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

Percentage Accurate: 100.0% → 100.0%

Time: 8.5s

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, 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]]

Derivation

1. Initial program 100.0%

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

   1. associate--r+ 100.0%

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

3. Simplified 100.0%

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

   1. div-sub 100.0%

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

   2. associate--l- 100.0%

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

   3. associate--l- 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 60.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -0.076:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-187}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-280}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-145}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.9:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.4e+34)
   -1.0
   (if (<= x -0.076)
     1.0
     (if (<= x -2e-44)
       (* x 0.5)
       (if (<= x -3e-187)
         1.0
         (if (<= x 9.5e-280)
           (* y -0.5)
           (if (<= x 2.15e-145) 1.0 (if (<= x 3.9) (* x 0.5) -1.0))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.4e+34) {
		tmp = -1.0;
	} else if (x <= -0.076) {
		tmp = 1.0;
	} else if (x <= -2e-44) {
		tmp = x * 0.5;
	} else if (x <= -3e-187) {
		tmp = 1.0;
	} else if (x <= 9.5e-280) {
		tmp = y * -0.5;
	} else if (x <= 2.15e-145) {
		tmp = 1.0;
	} else if (x <= 3.9) {
		tmp = x * 0.5;
	} 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 <= (-5.4d+34)) then
        tmp = -1.0d0
    else if (x <= (-0.076d0)) then
        tmp = 1.0d0
    else if (x <= (-2d-44)) then
        tmp = x * 0.5d0
    else if (x <= (-3d-187)) then
        tmp = 1.0d0
    else if (x <= 9.5d-280) then
        tmp = y * (-0.5d0)
    else if (x <= 2.15d-145) then
        tmp = 1.0d0
    else if (x <= 3.9d0) then
        tmp = x * 0.5d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.4e+34) {
		tmp = -1.0;
	} else if (x <= -0.076) {
		tmp = 1.0;
	} else if (x <= -2e-44) {
		tmp = x * 0.5;
	} else if (x <= -3e-187) {
		tmp = 1.0;
	} else if (x <= 9.5e-280) {
		tmp = y * -0.5;
	} else if (x <= 2.15e-145) {
		tmp = 1.0;
	} else if (x <= 3.9) {
		tmp = x * 0.5;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.4e+34:
		tmp = -1.0
	elif x <= -0.076:
		tmp = 1.0
	elif x <= -2e-44:
		tmp = x * 0.5
	elif x <= -3e-187:
		tmp = 1.0
	elif x <= 9.5e-280:
		tmp = y * -0.5
	elif x <= 2.15e-145:
		tmp = 1.0
	elif x <= 3.9:
		tmp = x * 0.5
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.4e+34)
		tmp = -1.0;
	elseif (x <= -0.076)
		tmp = 1.0;
	elseif (x <= -2e-44)
		tmp = Float64(x * 0.5);
	elseif (x <= -3e-187)
		tmp = 1.0;
	elseif (x <= 9.5e-280)
		tmp = Float64(y * -0.5);
	elseif (x <= 2.15e-145)
		tmp = 1.0;
	elseif (x <= 3.9)
		tmp = Float64(x * 0.5);
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.4e+34)
		tmp = -1.0;
	elseif (x <= -0.076)
		tmp = 1.0;
	elseif (x <= -2e-44)
		tmp = x * 0.5;
	elseif (x <= -3e-187)
		tmp = 1.0;
	elseif (x <= 9.5e-280)
		tmp = y * -0.5;
	elseif (x <= 2.15e-145)
		tmp = 1.0;
	elseif (x <= 3.9)
		tmp = x * 0.5;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.4e+34], -1.0, If[LessEqual[x, -0.076], 1.0, If[LessEqual[x, -2e-44], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -3e-187], 1.0, If[LessEqual[x, 9.5e-280], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 2.15e-145], 1.0, If[LessEqual[x, 3.9], N[(x * 0.5), $MachinePrecision], -1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.4000000000000001e34 or 3.89999999999999991 < x

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 82.3%

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

   if -5.4000000000000001e34 < x < -0.0759999999999999981 or -1.99999999999999991e-44 < x < -3.00000000000000004e-187 or 9.50000000000000082e-280 < x < 2.15e-145

