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

Percentage Accurate: 100.0% → 100.0%

Time: 6.7s

Alternatives: 10

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. Final simplification 100.0%

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

Alternative 2: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-145}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-187}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-270}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-190}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.3e+61)
   1.0
   (if (<= y -1.8e-35)
     -1.0
     (if (<= y -3.05e-145)
       (* y -0.5)
       (if (<= y -7.2e-187)
         -1.0
         (if (<= y -5.8e-270)
           (* x 0.5)
           (if (<= y 1.8e-190)
             -1.0
             (if (<= y 9.2e-148) (* x 0.5) (if (<= y 2.7e+34) -1.0 1.0)))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.3e+61) {
		tmp = 1.0;
	} else if (y <= -1.8e-35) {
		tmp = -1.0;
	} else if (y <= -3.05e-145) {
		tmp = y * -0.5;
	} else if (y <= -7.2e-187) {
		tmp = -1.0;
	} else if (y <= -5.8e-270) {
		tmp = x * 0.5;
	} else if (y <= 1.8e-190) {
		tmp = -1.0;
	} else if (y <= 9.2e-148) {
		tmp = x * 0.5;
	} else if (y <= 2.7e+34) {
		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 <= (-3.3d+61)) then
        tmp = 1.0d0
    else if (y <= (-1.8d-35)) then
        tmp = -1.0d0
    else if (y <= (-3.05d-145)) then
        tmp = y * (-0.5d0)
    else if (y <= (-7.2d-187)) then
        tmp = -1.0d0
    else if (y <= (-5.8d-270)) then
        tmp = x * 0.5d0
    else if (y <= 1.8d-190) then
        tmp = -1.0d0
    else if (y <= 9.2d-148) then
        tmp = x * 0.5d0
    else if (y <= 2.7d+34) 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 <= -3.3e+61) {
		tmp = 1.0;
	} else if (y <= -1.8e-35) {
		tmp = -1.0;
	} else if (y <= -3.05e-145) {
		tmp = y * -0.5;
	} else if (y <= -7.2e-187) {
		tmp = -1.0;
	} else if (y <= -5.8e-270) {
		tmp = x * 0.5;
	} else if (y <= 1.8e-190) {
		tmp = -1.0;
	} else if (y <= 9.2e-148) {
		tmp = x * 0.5;
	} else if (y <= 2.7e+34) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.3e+61:
		tmp = 1.0
	elif y <= -1.8e-35:
		tmp = -1.0
	elif y <= -3.05e-145:
		tmp = y * -0.5
	elif y <= -7.2e-187:
		tmp = -1.0
	elif y <= -5.8e-270:
		tmp = x * 0.5
	elif y <= 1.8e-190:
		tmp = -1.0
	elif y <= 9.2e-148:
		tmp = x * 0.5
	elif y <= 2.7e+34:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.3e+61)
		tmp = 1.0;
	elseif (y <= -1.8e-35)
		tmp = -1.0;
	elseif (y <= -3.05e-145)
		tmp = Float64(y * -0.5);
	elseif (y <= -7.2e-187)
		tmp = -1.0;
	elseif (y <= -5.8e-270)
		tmp = Float64(x * 0.5);
	elseif (y <= 1.8e-190)
		tmp = -1.0;
	elseif (y <= 9.2e-148)
		tmp = Float64(x * 0.5);
	elseif (y <= 2.7e+34)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.3e+61)
		tmp = 1.0;
	elseif (y <= -1.8e-35)
		tmp = -1.0;
	elseif (y <= -3.05e-145)
		tmp = y * -0.5;
	elseif (y <= -7.2e-187)
		tmp = -1.0;
	elseif (y <= -5.8e-270)
		tmp = x * 0.5;
	elseif (y <= 1.8e-190)
		tmp = -1.0;
	elseif (y <= 9.2e-148)
		tmp = x * 0.5;
	elseif (y <= 2.7e+34)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.3e+61], 1.0, If[LessEqual[y, -1.8e-35], -1.0, If[LessEqual[y, -3.05e-145], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -7.2e-187], -1.0, If[LessEqual[y, -5.8e-270], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1.8e-190], -1.0, If[LessEqual[y, 9.2e-148], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 2.7e+34], -1.0, 1.0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.2999999999999998e61 or 2.7e34 < 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 87.7%

