e-39], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.10000000000000001e64

   1. Initial program 100.0%

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

      1. flip-- 28.6%

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

      2. associate-/r/ 28.6%

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

      3. metadata-eval 28.6%

         \[\leadsto \frac{x - y}{\color{blue}{4} - \left(x + y\right) \cdot \left(x + y\right)} \cdot \left(2 + \left(x + y\right)\right) \]

      4. pow2 28.6%

         \[\leadsto \frac{x - y}{4 - \color{blue}{{\left(x + y\right)}^{2}}} \cdot \left(2 + \left(x + y\right)\right) \]

   4. Applied egg-rr 28.6%

      \[\leadsto \color{blue}{\frac{x - y}{4 - {\left(x + y\right)}^{2}} \cdot \left(2 + \left(x + y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*l/ 26.4%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot \left(2 + \left(x + y\right)\right)}{4 - {\left(x + y\right)}^{2}}} \]

      2. associate-+r+ 26.4%

         \[\leadsto \frac{\left(x - y\right) \cdot \color{blue}{\left(\left(2 + x\right) + y\right)}}{4 - {\left(x + y\right)}^{2}} \]

      3. +-commutative 26.4%

         \[\leadsto \frac{\left(x - y\right) \cdot \left(\left(2 + x\right) + y\right)}{4 - {\color{blue}{\left(y + x\right)}}^{2}} \]

   6. Simplified 26.4%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot \left(\left(2 + x\right) + y\right)}{4 - {\left(y + x\right)}^{2}}} \]

   7. Taylor expanded in y around -inf 82.2%

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

   9. Simplified 82.2%

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

   if -1.10000000000000001e64 < y < 8.80000000000000003e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.1%

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

   if 8.80000000000000003e-39 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. distribute-neg-frac 78.7%

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

   5. Simplified 78.7%

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

      1. expm1-log1p-u 78.4%

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

      2. expm1-udef 71.2%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 4.8%

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

      5. sqr-neg 4.8%

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

      6. sqrt-unprod 13.4%

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

      7. add-sqr-sqrt 16.4%

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

      8. frac-2neg 16.4%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 32.6%

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

      11. sqr-neg 32.6%

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

      12. sqrt-unprod 71.0%

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

      13. add-sqr-sqrt 71.2%

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

      14. sub-neg 71.2%

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

      15. distribute-neg-in 71.2%

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

      16. metadata-eval 71.2%

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

      17. remove-double-neg 71.2%

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

   7. Applied egg-rr 71.2%

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

      1. expm1-def 78.4%

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

      2. expm1-log1p 78.7%

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

      3. +-commutative 78.7%

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

   9. Simplified 78.7%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;1 + \frac{2 + x \cdot -2}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.15e+64) 1.0 (if (<= y 330.0) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.15e+64) {
		tmp = 1.0;
	} else if (y <= 330.0) {
		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 (y <= (-1.15d+64)) then
        tmp = 1.0d0
    else if (y <= 330.0d0) 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 (y <= -1.15e+64) {
		tmp = 1.0;
	} else if (y <= 330.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.15e+64:
		tmp = 1.0
	elif y <= 330.0:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.15e+64)
		tmp = 1.0;
	elseif (y <= 330.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.15e+64)
		tmp = 1.0;
	elseif (y <= 330.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.15e+64], 1.0, If[LessEqual[y, 330.0], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e64 or 330 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.8%

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

   if -1.15e64 < y < 330

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 49.4%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.1% 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 35.6%

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

4. Final simplification 35.6%

   \[\leadsto -1 \]
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 2024027 
(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))))