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 65.4%

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

   if -0.0759999999999999981 < x < -1.99999999999999991e-44 or 2.15e-145 < x < 3.89999999999999991

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 63.2%

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

   5. Taylor expanded in x around 0 58.7%

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

      1. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   if -3.00000000000000004e-187 < x < 9.50000000000000082e-280

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. neg-mul-1 96.8%

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

   6. Simplified 96.8%

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

   7. Taylor expanded in y around 0 60.3%

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

      1. *-commutative 60.3%

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

   9. Simplified 60.3%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -0.076:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-187}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-280}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-145}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.9:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -0.076:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-46}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-280}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 10^{-144}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.2:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= x -5.1e+34)
     -1.0
     (if (<= x -0.076)
       t_0
       (if (<= x -5.5e-46)
         (* x 0.5)
         (if (<= x -7.8e-187)
           t_0
           (if (<= x 9e-280)
             (* y -0.5)
             (if (<= x 1e-144) 1.0 (if (<= x 9.2) (* x 0.5) -1.0)))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (x <= -5.1e+34) {
		tmp = -1.0;
	} else if (x <= -0.076) {
		tmp = t_0;
	} else if (x <= -5.5e-46) {
		tmp = x * 0.5;
	} else if (x <= -7.8e-187) {
		tmp = t_0;
	} else if (x <= 9e-280) {
		tmp = y * -0.5;
	} else if (x <= 1e-144) {
		tmp = 1.0;
	} else if (x <= 9.2) {
		tmp = x * 0.5;
	} 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 = 1.0d0 - (x / y)
    if (x <= (-5.1d+34)) then
        tmp = -1.0d0
    else if (x <= (-0.076d0)) then
        tmp = t_0
    else if (x <= (-5.5d-46)) then
        tmp = x * 0.5d0
    else if (x <= (-7.8d-187)) then
        tmp = t_0
    else if (x <= 9d-280) then
        tmp = y * (-0.5d0)
    else if (x <= 1d-144) then
        tmp = 1.0d0
    else if (x <= 9.2d0) then
        tmp = x * 0.5d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (x <= -5.1e+34) {
		tmp = -1.0;
	} else if (x <= -0.076) {
		tmp = t_0;
	} else if (x <= -5.5e-46) {
		tmp = x * 0.5;
	} else if (x <= -7.8e-187) {
		tmp = t_0;
	} else if (x <= 9e-280) {
		tmp = y * -0.5;
	} else if (x <= 1e-144) {
		tmp = 1.0;
	} else if (x <= 9.2) {
		tmp = x * 0.5;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if x <= -5.1e+34:
		tmp = -1.0
	elif x <= -0.076:
		tmp = t_0
	elif x <= -5.5e-46:
		tmp = x * 0.5
	elif x <= -7.8e-187:
		tmp = t_0
	elif x <= 9e-280:
		tmp = y * -0.5
	elif x <= 1e-144:
		tmp = 1.0
	elif x <= 9.2:
		tmp = x * 0.5
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (x <= -5.1e+34)
		tmp = -1.0;
	elseif (x <= -0.076)
		tmp = t_0;
	elseif (x <= -5.5e-46)
		tmp = Float64(x * 0.5);
	elseif (x <= -7.8e-187)
		tmp = t_0;
	elseif (x <= 9e-280)
		tmp = Float64(y * -0.5);
	elseif (x <= 1e-144)
		tmp = 1.0;
	elseif (x <= 9.2)
		tmp = Float64(x * 0.5);
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (x <= -5.1e+34)
		tmp = -1.0;
	elseif (x <= -0.076)
		tmp = t_0;
	elseif (x <= -5.5e-46)
		tmp = x * 0.5;
	elseif (x <= -7.8e-187)
		tmp = t_0;
	elseif (x <= 9e-280)
		tmp = y * -0.5;
	elseif (x <= 1e-144)
		tmp = 1.0;
	elseif (x <= 9.2)
		tmp = x * 0.5;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.1e+34], -1.0, If[LessEqual[x, -0.076], t$95$0, If[LessEqual[x, -5.5e-46], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -7.8e-187], t$95$0, If[LessEqual[x, 9e-280], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1e-144], 1.0, If[LessEqual[x, 9.2], N[(x * 0.5), $MachinePrecision], -1.0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.10000000000000036e34 or 9.1999999999999993 < x