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

   if -3.2999999999999998e61 < y < -1.80000000000000009e-35 or -3.05e-145 < y < -7.19999999999999989e-187 or -5.79999999999999965e-270 < y < 1.80000000000000003e-190 or 9.1999999999999999e-148 < y < 2.7e34

   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 64.7%

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

   if -1.80000000000000009e-35 < y < -3.05e-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 x around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-neg-frac 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in y around 0 63.2%

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

      1. *-commutative 63.2%

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

   9. Simplified 63.2%

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

   if -7.19999999999999989e-187 < y < -5.79999999999999965e-270 or 1.80000000000000003e-190 < y < 9.1999999999999999e-148

   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 86.6%

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

   5. Taylor expanded in x around 0 65.1%

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

      1. *-commutative 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-145}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-187}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-270}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-190}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 62.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - y\right) \cdot 0.5\\ t_1 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-41}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-272}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-192}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+33}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- x y) 0.5)) (t_1 (- 1.0 (/ x y))))
   (if (<= y -6.5e+70)
     t_1
     (if (<= y -2.8e-41)
       -1.0
       (if (<= y -1.05e-272)
         t_0
         (if (<= y 1.35e-192)
           -1.0
           (if (<= y 3.2e-147) t_0 (if (<= y 1.35e+33) -1.0 t_1))))))))

C

double code(double x, double y) {
	double t_0 = (x - y) * 0.5;
	double t_1 = 1.0 - (x / y);
	double tmp;
	if (y <= -6.5e+70) {
		tmp = t_1;
	} else if (y <= -2.8e-41) {
		tmp = -1.0;
	} else if (y <= -1.05e-272) {
		tmp = t_0;
	} else if (y <= 1.35e-192) {
		tmp = -1.0;
	} else if (y <= 3.2e-147) {
		tmp = t_0;
	} else if (y <= 1.35e+33) {
		tmp = -1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x - y) * 0.5d0
    t_1 = 1.0d0 - (x / y)
    if (y <= (-6.5d+70)) then
        tmp = t_1
    else if (y <= (-2.8d-41)) then
        tmp = -1.0d0
    else if (y <= (-1.05d-272)) then
        tmp = t_0
    else if (y <= 1.35d-192) then
        tmp = -1.0d0
    else if (y <= 3.2d-147) then
        tmp = t_0
    else if (y <= 1.35d+33) then
        tmp = -1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) * 0.5;
	double t_1 = 1.0 - (x / y);
	double tmp;
	if (y <= -6.5e+70) {
		tmp = t_1;
	} else if (y <= -2.8e-41) {
		tmp = -1.0;
	} else if (y <= -1.05e-272) {
		tmp = t_0;
	} else if (y <= 1.35e-192) {
		tmp = -1.0;
	} else if (y <= 3.2e-147) {
		tmp = t_0;
	} else if (y <= 1.35e+33) {
		tmp = -1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) * 0.5
	t_1 = 1.0 - (x / y)
	tmp = 0
	if y <= -6.5e+70:
		tmp = t_1
	elif y <= -2.8e-41:
		tmp = -1.0
	elif y <= -1.05e-272:
		tmp = t_0
	elif y <= 1.35e-192:
		tmp = -1.0
	elif y <= 3.2e-147:
		tmp = t_0
	elif y <= 1.35e+33:
		tmp = -1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) * 0.5)
	t_1 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -6.5e+70)
		tmp = t_1;
	elseif (y <= -2.8e-41)
		tmp = -1.0;
	elseif (y <= -1.05e-272)
		tmp = t_0;
	elseif (y <= 1.35e-192)
		tmp = -1.0;
	elseif (y <= 3.2e-147)
		tmp = t_0;
	elseif (y <= 1.35e+33)
		tmp = -1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) * 0.5;
	t_1 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -6.5e+70)
		tmp = t_1;
	elseif (y <= -2.8e-41)
		tmp = -1.0;
	elseif (y <= -1.05e-272)
		tmp = t_0;
	elseif (y <= 1.35e-192)
		tmp = -1.0;
	elseif (y <= 3.2e-147)
		tmp = t_0;
	elseif (y <= 1.35e+33)
		tmp = -1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] * 0.5), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+70], t$95$1, If[LessEqual[y, -2.8e-41], -1.0, If[LessEqual[y, -1.05e-272], t$95$0, If[LessEqual[y, 1.35e-192], -1.0, If[LessEqual[y, 3.2e-147], t$95$0, If[LessEqual[y, 1.35e+33], -1.0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.49999999999999978e70 or 1.34999999999999996e33 < 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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 99.7%

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

      3. associate--l- 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 88.4%

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

   7. Taylor expanded in y around 0 88.7%

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

      1. mul-1-neg 88.7%

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

      2. unsub-neg 88.7%

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

   9. Simplified 88.7%

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

   if -6.49999999999999978e70 < y < -2.8000000000000002e-41 or -1.04999999999999993e-272 < y < 1.34999999999999996e-192 or 3.19999999999999979e-147 < y < 1.34999999999999996e33

   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 64.8%

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

   if -2.8000000000000002e-41 < y < -1.04999999999999993e-272 or 1.34999999999999996e-192 < y < 3.19999999999999979e-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. Step-by-step derivation

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

      3. associate--l- 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 70.8%

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

   7. Taylor expanded in y around 0 70.8%

      \[\leadsto \color{blue}{0.5} \cdot \left(x - y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+70}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-41}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-272}:\\ \;\;\;\;\left(x - y\right) \cdot 0.5\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-192}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-147}:\\ \;\;\;\;\left(x - y\right) \cdot 0.5\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+33}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 4: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - y\right) \cdot 0.5\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.56 \cdot 10^{-40}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-271}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-192}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-148}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 10^{+33}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- x y) 0.5)))
   (if (<= y -1.9e+61)
     1.0
     (if (<= y -1.56e-40)
       -1.0
       (if (<= y -2.05e-271)
         t_0
         (if (<= y 1.1e-192)
           -1.0
           (if (<= y 7.6e-148) t_0 (if (<= y 1e+33) -1.0 1.0))))))))