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 82.3%

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

   if -5.10000000000000036e34 < x < -0.0759999999999999981 or -5.49999999999999983e-46 < x < -7.7999999999999998e-187

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 69.5%

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

      1. neg-mul-1 69.5%

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

   6. Simplified 69.5%

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

   7. Taylor expanded in x around 0 69.5%

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

      1. mul-1-neg 69.5%

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

      2. unsub-neg 69.5%

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

   9. Simplified 69.5%

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

   if -0.0759999999999999981 < x < -5.49999999999999983e-46 or 9.9999999999999995e-145 < x < 9.1999999999999993

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 63.2%

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

   5. Taylor expanded in x around 0 58.7%

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

      1. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   if -7.7999999999999998e-187 < x < 8.9999999999999991e-280

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. neg-mul-1 96.8%

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

   6. Simplified 96.8%

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

   7. Taylor expanded in y around 0 60.3%

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

      1. *-commutative 60.3%

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

   9. Simplified 60.3%

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

   if 8.9999999999999991e-280 < x < 9.9999999999999995e-145

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 61.1%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -0.076:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-46}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-187}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-280}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 10^{-144}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.2:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-187}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 10^{-279}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-145}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.2:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -1.15e+35)
     t_0
     (if (<= x -3.9e-187)
       (- 1.0 (/ x y))
       (if (<= x 1e-279)
         (* y -0.5)
         (if (<= x 9.8e-145) 1.0 (if (<= x 2.2) (* x 0.5) t_0)))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -1.15e+35) {
		tmp = t_0;
	} else if (x <= -3.9e-187) {
		tmp = 1.0 - (x / y);
	} else if (x <= 1e-279) {
		tmp = y * -0.5;
	} else if (x <= 9.8e-145) {
		tmp = 1.0;
	} else if (x <= 2.2) {
		tmp = x * 0.5;
	} 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 <= (-1.15d+35)) then
        tmp = t_0
    else if (x <= (-3.9d-187)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= 1d-279) then
        tmp = y * (-0.5d0)
    else if (x <= 9.8d-145) then
        tmp = 1.0d0
    else if (x <= 2.2d0) then
        tmp = x * 0.5d0
    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 <= -1.15e+35) {
		tmp = t_0;
	} else if (x <= -3.9e-187) {
		tmp = 1.0 - (x / y);
	} else if (x <= 1e-279) {
		tmp = y * -0.5;
	} else if (x <= 9.8e-145) {
		tmp = 1.0;
	} else if (x <= 2.2) {
		tmp = x * 0.5;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -1.15e+35:
		tmp = t_0
	elif x <= -3.9e-187:
		tmp = 1.0 - (x / y)
	elif x <= 1e-279:
		tmp = y * -0.5
	elif x <= 9.8e-145:
		tmp = 1.0
	elif x <= 2.2:
		tmp = x * 0.5
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	tmp = 0.0
	if (x <= -1.15e+35)
		tmp = t_0;
	elseif (x <= -3.9e-187)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= 1e-279)
		tmp = Float64(y * -0.5);
	elseif (x <= 9.8e-145)
		tmp = 1.0;
	elseif (x <= 2.2)
		tmp = Float64(x * 0.5);
	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 <= -1.15e+35)
		tmp = t_0;
	elseif (x <= -3.9e-187)
		tmp = 1.0 - (x / y);
	elseif (x <= 1e-279)
		tmp = y * -0.5;
	elseif (x <= 9.8e-145)
		tmp = 1.0;
	elseif (x <= 2.2)
		tmp = x * 0.5;
	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, -1.15e+35], t$95$0, If[LessEqual[x, -3.9e-187], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e-279], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 9.8e-145], 1.0, If[LessEqual[x, 2.2], N[(x * 0.5), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.1499999999999999e35 or 2.2000000000000002 < x

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 82.9%

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

      1. neg-mul-1 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in x around 0 82.9%

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

   if -1.1499999999999999e35 < x < -3.8999999999999999e-187

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 58.4%

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

      1. neg-mul-1 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in x around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   9. Simplified 58.4%