C

double code(double x, double y) {
	double t_0 = (x - y) * 0.5;
	double tmp;
	if (y <= -1.9e+61) {
		tmp = 1.0;
	} else if (y <= -1.56e-40) {
		tmp = -1.0;
	} else if (y <= -2.05e-271) {
		tmp = t_0;
	} else if (y <= 1.1e-192) {
		tmp = -1.0;
	} else if (y <= 7.6e-148) {
		tmp = t_0;
	} else if (y <= 1e+33) {
		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) :: t_0
    real(8) :: tmp
    t_0 = (x - y) * 0.5d0
    if (y <= (-1.9d+61)) then
        tmp = 1.0d0
    else if (y <= (-1.56d-40)) then
        tmp = -1.0d0
    else if (y <= (-2.05d-271)) then
        tmp = t_0
    else if (y <= 1.1d-192) then
        tmp = -1.0d0
    else if (y <= 7.6d-148) then
        tmp = t_0
    else if (y <= 1d+33) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) * 0.5;
	double tmp;
	if (y <= -1.9e+61) {
		tmp = 1.0;
	} else if (y <= -1.56e-40) {
		tmp = -1.0;
	} else if (y <= -2.05e-271) {
		tmp = t_0;
	} else if (y <= 1.1e-192) {
		tmp = -1.0;
	} else if (y <= 7.6e-148) {
		tmp = t_0;
	} else if (y <= 1e+33) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) * 0.5
	tmp = 0
	if y <= -1.9e+61:
		tmp = 1.0
	elif y <= -1.56e-40:
		tmp = -1.0
	elif y <= -2.05e-271:
		tmp = t_0
	elif y <= 1.1e-192:
		tmp = -1.0
	elif y <= 7.6e-148:
		tmp = t_0
	elif y <= 1e+33:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) * 0.5)
	tmp = 0.0
	if (y <= -1.9e+61)
		tmp = 1.0;
	elseif (y <= -1.56e-40)
		tmp = -1.0;
	elseif (y <= -2.05e-271)
		tmp = t_0;
	elseif (y <= 1.1e-192)
		tmp = -1.0;
	elseif (y <= 7.6e-148)
		tmp = t_0;
	elseif (y <= 1e+33)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) * 0.5;
	tmp = 0.0;
	if (y <= -1.9e+61)
		tmp = 1.0;
	elseif (y <= -1.56e-40)
		tmp = -1.0;
	elseif (y <= -2.05e-271)
		tmp = t_0;
	elseif (y <= 1.1e-192)
		tmp = -1.0;
	elseif (y <= 7.6e-148)
		tmp = t_0;
	elseif (y <= 1e+33)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[y, -1.9e+61], 1.0, If[LessEqual[y, -1.56e-40], -1.0, If[LessEqual[y, -2.05e-271], t$95$0, If[LessEqual[y, 1.1e-192], -1.0, If[LessEqual[y, 7.6e-148], t$95$0, If[LessEqual[y, 1e+33], -1.0, 1.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.89999999999999998e61 or 9.9999999999999995e32 < 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 87.7%

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

   if -1.89999999999999998e61 < y < -1.55999999999999996e-40 or -2.0500000000000001e-271 < y < 1.10000000000000003e-192 or 7.60000000000000028e-148 < y < 9.9999999999999995e32

   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 65.1%

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

   if -1.55999999999999996e-40 < y < -2.0500000000000001e-271 or 1.10000000000000003e-192 < y < 7.60000000000000028e-148

   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. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

      3. associate--l- 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 70.8%

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

   7. Taylor expanded in y around 0 70.8%

      \[\leadsto \color{blue}{0.5} \cdot \left(x - y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.56 \cdot 10^{-40}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-271}:\\ \;\;\;\;\left(x - y\right) \cdot 0.5\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-192}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-148}:\\ \;\;\;\;\left(x - y\right) \cdot 0.5\\ \mathbf{elif}\;y \leq 10^{+33}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-187}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-269}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-190}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-150}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1e+74)
   1.0
   (if (<= y -7.2e-187)
     -1.0
     (if (<= y -1.65e-269)
       (* x 0.5)
       (if (<= y 4.6e-190)
         -1.0
         (if (<= y 1.65e-150) (* x 0.5) (if (<= y 5.5e+32) -1.0 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1e+74) {
		tmp = 1.0;
	} else if (y <= -7.2e-187) {
		tmp = -1.0;
	} else if (y <= -1.65e-269) {
		tmp = x * 0.5;
	} else if (y <= 4.6e-190) {
		tmp = -1.0;
	} else if (y <= 1.65e-150) {
		tmp = x * 0.5;
	} else if (y <= 5.5e+32) {
		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 <= (-1d+74)) then
        tmp = 1.0d0
    else if (y <= (-7.2d-187)) then
        tmp = -1.0d0
    else if (y <= (-1.65d-269)) then
        tmp = x * 0.5d0
    else if (y <= 4.6d-190) then
        tmp = -1.0d0
    else if (y <= 1.65d-150) then
        tmp = x * 0.5d0
    else if (y <= 5.5d+32) 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 <= -1e+74) {
		tmp = 1.0;
	} else if (y <= -7.2e-187) {
		tmp = -1.0;
	} else if (y <= -1.65e-269) {
		tmp = x * 0.5;
	} else if (y <= 4.6e-190) {
		tmp = -1.0;
	} else if (y <= 1.65e-150) {
		tmp = x * 0.5;
	} else if (y <= 5.5e+32) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1e+74:
		tmp = 1.0
	elif y <= -7.2e-187:
		tmp = -1.0
	elif y <= -1.65e-269:
		tmp = x * 0.5
	elif y <= 4.6e-190:
		tmp = -1.0
	elif y <= 1.65e-150:
		tmp = x * 0.5
	elif y <= 5.5e+32:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1e+74)
		tmp = 1.0;
	elseif (y <= -7.2e-187)
		tmp = -1.0;
	elseif (y <= -1.65e-269)
		tmp = Float64(x * 0.5);
	elseif (y <= 4.6e-190)
		tmp = -1.0;
	elseif (y <= 1.65e-150)
		tmp = Float64(x * 0.5);
	elseif (y <= 5.5e+32)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1e+74)
		tmp = 1.0;
	elseif (y <= -7.2e-187)
		tmp = -1.0;
	elseif (y <= -1.65e-269)
		tmp = x * 0.5;
	elseif (y <= 4.6e-190)
		tmp = -1.0;
	elseif (y <= 1.65e-150)
		tmp = x * 0.5;
	elseif (y <= 5.5e+32)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1e+74], 1.0, If[LessEqual[y, -7.2e-187], -1.0, If[LessEqual[y, -1.65e-269], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 4.6e-190], -1.0, If[LessEqual[y, 1.65e-150], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 5.5e+32], -1.0, 1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999952e73 or 5.49999999999999984e32 < 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 88.4%