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

   if -3.8999999999999999e-187 < x < 1.00000000000000006e-279

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. neg-mul-1 96.8%

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

   6. Simplified 96.8%

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

   7. Taylor expanded in y around 0 60.3%

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

      1. *-commutative 60.3%

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

   9. Simplified 60.3%

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

   if 1.00000000000000006e-279 < x < 9.79999999999999934e-145

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 61.1%

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

   if 9.79999999999999934e-145 < x < 2.2000000000000002

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 59.3%

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

   5. Taylor expanded in x around 0 58.3%

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

      1. *-commutative 58.3%

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

   7. Simplified 58.3%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+35}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-187}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 10^{-279}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-145}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.2:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 5: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -0.076:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-147}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.3:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2e+35)
   -1.0
   (if (<= x -0.076)
     1.0
     (if (<= x -5.2e-45)
       (* x 0.5)
       (if (<= x 3.7e-147) 1.0 (if (<= x 3.3) (* x 0.5) -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e+35) {
		tmp = -1.0;
	} else if (x <= -0.076) {
		tmp = 1.0;
	} else if (x <= -5.2e-45) {
		tmp = x * 0.5;
	} else if (x <= 3.7e-147) {
		tmp = 1.0;
	} else if (x <= 3.3) {
		tmp = x * 0.5;
	} 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 <= (-2d+35)) then
        tmp = -1.0d0
    else if (x <= (-0.076d0)) then
        tmp = 1.0d0
    else if (x <= (-5.2d-45)) then
        tmp = x * 0.5d0
    else if (x <= 3.7d-147) then
        tmp = 1.0d0
    else if (x <= 3.3d0) then
        tmp = x * 0.5d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2e+35) {
		tmp = -1.0;
	} else if (x <= -0.076) {
		tmp = 1.0;
	} else if (x <= -5.2e-45) {
		tmp = x * 0.5;
	} else if (x <= 3.7e-147) {
		tmp = 1.0;
	} else if (x <= 3.3) {
		tmp = x * 0.5;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e+35:
		tmp = -1.0
	elif x <= -0.076:
		tmp = 1.0
	elif x <= -5.2e-45:
		tmp = x * 0.5
	elif x <= 3.7e-147:
		tmp = 1.0
	elif x <= 3.3:
		tmp = x * 0.5
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e+35)
		tmp = -1.0;
	elseif (x <= -0.076)
		tmp = 1.0;
	elseif (x <= -5.2e-45)
		tmp = Float64(x * 0.5);
	elseif (x <= 3.7e-147)
		tmp = 1.0;
	elseif (x <= 3.3)
		tmp = Float64(x * 0.5);
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e+35)
		tmp = -1.0;
	elseif (x <= -0.076)
		tmp = 1.0;
	elseif (x <= -5.2e-45)
		tmp = x * 0.5;
	elseif (x <= 3.7e-147)
		tmp = 1.0;
	elseif (x <= 3.3)
		tmp = x * 0.5;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e+35], -1.0, If[LessEqual[x, -0.076], 1.0, If[LessEqual[x, -5.2e-45], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 3.7e-147], 1.0, If[LessEqual[x, 3.3], N[(x * 0.5), $MachinePrecision], -1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9999999999999999e35 or 3.2999999999999998 < x

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 82.3%

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

   if -1.9999999999999999e35 < x < -0.0759999999999999981 or -5.19999999999999973e-45 < x < 3.7000000000000002e-147

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 56.5%

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

   if -0.0759999999999999981 < x < -5.19999999999999973e-45 or 3.7000000000000002e-147 < x < 3.2999999999999998

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 63.2%

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

   5. Taylor expanded in x around 0 58.7%

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

      1. *-commutative 58.7%

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

   7. Simplified 58.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -0.076:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-147}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.3:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{+34} \lor \neg \left(x \leq 1.1 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.1e+34) (not (<= x 1.1e+29)))
   (+ (/ y x) -1.0)
   (/ (- x y) (- 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.1e+34) || !(x <= 1.1e+29)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-5.1d+34)) .or. (.not. (x <= 1.1d+29))) then
        tmp = (y / x) + (-1.0d0)
    else
        tmp = (x - y) / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -5.1e+34) || !(x <= 1.1e+29)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.1e+34) or not (x <= 1.1e+29):
		tmp = (y / x) + -1.0
	else:
		tmp = (x - y) / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.1e+34) || !(x <= 1.1e+29))
		tmp = Float64(Float64(y / x) + -1.0);
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5.1e+34) || ~((x <= 1.1e+29)))
		tmp = (y / x) + -1.0;
	else
		tmp = (x - y) / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.1e+34], N[Not[LessEqual[x, 1.1e+29]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.10000000000000036e34 or 1.1000000000000001e29 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 85.8%