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

   if -9.99999999999999952e73 < y < -7.19999999999999989e-187 or -1.65e-269 < y < 4.59999999999999984e-190 or 1.6500000000000001e-150 < y < 5.49999999999999984e32

   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 59.6%

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

   if -7.19999999999999989e-187 < y < -1.65e-269 or 4.59999999999999984e-190 < y < 1.6500000000000001e-150

   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 86.6%

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

   5. Taylor expanded in x around 0 65.1%

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

      1. *-commutative 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-187}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-269}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-190}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-150}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-146}:\\ \;\;\;\;\left(x - y\right) \cdot 0.5\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -4.4e+71)
     t_0
     (if (<= y -2.2e-41)
       t_1
       (if (<= y -1.75e-146) (* (- x y) 0.5) (if (<= y 2.7e+34) 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 <= -4.4e+71) {
		tmp = t_0;
	} else if (y <= -2.2e-41) {
		tmp = t_1;
	} else if (y <= -1.75e-146) {
		tmp = (x - y) * 0.5;
	} else if (y <= 2.7e+34) {
		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 <= (-4.4d+71)) then
        tmp = t_0
    else if (y <= (-2.2d-41)) then
        tmp = t_1
    else if (y <= (-1.75d-146)) then
        tmp = (x - y) * 0.5d0
    else if (y <= 2.7d+34) 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 <= -4.4e+71) {
		tmp = t_0;
	} else if (y <= -2.2e-41) {
		tmp = t_1;
	} else if (y <= -1.75e-146) {
		tmp = (x - y) * 0.5;
	} else if (y <= 2.7e+34) {
		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 <= -4.4e+71:
		tmp = t_0
	elif y <= -2.2e-41:
		tmp = t_1
	elif y <= -1.75e-146:
		tmp = (x - y) * 0.5
	elif y <= 2.7e+34:
		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 <= -4.4e+71)
		tmp = t_0;
	elseif (y <= -2.2e-41)
		tmp = t_1;
	elseif (y <= -1.75e-146)
		tmp = Float64(Float64(x - y) * 0.5);
	elseif (y <= 2.7e+34)
		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 <= -4.4e+71)
		tmp = t_0;
	elseif (y <= -2.2e-41)
		tmp = t_1;
	elseif (y <= -1.75e-146)
		tmp = (x - y) * 0.5;
	elseif (y <= 2.7e+34)
		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, -4.4e+71], t$95$0, If[LessEqual[y, -2.2e-41], t$95$1, If[LessEqual[y, -1.75e-146], N[(N[(x - y), $MachinePrecision] * 0.5), $MachinePrecision], If[LessEqual[y, 2.7e+34], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.39999999999999989e71 or 2.7e34 < 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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 99.7%

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

      3. associate--l- 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 88.4%

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

   7. Taylor expanded in y around 0 88.7%

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

      1. mul-1-neg 88.7%

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

      2. unsub-neg 88.7%

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

   9. Simplified 88.7%

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

   if -4.39999999999999989e71 < y < -2.2e-41 or -1.7500000000000001e-146 < y < 2.7e34

   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 80.1%

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

   if -2.2e-41 < y < -1.7500000000000001e-146

   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. clear-num 99.8%

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

      2. associate-/r/ 100.0%

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

      3. associate--l- 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 79.1%

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

   7. Taylor expanded in y around 0 79.1%

      \[\leadsto \color{blue}{0.5} \cdot \left(x - y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+71}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-146}:\\ \;\;\;\;\left(x - y\right) \cdot 0.5\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 7: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-145}:\\ \;\;\;\;\left(x - y\right) \cdot 0.5\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+32}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -7.5e+70)
     (/ (- y x) y)
     (if (<= y -8.2e-41)
       t_0
       (if (<= y -3.9e-145)
         (* (- x y) 0.5)
         (if (<= y 5.7e+32) t_0 (- 1.0 (/ x y))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -7.5e+70) {
		tmp = (y - x) / y;
	} else if (y <= -8.2e-41) {
		tmp = t_0;
	} else if (y <= -3.9e-145) {
		tmp = (x - y) * 0.5;
	} else if (y <= 5.7e+32) {
		tmp = t_0;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-7.5d+70)) then
        tmp = (y - x) / y
    else if (y <= (-8.2d-41)) then
        tmp = t_0
    else if (y <= (-3.9d-145)) then
        tmp = (x - y) * 0.5d0
    else if (y <= 5.7d+32) then
        tmp = t_0
    else
        tmp = 1.0d0 - (x / y)
    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 <= -7.5e+70) {
		tmp = (y - x) / y;
	} else if (y <= -8.2e-41) {
		tmp = t_0;
	} else if (y <= -3.9e-145) {
		tmp = (x - y) * 0.5;
	} else if (y <= 5.7e+32) {
		tmp = t_0;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -7.5e+70:
		tmp = (y - x) / y
	elif y <= -8.2e-41:
		tmp = t_0
	elif y <= -3.9e-145:
		tmp = (x - y) * 0.5
	elif y <= 5.7e+32:
		tmp = t_0
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -7.5e+70)
		tmp = Float64(Float64(y - x) / y);
	elseif (y <= -8.2e-41)
		tmp = t_0;
	elseif (y <= -3.9e-145)
		tmp = Float64(Float64(x - y) * 0.5);
	elseif (y <= 5.7e+32)
		tmp = t_0;
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -7.5e+70)
		tmp = (y - x) / y;
	elseif (y <= -8.2e-41)
		tmp = t_0;
	elseif (y <= -3.9e-145)
		tmp = (x - y) * 0.5;
	elseif (y <= 5.7e+32)
		tmp = t_0;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+70], N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -8.2e-41], t$95$0, If[LessEqual[y, -3.9e-145], N[(N[(x - y), $MachinePrecision] * 0.5), $MachinePrecision], If[LessEqual[y, 5.7e+32], t$95$0, N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.50000000000000031e70

   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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.6%