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

      1. neg-mul-1 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in x around 0 85.8%

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

   if -5.10000000000000036e34 < x < 1.1000000000000001e29

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 94.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{+34} \lor \neg \left(x \leq 1.1 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \]

Alternative 7: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+102} \lor \neg \left(y \leq 2.35 \cdot 10^{+32}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.5e+102) (not (<= y 2.35e+32)))
   (- 1.0 (/ x y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.5e+102) || !(y <= 2.35e+32)) {
		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 <= (-7.5d+102)) .or. (.not. (y <= 2.35d+32))) 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 <= -7.5e+102) || !(y <= 2.35e+32)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.5e+102) or not (y <= 2.35e+32):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.5e+102) || !(y <= 2.35e+32))
		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 <= -7.5e+102) || ~((y <= 2.35e+32)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.5e+102], N[Not[LessEqual[y, 2.35e+32]], $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 < -7.5e102 or 2.35000000000000012e32 < y

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 84.6%

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

      1. neg-mul-1 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in x around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

   9. Simplified 84.6%

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

   if -7.5e102 < y < 2.35000000000000012e32

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 70.8%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+102} \lor \neg \left(y \leq 2.35 \cdot 10^{+32}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 8: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-45} \lor \neg \left(x \leq 5.5 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.6e-45) (not (<= x 5.5e-81)))
   (/ x (- 2.0 x))
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.6e-45) || !(x <= 5.5e-81)) {
		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 <= (-2.6d-45)) .or. (.not. (x <= 5.5d-81))) 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 <= -2.6e-45) || !(x <= 5.5e-81)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.6e-45) or not (x <= 5.5e-81):
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.6e-45) || !(x <= 5.5e-81))
		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 <= -2.6e-45) || ~((x <= 5.5e-81)))
		tmp = x / (2.0 - x);
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.6e-45], N[Not[LessEqual[x, 5.5e-81]], $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 < -2.59999999999999987e-45 or 5.50000000000000026e-81 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 79.0%

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

   if -2.59999999999999987e-45 < x < 5.50000000000000026e-81

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 86.9%

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

      1. associate-*r/ 86.9%

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

      2. neg-mul-1 86.9%

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

   6. Simplified 86.9%

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

      1. frac-2neg 86.9%

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

      2. div-inv 86.8%

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

      3. remove-double-neg 86.8%

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

      4. sub-neg 86.8%

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

      5. distribute-neg-in 86.8%

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

      6. metadata-eval 86.8%

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

      7. remove-double-neg 86.8%

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

   8. Applied egg-rr 86.8%

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

      1. associate-*r/ 86.9%

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

      2. *-rgt-identity 86.9%

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

      3. +-commutative 86.9%

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

   10. Simplified 86.9%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-45} \lor \neg \left(x \leq 5.5 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 9: 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. Final simplification 100.0%

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

Alternative 10: 62.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+28}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+35) -1.0 (if (<= x 1.4e+28) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+35) {
		tmp = -1.0;
	} else if (x <= 1.4e+28) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1d+35)) then
        tmp = -1.0d0
    else if (x <= 1.4d+28) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1e+35) {
		tmp = -1.0;
	} else if (x <= 1.4e+28) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+35:
		tmp = -1.0
	elif x <= 1.4e+28:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+35)
		tmp = -1.0;
	elseif (x <= 1.4e+28)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+35)
		tmp = -1.0;
	elseif (x <= 1.4e+28)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+35], -1.0, If[LessEqual[x, 1.4e+28], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999997e34 or 1.4000000000000001e28 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 85.3%

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

   if -9.9999999999999997e34 < x < 1.4000000000000001e28

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 48.7%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+28}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 11: 39.1% 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. Step-by-step derivation

   1. associate--r+ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 39.4%

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

5. Final simplification 39.4%

   \[\leadsto -1 \]

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 2023285 
(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))))