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

      3. associate--l- 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 91.8%

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

      1. *-commutative 91.8%

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

      2. frac-2neg 91.8%

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

      3. metadata-eval 91.8%

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

      4. un-div-inv 92.1%

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

   8. Applied egg-rr 92.1%

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

      1. frac-2neg 92.1%

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

      2. div-inv 91.8%

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

      3. sub-neg 91.8%

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

      4. distribute-neg-in 91.8%

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

      5. neg-mul-1 91.8%

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

      6. remove-double-neg 91.8%

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

      7. fma-def 91.8%

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

      8. remove-double-neg 91.8%

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

   10. Applied egg-rr 91.8%

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

       1. associate-*r/ 92.1%

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

       2. *-rgt-identity 92.1%

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

       3. fma-udef 92.1%

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

       4. neg-mul-1 92.1%

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

       5. +-commutative 92.1%

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

       6. unsub-neg 92.1%

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

   12. Simplified 92.1%

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

   if -7.50000000000000031e70 < y < -8.20000000000000028e-41 or -3.90000000000000029e-145 < y < 5.7e32

   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 80.1%

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

   if -8.20000000000000028e-41 < y < -3.90000000000000029e-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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. associate-/r/ 100.0%

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

      3. associate--l- 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 79.1%

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

   7. Taylor expanded in y around 0 79.1%

      \[\leadsto \color{blue}{0.5} \cdot \left(x - y\right) \]

   if 5.7e32 < 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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 99.7%

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

      3. associate--l- 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 86.0%

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

   7. Taylor expanded in y around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   9. Simplified 86.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-145}:\\ \;\;\;\;\left(x - y\right) \cdot 0.5\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 8: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+15}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-1}{x}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+99}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{1}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e+15)
   (* (- x y) (/ -1.0 x))
   (if (<= x 2.7e+99) (* (- x y) (/ 1.0 (- 2.0 y))) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+15) {
		tmp = (x - y) * (-1.0 / x);
	} else if (x <= 2.7e+99) {
		tmp = (x - y) * (1.0 / (2.0 - y));
	} 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 <= (-9.5d+15)) then
        tmp = (x - y) * ((-1.0d0) / x)
    else if (x <= 2.7d+99) then
        tmp = (x - y) * (1.0d0 / (2.0d0 - y))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+15) {
		tmp = (x - y) * (-1.0 / x);
	} else if (x <= 2.7e+99) {
		tmp = (x - y) * (1.0 / (2.0 - y));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e+15:
		tmp = (x - y) * (-1.0 / x)
	elif x <= 2.7e+99:
		tmp = (x - y) * (1.0 / (2.0 - y))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e+15)
		tmp = Float64(Float64(x - y) * Float64(-1.0 / x));
	elseif (x <= 2.7e+99)
		tmp = Float64(Float64(x - y) * Float64(1.0 / Float64(2.0 - y)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e+15)
		tmp = (x - y) * (-1.0 / x);
	elseif (x <= 2.7e+99)
		tmp = (x - y) * (1.0 / (2.0 - y));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e+15], N[(N[(x - y), $MachinePrecision] * N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+99], N[(N[(x - y), $MachinePrecision] * N[(1.0 / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5e15

   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. clear-num 99.9%

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

      2. associate-/r/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 78.0%

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

   if -9.5e15 < x < 2.69999999999999989e99

   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. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 92.9%

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

   if 2.69999999999999989e99 < 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 97.2%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+15}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-1}{x}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+99}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{1}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9: 63.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.9e+61) 1.0 (if (<= y 5.2e+32) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.9e+61) {
		tmp = 1.0;
	} else if (y <= 5.2e+32) {
		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 <= (-1.9d+61)) then
        tmp = 1.0d0
    else if (y <= 5.2d+32) 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 <= -1.9e+61) {
		tmp = 1.0;
	} else if (y <= 5.2e+32) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.9e+61:
		tmp = 1.0
	elif y <= 5.2e+32:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.9e+61)
		tmp = 1.0;
	elseif (y <= 5.2e+32)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.9e+61)
		tmp = 1.0;
	elseif (y <= 5.2e+32)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.9e+61], 1.0, If[LessEqual[y, 5.2e+32], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.89999999999999998e61 or 5.2000000000000004e32 < 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 87.7%

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

   if -1.89999999999999998e61 < y < 5.2000000000000004e32

   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 53.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 38.4% 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 35.6%

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

5. Final simplification 35.6%

   \[\leadsto -1 \]

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 2023195 
(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))))